Nov 13, 2013 ... Invited Speakers .... Heat capacity of a Bose-Einstein condensate [Ruddell] . ... for
a hollow core terahertz waveguide with embedded metal wires [Yu- dasari] . .... λ
= ωz/ω⊥) and temperature giving the stability diagram shown in Fig. ...... -4 -3 -2 -
1 0 1 2 3 4 ... [8] J. Bosse, K. N. Pathak, and G. S. Singh, Phys.
7t h Annual
Dodd-Walls Symposium B OOK OF A BSTRACTS
Dunedin 11—13 November 2013
B OOK OF A BSTRACTS Editor: Ashton Bradley
7t h Annual
Dodd-Walls Symposium Saint Margaret’s College Dunedin 11—13 November 2013
Ben Eggleton Jochen Schroeder Tapio Simula Rainer Dumke
Invited Speakers University of Sydney, CUDOS University of Sydney, CUDOS Monash University National University of Singapore
Local Organizing Committee David Hutchinson Margaret Tompkins Scientific Programme Committee Stuart Murdoch Ashton Bradley (Chair)
Research conducted at the Dodd-Walls Centre ranges from studies of the coldest matter in the universe and its applications in quantum computing, to photonic systems for communication, metrology, sensing, and medical devices. The synergies inherent in this broad research platform promote the development of new ideas and technical advances. We envisage the Centre providing a platform in photonics critical to the success of New Zealand’s emerging high-tech and biotechnology industries.
The Dodd-Walls Centre is a partnership between leading research groups at the Universities of Otago and Auckland, and the company Southern Photonics.
Mon 8:30 9:10 9:15 9:30 9:45 10:00 10:15 10:30 10:45 11:00 11:15 11:30 11:45 12:00 12:15 12:30 12:45 13:00 13:15 13:30 13:45 14:00 14:15 14:30 14:45 15:00 15:15 15:30 15:45 16:00 16:15 16:30 16:45 17:00 17:15 17:30 17:45 18:00 18:15 18:30 18:45 19:00 19:15 19:30 19:45 20:00 20:15 20:30 20:45 21:00
Tue
Wed
Opening address Invited Talk: Eggleton Chair: Murdoch Jang Webb Erkintalo Morning Tea
Carmichael Chair: Andersen Parkins Sadgrove Krauskopf Morning Tea
Invited Talk: Simula Chair: Blakie Billam Rooney Fialko Lunch
Invited Talk: Dumke Chair: Hutchinson Fung White Ruddell Lunch
Zuelicke Chair: Ballagh Brand Danieli Yu Conclusion Morning Tea CoRE Meeting
Invited Talk: Schroeder Chair: Longdell Runge Chen Taylor Afternoon Tea
Meglinski Chair: Kjaergaard Doronin Rayanov McKague Afternoon Tea
Registration
Ballagh Chair: Brand Bromley Blakie
Dinner: St Margarets College
Drinks: Etrusco Poster Session
Dinner: Etrusco
Lunch
CoRE Meeting
Afternoon Tea
Abstracts Quantum Gases Characterising the rotonic regime of a dipolar BEC using light scattering [Ballagh] . . . . . . . . . . Effect of exchange on finite temperature stability of a trapped dipolar Bose gas [Baillie] . . . . . . . Emergence of classical flows in negative-temperature quantum vortex states [Reeves] . . . . . . . . Emergent phenomena in two-dimensional quantum turbulence [Billam] . . . . . . . . . . . . . . . The stochastic projected Gross-Pitaevskii equation [Rooney] . . . . . . . . . . . . . . . . . . . . . . . Atom-optical diffraction catastrophes: the emergence of quantized vortex skeletons [Simula] . . . Rotons in a Dipolar Bose-Einstein Condensate [Blakie] . . . . . . . . . . . . . . . . . . . . . . . . . . Sakharov oscillations in trapped Bose gases [Martin] . . . . . . . . . . . . . . . . . . . . . . . . . . . . Isolated Quantum Heat Engine [Fialko] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nonlinearities and dephasing destroy wave localisation [Rayanov] . . . . . . . . . . . . . . . . . . . . Solitons in spin-orbit-coupled Bose-Einstein condensates [Zülicke] . . . . . . . . . . . . . . . . . . . Superconducting Atom Chips [Dumke] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Three-dimensional solitary waves with large inertial to physical mass ratio [Brand] . . . . . . . . . . Approximating Metal/Insulator Transition [Danieli] . . . . . . . . . . . . . . . . . . . . . . . . . . . . Heat capacity of a Bose-Einstein condensate [Ruddell] . . . . . . . . . . . . . . . . . . . . . . . . . . . Dynamics of two atoms undergoing collisions and molecule formation in an optical microtrap [Fung] Nonlinear waves in disordered lattices with broken time reversal symmetry [Yu] . . . . . . . . . . . A Phase Engineered Quantum Ratchet [White] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fluctuations in Uniform Spin-1 Bose-Einstein Condensates [Symes] . . . . . . . . . . . . . . . . . . A Born-Oppenheimer-inspired approach towards the stabilisation of vortices and solitons [Bromley] Path integral Monte Carlo Study of the Hanbury Brown Twiss effect in a finite-sized Bose gas system [Oh] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
Photonics and Quantum Optics 31 The open Dicke model with linear and nonlinear atom-photon interactions [Parkins] . . . . . . . . 33 Breakdown of Photon Blockade: A Dissipative Quantum Phase Transition in Zero Dimensions [Carmichael] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Photonic crystal nanofibers: a workbench for quantum optics [Sadgrove] . . . . . . . . . . . . . . . 35 Control of Temporal Cavity Solitons [Murdoch] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Ultra-weak long-range acoustic interactions of temporal cavity solitons [Jang] . . . . . . . . . . . . 37 Sensitivity Optimization of Portable Ammonia Sensor Wu] . . . . . . . . . . . . . . . . . . . . . . . . 38 Laser Fabrication of Single-mode Amorphous Polycarbonate Waveguides [Song] . . . . . . . . . . . 39 Dispersive Wave Generation by Four-Wave Mixing Cascades [Webb] . . . . . . . . . . . . . . . . . . . 40 Stability and coherence of microresonator-based optical frequency combs [Erkintalo] . . . . . . . . 41 Coherence and single-shot spectra of noise-like pulses [Runge] . . . . . . . . . . . . . . . . . . . . . 42 Pushing the limits of environmentally stable fibre lasers: 120 fs, 4.2 nJ, all-PM all-fibre [Aguergaray] 43 Delay effects in a semiconductor laser with optical feedback from two filter loops [Krauskopf ] . . . 44 Numerical investigations for a hollow core terahertz waveguide with embedded metal wires [Yudasari] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Co-linear wire waveguide for the terahertz region [Zia] . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Self-testing and interactive proofs for quantum experiments [McKague] . . . . . . . . . . . . . . . . 47 Exploring the Hyperfine Structure of 167 Er : Y2 SiO 5 via Spectral Hole Burning [Fernandez-Gonzalvo] 48 Shaping the light from a tiny hole [Chen] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Atomic frequency combs and the optical detection of ultrasound [Taylor] . . . . . . . . . . . . . . . 50 Mapping of cancer on the Poincaré Sphere [Macdonald] . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Towards propagation of circularly polarized light in multiple-scattering medium [Meglinski] . . . . 52 Propagation of complex structured vector light beams in turbid medium [Doronin] . . . . . . . . . 53 Imaging of the interaction of low frequency electric fields with biological tissues by Optical Coherence Tomography [Devine] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5
Author Index Aguergaray, 43 Andersen, 24 Anderson, 12 Anguergaray, 42
Paganin, 14 Parkins, 33 Pena, 54 Petersen, 14 Preece, 28
Baillie, 9, 10, 15, 27 Ballagh, 9 Billam, 11, 12 Bisset, 10, 15 Blakie, 9, 10, 13, 15, 16, 27 Bradley, 11–13 Brand, 19, 21 Broderick, 42, 43 Bromley, 28
Radons, 18 Rayanov, 18, 22 Reeves, 11, 12 Rooney, 13 Rubinsztein-Dunlop, 28 Ruddell, 23, 26 Runge, 42, 43 SŁowinski, ´ 44 Sadgrove, 35 Schumayer, 29 Simula, 14 Song, 39 Stilgoe, 28 Symes, 27
Capentier, 24 Carmichael, 34 Chen, 49 Coen, 36, 37, 41 Danieli, 22 Devine, 54 Doronin, 51–54 Dumke, 20
Taylor, 50 Towers, 29 Webb, 40 White, 23, 26 Wieczorek, 44 Wu, 38
Eccles, 51, 52 Erkintalo, 36, 37, 40–43 Fernandez-Gonzalvo, 48 Fialko, 17, 19 Flach, 18, 22, 25 Fung, 24
Yalla, 35 Yu, 25, 40 Yudasari, 45
G. Gligori´c, 18 Grimsmo, 33
Zülicke, 19 Zia, 46
Hakuta, 35 Hallwood, 17 Harvey, 38 Hirst, 38 Hoogerland, 23, 26 Hutchinson, 29 Jang, 36, 37 Krauskopf, 44 Leonhardt, 39, 45, 46 Longdell, 48, 50 Macdonald, 51, 52 Martin, 16 Mateo, 21 McKague, 47 Meglinski, 51–54 Murdoch, 36–40 Nayak, 35 Nourse, 28 Oh, 29 6
Quantum Gases
Kjærgaard group, Otago
7
8
C HARACTERISING THE ROTONIC REGIME OF A DIPOLAR BEC USING LIGHT SCATTERING R. J. Ballagh∗ , D. Baillie and P. B. Blakie Jack Dodd Centre for Quantum Technologies, Department of Physics, University of Otago, New Zealand Rotons are well known in superfluid Helium and are associated with a sharp peak in the static structure factor at finite momentum. It is predicted that roton-like features can occur in dipolar Bose condensates tightly confined along the direction of dipole orientation [1]. For these BEC systems, the static structure factor (essentially the Fourier transform of the density-density correlation function) exhibits a similar sharp peak for both one and two dimensional realisations which is predicted to increase with temperature and leads to enhanced density fluctuations [2]. There is great interest in developing robust signatures of this rotonic regime, but while several proposals have been made, a rotonic signature has not yet been experimentally observed. In this paper, we present and analyse a non-invasive method for characterising the rotonic regime, employing off-resonant light scattering. Using a quantum mechanical formalism similar to Mekhov et al. [3], we obtain explicit expressions that map the structure factor of both 1D and 2D dipolar condensates onto the intensity fluctuations of the scattered light. The plots in Fig. 1 show the intensity variance of the light scattered from a 1D dipolar condensate as a function of scattering angle θs for rotonic and non-rotonic regimes. Both cases are for zero temperature, so the fluctuations are entirely quantum mechanical. In the non-rotonic regime we see that the (normalised) intensity variance has a background level of 1, arising from the atomic shot noise, but around θs = 0, the intensity fluctuations are squeezed, indicating that the density fluctuations of the condensate are locally anti-bunched. In the rotonic regime, we see that the intensity variance provides a clear signature of the rotons, namely peaks of greatly enhanced intensity fluctuations appear immediately neighbouring the anti-bunching dip. We investigate the behaviour of this signature for various parameter regimes, and explore its dependence on temperature. 4.5 4 3.5
Intensity variance
3 2.5 2 1.5 1 0.5 0 -1
-0.5
0 θs /π
0.5
1
Figure 1: Intensity variance of scattered light as a function of scattering angle for the non-rotonic regime (dashed) and rotonic regime (solid). Both cases are for T = 0.
References [1] L. Santos, et al., Phys. Rev. Lett. 90, 250403 (2003) [2] K. Klawunn, et al., Phys. Rev. A 84, 033612 (2011); R. N. Bisset and P. B. Blakie, Phys. Rev. Lett. 110, 265302 (2013); P. B. Blakie, et al., Phys. Rev. A 88, 013638 (2013) [3] I. B. Mekhov, et al., Phys. Rev. Lett. 98, 100402 (2007)
∗ Contact email:
[email protected]
9
E FFECT OF EXCHANGE ON FINITE TEMPERATURE STABILITY OF A TRAPPED DIPOLAR B OSE GAS D. Baillie∗ , R. N. Bisset and P. B. Blakie Jack Dodd Centre for Quantum Technologies, Department of Physics, University of Otago, New Zealand Bose-Einstein condensates have been produced with highly magnetic atoms which have a long-ranged and anisotropic dipole-dipole interaction. Due to an attractive component of the interaction, an important consideration is when the system is mechanically unstable to collapse to a high density state. Theoretical studies have been performed at zero temperature where there is some stabilization from the quantum pressure of confinement and from repulsive short-range interactions [1] and there is good agreement between the zero-temperature theories and experiments with 52 Cr [2]. Stability at finite temperature, pertinent to current experimental work with polar molecules, remains much less clear. In particular, while there has been some work on stability of a normal dipolar Fermi gas [3], the finite-temperature bosonic system has so far been limited to Hartree theory [4] which ignores exchange interactions. By considering the effect of a perturbation on the gas we derive a Hartree-Fock stability condition. By solving the stability condition, our study characterizes the roles of trap geometry (in particular the aspect ratio of the trapping frequencies, λ = ωz /ω⊥ ) and temperature giving the stability diagram shown in Fig. 1. We find that exchange appreciably reduces stability, and that the double instability feature in oblate trapping geometries predicted previously by Hartree theory [4] is still predicted by the Hartree-Fock theory. Our results are relevant to current experiments with polar molecules and will be useful in developing strategies to obtain a polar molecule Bose-Einstein condensate. 8 7 6
Dt
5 4 3 2 1 0
1
1.2
1.4 T /Tc0
1.6
1.8
2
Figure 1: Critical interaction strength, D t , for a purely dipolar gas for oblate (λ = 10, green/top), spherical (λ = 1, red/middle) and prolate (λ = 0.1, blue/bottom) geometries for Hartree Fock (solid) and Hartree (dashed). The stable region is to the right of the lines.
References [1] S. Ronen, D. C. E. Bortolotti, and J. L. Bohn, Phys. Rev. Lett. 98, 030406 (2007); H.-Y. Lu, H. Lu, J.-N. Zhang, R.-Z. Qiu, H. Pu, and S. Yi, Phys. Rev. A 82, 023622 (2010). [2] T. Koch, T. Lahaye, J. Metz, B. Froehlich, A. Griesmaier, and T. Pfau, Nat. Phys. 4, 218 (2008). [3] J.-N. Zhang and S. Yi, Phys. Rev. A 81, 033617 (2010). [4] R. N. Bisset, D. Baillie and P. B. Blakie, Phys. Rev. A 83, 061602 (2011); 86, 033609 (2012).
∗ Contact email:
[email protected]
10
E MERGENCE OF CLASSICAL FLOWS IN NEGATIVE - TEMPERATURE QUANTUM VORTEX STATES M. T. Reeves1∗ , T. P. Billam1 , and A. S. Bradley1† 1
Jack Dodd Centre for Quantum Technologies, Department of Physics, University of Otago, New Zealand
E(k)/µξ
Large-scale clustering of quantum vortices arises in negative-temperature end-states of decaying, twodimensional quantum vortex turbulence. This clustering induces a rotational velocity field, when considered in the appropriate classical limit. We show that a clear power-law signature of this vortex ordering emerges in the kinetic energy spectrum of the superfluid described by the Gross-Pitaevskii equation. This is explained by analysis of the velocity probability distribution, and the spatial distribution of quantum vortices. The clusters obey the Feynman rule, exhibiting constant areal vortex density. These clusters can thus be considered a disordered analgoue of the Abrikosov lattice.
104
ǫ=0
ǫ = −3
ǫ = 10
ǫ=5
ǫ = 20
ǫ = 100
ǫ = 200
102 100
10−1
100
10−1
100
10−1
100
10−1
kξ
100
10−1
100
10−1
100
10−1
100
Figure 1: (Top row) Vortex distributions for a range of vortex configuration energies ². The distributions have been decomposed into clusters, dipoles and free vortices using a Recursive Cluster Algorithm [1]. (Bottom row) Log-log graphs of the full kinetic energy spectrum E (k) for a range of point vortex energies. Lines proportional to k 3 (green) are shown for comparison.
References [1] M. T. Reeves, T. P. Billam, B. P. Anderson, and A. S. Bradley, Phys. Rev. Lett. 110, 104501 (2013).
∗ Contact email:
[email protected]
† Group URL: http://www.physics.otago.ac.nz/research/btg/
11
E MERGENT PHENOMENA IN TWO - DIMENSIONAL QUANTUM TURBULENCE T. P. Billam1∗ , M. T. Reeves1 , B. P. Anderson2 and A. S. Bradley1† 1 Jack Dodd Centre for Quantum Technology, Department of Physics, University of Otago, Dunedin 9016, New Zealand 2 College of Optical Sciences, University of Arizona, Tucson, AZ 85721, USA
Two-dimensional quantum turbulence (2DQT) may represent the minimally-complex physical system exhibiting hydrodynamic turbulence. Quasi-2D atomic Bose-Einstein condensates represent an excellent theoretical and experimental system with which to study both forced and decaying quantum vortex turbulence. In a minimal model of forced 2DQT, our large-scale Gross-Pitaevskii simulations demonstrate that an inverse energy cascade — a self-organizing transfer of energy to large scales ubiquitous in classical 2D turbulence — can occur in the quantum case [1]. We also present ongoing work on homogeneous, decaying 2DQT in a doubly-periodic domain, in which we develop new theoretical methods to create and characterize 2DQT. These methods reveal striking connections to the theory of classical fluids, and allow us to study 2DQT analogues of far-from-equilibrium classical flows [2].
Figure 1: (a): Dynamical dGPE evolution of non-equilibrium N -vortex states with initial point-vortex energy ε(0) towards statistical equilibrium. Shown is a decomposition into dipoles (green) and vortex clusters [red (positive circulation) and blue (negative circulation)] using a recursive cluster algorithm after equilibriation (t = 9500ħ/µ, main figures) and for the initial condition (insets). Streamlines show the incompressible velocity field. The field of view is the system size, 512 × 512 healing lengths.
References [1] M. T. Reeves, T. P. Billam, B. P. Anderson, and A. S. Bradley, Inverse Energy Cascade in Forced Two-Dimensional Quantum Turbulence Phys. Rev. Lett. 110, 104501 (2013). [2] T. P. Billam, M. T. Reeves, B. P. Anderson, and A. S. Bradley, Onsager–Kraichnan Condensation in Decaying Two-Dimensional Quantum Turbulence arXiv:1307.6374 (2013).
∗ Contact email:
[email protected]
† Group URL: http://www.physics.otago.ac.nz/research/btg
12
T HE STOCHASTIC PROJECTED G ROSS -P ITAEVSKII EQUATION S. J. Rooney∗ , P. B. Blakie, and A. S. Bradley† Jack Dodd Centre for Quantum Technologies, Department of Physics, University of Otago, New Zealand
!N T!N " " T
20 15
35
15 10 105
35
1 1
1.5 1.5
2 2
0.5 1 0.5 251
2.5 2.5
1.5 1.5
3
Experiment: equilibrium Experiment: dynamics 2 SPGPE 2.5 (a) 3 3.5 4 t/s2.5 (b) 3 2 SPGPE 3.5 4 t/s (a) dGPE dGPE (b)
4 4.5 τ3.5 a 20 3 τ3.5 4 4.5 b
30
9
12 12
15 15
18 18
21 24 21 t/s10 24
t/s
27 27
30 30
33 33
3
6
9
36 36
τb
10 5
15
9
τa
25 4.5 20 4.5 15
!N T "
30
50 0 0 0
!N T "
periment: equilibrium periment: dynamics riment: equilibrium GPE (a) dynamics riment: GPE(a)(b) PE PE (b) (a) PE EPE(a)(b) E (b)
The stochastic projected Gross-Pitaevskii equation (SPGPE) is a classical field theory which provides a quantitative description of Bose-Einstein condensate (BEC) dynamics at finite temperature. The SPGPE is based on the GPE, with additional noise and damping terms arising from the interaction between a low energy coherent region and a thermal reservoir. There are two distinct reservoir interactions: growth where two reservoir atoms collide resulting in growth of the coherent region, and the number-conserving scattering interaction where reservoir and coherent region atoms collide leading to energy exchange. Collision rates can be derived when the reservoir is treated semi-classically, allowing the SPGPE to make ab initio predictions of BEC dynamics at finite temperature. Terms in the SPGPE arising from the scattering reservoir interaction are important in non-equilibrium systems [1], but are numerically challenging [2]. The simple growth SPGPE is obtained by neglecting the scattering terms, which is valid for quasi-equilibrium systems. We apply the simple growth theory to a recent persistent current formation experiment, where a persistent current is formed in a toroidal BEC after vortices are nucleated by stirring [3]. We model the experimental procedure with no fitted parameters, finding the simple growth SPGPE reproduces the time evolution of the total vorticity observed in experiment [4] (see Fig. 1). In comparison the damped GPE (dGPE) does not produce such accuracy, showing the 35 stochastic approach is necessary to provide a quantitative account of the experiment. 35 30 Finally we apply the full SPGPE theory to the dynamics of a BEC excited into a large amplitude breathing 30 25 mode. We find scattering dominates over growth during the non-equilibrium dynamics, and provides a 25 20 highly coherent energy damping mechanism that is qualitatively different to growth [1].
39 39
42 42
15
18
0 0
0.5 45 45
1
1.5
2
2.5
3
3.5
4
4.5
t/s
κa κb
5 0 0
36
39
42
12
45
21
t/s
24
27
30
33
36
39
42
45
27
30
33
7
30
33Figure 1:36Comparison 39 of the total 42 vorticity45〈NT 〉 between the simple growth SPGPE theory and experiment. The two
parameter sets (a/b) correspond to different heights of the stirring potential, both within experimental uncertainty. The shading for each SPGPE curve shows one standard deviation, where the lower bound for parameter set (a), and upper bound for parameter set (b) are shown.
References [1] [2] [3] [4]
S. J. Rooney, P. B. Blakie, and A. S. Bradley, Stochastic projected Gross-Pitaevskii equation, Phys. Rev. A 86, 053634 (2012). S. J. Rooney, P. B. Blakie, and A. S. Bradley, Numerical method for the stochastic projected Gross-Pitaevskii equation, arxiv:1310.0161 (2013). T. W. Neely et al., Characteristics of Two-Dimensional Quantum Turbulence in a Compressible Superfluid, arxiv:1204.1102 (2012). S. J. Rooney, T. W. Neely, B. P. Anderson, and A. S. Bradley, Persistent current formation in a high-temperature Bose-Einstein condensate: an experimental test for c-field theory, arxiv:1208.4421 (2012).
∗ Contact email:
[email protected]
† Group URL: http://www.physics.otago.ac.nz/research/btg
13
ATOM - OPTICAL DIFFRACTION CATASTROPHES : THE EMERGENCE OF QUANTIZED VORTEX SKELETONS T. P. Simula1∗ , T. C. Petersen1,2 , and D. M. Paganin1 1 School of Physics, Monash University, Victoria 3800, Australia 2 Monash Centre for Electron Microscopy, Monash University, Victoria 3800, Australia
Optical lenses focus rays of light to form an image of an object. Optical aberrations due to lens imperfections cause distortions in such images. According to the wave-particle duality, similar phenomena emerge when matter waves such as electron beams are collimated in a small volume of space where multiple particle orbits intersect. In ray optics the resulting crossroads of rays is a caustic region of infinite light intensity whereas in the wave picture interference may result in ordered structures of optical maelstroms whose cores are void of light. But does this qualitative picture apply to an interacting quantum gas undergoing a Bose-nova or being focused by aberrated atom-optical lenses? We have studied matterwave lensing of Bose–Einstein condensates [1]. In contrast to electron waves [2], nonlinearities due to particle interactions in atomic gases allow lens aberrations to be produced either externally or by internal agents. The high level of tuneability of the particle interactions and external potentials in these systems enable a great variety of caustics and diffraction catastrophes to be generated in experimentally realistic systems. Our results show that aberrated singular and nonlinear lensing does indeed produce staggered arrays of quantized vortices which nucleate inside the caustics and that the resulting vortex skeletons and caustic patterns can reveal the symmetry of the underlying microscopic particle interactions at macroscopic scales. In particular, interpreting Bose-novae in terms of aberrated matter wave lensing, we show that the effects of anisotropic harmonic trapping potentials and dipolar particle interactions can be detected by imaging the telltale caustic pattern produced by such lens astigmatism. Stable diffraction catastrophes of light could also be created in single laser beams which could be used for creating optical flux potentials for quantum gas experiments and for studies of emergent topological quantum matter.
source BEC
aberrated lens
gravity, time
(i)
(ii)
diffraction catastrophe
time-of-flight
(iii)
Figure 1: Schematic of a singular atom-optics experiment. (i) Bose–Einstein condensate in ground state of a ring trap is aberrated by an atom-optical lens (ii) applying a perturbation to the trapping potential which imprints a phase profile to the condensate wavefunction affecting its momentum distribution. The diffraction catastrophe and the associated quantized vortex skeleton emerge during the time-of-flight due to multi-wave interference. The colored circles in (iii) illustrate the cross-section of the vortex skeleton nucleated inside the diffraction catastrophe with a staggered vortex lattice of opposite signs of quantized circulation.
References [1] T. P. Simula, T. C. Petersen, D. M. Paganin, Diffraction catastrophes threaded by quantized vortex skeletons caused by atom-optical aberrations induced in trapped Bose–Einstein condensates, Phys. Rev. A (accepted for publication 2013). [2] T. C. Petersen, M. Weyland, D. M. Paganin, T. P. Simula, S. A. Eastwood, and M. J. Morgan, Electron Vortex Production and Control Using Aberration Induced Diffraction Catastrophes, Phys. Rev. Lett. 110, 033901 (2013).
∗ Contact email:
[email protected]
14
R OTONS IN A D IPOLAR B OSE -E INSTEIN C ONDENSATE P. B. Blakie1∗ , D. Baillie1 , and R. N. Bisset1,2 1 Jack Dodd Centre for Quantum Technologies, Department of Physics, University of Otago 2 Theoretical Division, Los Alamos National Laboratory
Bose-Einstein condensates (BECs) have been created with the highly magnetic atoms Cr, Dy and Er. The key new feature of these systems is a long ranged and anisotropic dipole-dipole interaction (DDI), which gives rise to a rich array of new physics for ultra-cold gases [5]. An important prediction made in 2003 was that a rotonic-like excitation would emerge in a condensate that is tightly confined along the direction that the dipoles are polarized. To date there has been no experimental evidence for the existence of these excitations, and increasing attention is turning to developing signatures for detecting their presence. Our group has undertaken extensive work on the properties of rotons within trapped dipolar BECs [6, 1] (e.g. see Fig. 1). A focus of our work has been elucidating the role of rotons in causing enhanced density fluctuations [2], which could be used to provide practical signatures for the roton using Bragg spectroscopy [4] or in situ measurements of density fluctuations [3]. In this presentation I will overview the developments in the field of dipolar quantum gases and overview the progress toward observing rotons in this system. 12
(a)
ǫ j /¯hω ρ
10
12
(b)
8 10
ǫ j /¯hω ρ
non-rotonic background
6 4 2
8 6 4
30 2
20
roton fingers
10
m
0
2
1
3
4
h k ρ ij a
hk ρ ij a ρ
(c)
5
5
ǫ j /¯hω ρ
ǫ j /¯hω ρ
0
m
ρ
6
6
4 3
20
2 5
4
n = 1
2
m
ij
3 4
aρ
5 0
3 n = 1
n = 0
ρ
4
hk ρ ij a ρ
10
hk
3
4
2
20 n = 0
(d)
0
10
5
15
m
Figure 1: Roton fingers in the spectrum of a trapped dipolar BEC in a 20:1 pancake trap. (a), (b) Two views of the quasiparticle excitations of a trapped dipolar condensate mapped against their angular momentum projection m and effective linear momentum 〈k ρ 〉 j .
References [1] R. N. Bisset, D. Baillie, and P. B. Blakie. Roton excitations in a trapped dipolar Bose-Einstein condensate. arxiv-1308.5812, (2013). [2] P. B. Blakie, D. Baillie, and R. N. Bisset. Depletion and fluctuations of a trapped dipolar Bose-Einstein condensate in the roton regime. Phys. Rev. A, 88, 013638 (2013). [3] R. N. Bisset and P. B. Blakie. Fingerprinting rotons in a dipolar condensate: Super-poissonian peak in the atom-number fluctuations. Phys. Rev. Lett., 110, 265302 (2013). [4] P. B. Blakie, D. Baillie, and R. N. Bisset. Roton spectroscopy in a harmonically trapped dipolar Bose-Einstein condensate. Phys. Rev. A, 86, 021604, (2012) [5] T Lahaye, C Menotti, L Santos, M Lewenstein, and T Pfau. The physics of dipolar bosonic quantum gases. Rep. Prog. Phys., 72, 126401 (2009) [6] A. D. Martin and P. B. Blakie. Stability and structure of an anisotropically trapped dipolar Bose-Einstein condensate: Angular and linear rotons. Phys. Rev. A, 86, 053623 (2012)
∗ Contact email:
[email protected]
15
S AKHAROV OSCILLATIONS IN TRAPPED B OSE GASES A. D. Martin and P. B. Blakie Jack Dodd Centre for Quantum Technologies, Department of Physics, University of Otago, New Zealand When the interactions in an ultra-cold Bose gas are quenched (suddenly increased or decreased via a rapid change in s-wave scattering length), oscillations in the static structure factor arise due to coherences between phonons. This process is analogous to so-called Sakharov oscillations in the power spectrum of the cosmic microwave background. A recent experiment by Hung, Gurarie and Chin [1] measured such oscillations in cesium atoms trapped in a tight 2D geometry, from which they deduced the energy dispersion. We study the same system theoretically, both within a homogeneous approximation and within a radial harmonic trapping potential, and investigate the structure factor, along with phonon mode populations and coherences. We find dramatic effects due to the trapping potential on particular mode populations and coherences, and consequently on the (quasi)-condensate depletion during the system dynamics. Interestingly, dynamics of the structure factor are largely unaffected by the trapping potential. References [1] Chen-Lung Hung, Victor Gurarie, Cheng Chin, From Cosmology to Cold Atoms: Observation of Sakharov Oscillations in a Quenched Atomic Superfluid, Science, 341, 6151 (2013).
16
I SOLATED QUANTUM H EAT E NGINE O. Fialko1∗ , and D. W. Hallwood1 1 Institute of Natural and Mathematical Sciences and Centre for Theoretical Chemistry and Physics, Massey University,
Auckland 0632, New Zealand
In this talk I will present our recent work [1], where a theoretical and numerical analysis of a quantum system (shown in Fig.1) that is capable of functioning as a heat engine is studied. This system could be realized experimentally using cold bosonic atoms confined to a double well potential that is created by splitting a harmonic trap with a focused laser. The system shows thermalization, and can model a reversible heat engine cycle. This is the first demonstration of the operation of a heat engine with a finite quantum heat bath. I will also show that the same system can serve as a finite heat bath for a different particle coupled to it. This is used to study decoherence of the single particle fully quantum-mechanically.
Figure 1: Schematic of a double well created by splitting a harmonic potential with a focused laser. The diagram shows the possible tunneling and how the energy levels change due to interactions.
References [1] O. Fialko, and D. W. Hallwood, Isolated quantum heat engine, Phys. Rev. Lett. 108, 085305 (2012).
∗ Contact email:
[email protected]
17
N ONLINEARITIES AND DEPHASING DESTROY WAVE LOCALISATION K. Rayanov1,2,3∗ , G. Gligori´c2,4 , G. Radons3 , and S. Flach1,2 1 New Zealand Institute for Advanced Study, Centre for Theoretical Chemistry and Physics, Massey University,
Auckland 0745, New Zealand 2 Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, D-01187 Dresden, Germany 3 Institute of Physics, Chemnitz University of Technology, D-09107 Chemnitz, Germany 4 Vinca Institute of Nuclear Sciences, University of Belgrade - P.O. Box 522, 11001 Belgrade, Serbia
In lattice systems, wave localisation takes place due to a lack of translational invariance, e.g. resulting from disorder, quasiperiodic potentials or DC-fields, or due to strong nonlinear interactions. The key ingredient, that distinguishes these phenomena from classical particle localisation in confining potentials, is phase coherence. When phase coherence is destroyed, wave localisation is inevitably lost. We analyse the characteristics of two dephasing mechanisms: random phase fluctuations due to dynamical disorder [1] and weak nonlinearity [2], and discuss, how dephasing can be adjusted in order to best observe the delocalisation effects. In the first case, where decoherence results from a dynamical random environment, linear and nonlinear localisation are destroyed with the onset of diffusive spreading. Optimal phase fluctuation characteristics maximise the wave packet extent at a given time, which is a consequence of the competition between diffusion and ballistic spreading within the mean free path distance. In the second case, we consider the destruction of Anderson localisation by weak interactions. The resulting spreading is slow and subdiffusive, thereby limiting the quantitative experimental and numerical analysis. We propose an elegant solution of the problem by proper ramping the interaction strength in time. We demonstrate that subdiffusion is speeded up to normal diffusion for interacting disordered and kicked atomic systems. The door is open to test these theoretical results experimentally, and to attack similiar computational quests in higher space dimensions.
References [1] K. Rayanov, G. Radons, and S. Flach. Decohering localized waves. Phys. Rev. E, 88:012901, July 2013. [2] G. Gligori´c, K. Rayanov, and S. Flach. Make slow fast – How to speed up interacting disordered matter. EPL, 101:10011, January 2013.
∗ Contact email:
[email protected]
18
S OLITONS IN SPIN - ORBIT- COUPLED B OSE -E INSTEIN CONDENSATES U. Zülicke1∗ , O. Fialko2 , and J. Brand2 1 School of Chemical and Physical Sciences & MacDiarmid Institute of Advanced Materials and Nanotechnology,
Victoria University of Wellington 2 Centre for Theoretical Chemistry and Physics, New Zealand Institute for Advanced Study, Massey University (Albany
Campus)
The recent experimental realisation [1, 2] of synthetic gauge fields in ultra-cold atom gases [3] has opened up the possibility for studying a host of interesting magnetic-field and spin-orbit-coupling effects for macroscopic quantum states [4, 5]. In our work, we focus on two-component (pseudo-)spin-1/2 systems that are subject to (pseudo-)spin-dependent gauge fields. In particular, ring-trapped Bose-Einstein condensates subject to spin-orbit coupling support localized dark-soliton excitations that show periodic density dynamics in real space. In addition to the density feature, the solitons also carry a localized pseudospin magnetization that exhibits a rich and tunable dynamics [6]. Analytical results for Rashba-type spinorbit coupling and spin-invariant interactions predict a conserved magnitude and precessional motion for the soliton magnetization that allows for the simulation of spin-related geometric phases recently seen in electronic transport measurements [7].
Figure 1: Magnetization dynamics associated with the periodic motion of a gray-bright soliton (a) and a gray-gray soliton (b) in a ring-trapped pseudo-spin-1/2 Bose-Einstein condensate.
References [1] [2] [3] [4] [5] [6] [7]
Y.-J. Lin, R. L. Compton, K. Jiménez-García, J. V. Porto, I. B. Spielman, Nature (London) 462, 628 (2009) Y.-J. Lin, K. Jiménez-García, I. B. Spielman, Nature (London) 471, 83 (2011). ¯ J. Dalibard, F. Gerbier, G. Juzeliunas, P. Öhberg, Rev. Mod. Phys. 83, 1523 (2011). H. Zhai, Int. J. Mod. Phys. B 26, 1230001 (2012). V. Galitski and I. B. Spielman, Nature (London) 494, 49 (2009). O. Fialko, J. Brand, U. Zülicke, Phys. Rev. A 85, 051605(R) (2012). K. Richter, Physics 5, 22 (2012).
∗ Contact email:
[email protected]
19
S UPERCONDUCTING ATOM C HIPS R. Dumke Centre for Quantum Technologies, National University of Singapore
The use of superconductors in atom chips is a recent development, presenting new opportunities for atom optics [1, 2]. One demonstrated advantage of superconductors over conventional conductors is the significant reduction of near-field noise in current-carrying structures leading to low atomic heating rates and enhanced spin-flip lifetimes [3]. Proposals in this area advocate experimental designs for coherent coupling with atomic or molecular quantum systems that exploit the distinct properties of superconductors. In our experiment we demonstrate the trapping of ultracold atoms in the magnetic field formed entirely by persistent supercurrents induced in a thin film type-II superconducting square. The supercurrents are carried by vortices induced in the 2D structure by applying two magnetic field pulses of varying amplitude perpendicular to its surface. This results in a selfsuficient quadrupole trap which does not require any externally applied fields. We investigate the trapping parameters for different supercurrent distributions. Furthermore, to demonstrate possible applications of these types of supercurrent traps we show how a central quadrupole trap can be split into four traps by use of a bias field.
Figure 1: Concept of loading supercurrents into a type-II superconducting square. a) Magnetic field pulses are applied perpendicular to the square surface, inducing vortices in the structure. The vortices carry a supercurrent giving rise to a magnetic field reflecting the current flow on the surface. b) Cloud of 87 Rb trapped in a quadrupole field produced by the magnetic field from the square and a bias field. A single field pulse was used to load supercurrents into the square (shaded area).
References [1] T. Muller, B. Zhang, R. Fermani, K. S. Chan, Z. W. Wang, C. B. Zhang, and M. J. Lim and R. Dumke„ New Journal of Physics 12, 043016 (2010). [2] T. Muller, B. Zhang, R. Fermani, K. S. Chan, M. J. Lim, and R. Dumke, Physical Review A 81, 053624 (2010). [3] R. Fermani, T. Muller, B. Zhang, M. J. Lim, and R. Dumke, Jour. of Phy. B 43, 095002 (2010).
20
T HREE - DIMENSIONAL SOLITARY WAVES WITH LARGE INERTIAL TO PHYSICAL MASS RATIO Joachim Brand∗ , Antonio Muñoz Mateo Centre for Theoretical Chemistry and Physics and New Zealand Institute for Advanced Study, Massey University, Private Bag 102904 NSMC, Auckland 0745, New Zealand
A recent MIT experiment [1] found dark solitons in a trapped and strongly interacting superfluid Fermi gas to oscillate with surprisingly low frequency, about an order of magnitude slower than predicted by mean field theory [2, 3]. In addition, dark solitons were observed in a parameter regime where mean-field theory predicts dark solitons to be unstable with respect to the snaking instability and to decay into vortices [4]. The experimental results have been interpreted as providing evidence for strong effects of quantum fluctuations. However, it was recently suggested that the experimental procedure may have indeed led to the generation of vortex rings whose oscillations may have been observed instead of those of dark solitons [5]. Here, we study the dynamics of the family of solitary wave excitations in a cylindrically confined superfluid including solitonic vortices, vortex rings, and more complex structures by analytical means and numerically within Gross-Pitaevskii mean field theory. Our results suggest that both solitonic vortices and vortex rings can have a very large ratio of inertial to physical mass, which in turn will lead to slow oscillations in a harmonically trapped gas. These results are consistent with the observed oscillation frequencies and suggest a possible reinterpretation of the Fermi gas experiment consistent with mean-field theory.
References [1] T. Yefsah, A. T. Sommer, M. J. H. Ku, L. W. Cheuk, and W. Ji, W. S. Bakr, and M. W. Zwierlein, Heavy solitons in a fermionic superfluid, Nature 499, 426 (2013). [2] R. Liao and J. Brand, Traveling dark solitons in superfluid Fermi gases. Phys. Rev. A, 83, 041604(R) (2011) [3] R. Scott, F. Dalfovo, L. P. Pitaevskii, S. Stringari, Dynamics of Dark Solitons in a Trapped Superfluid Fermi Gas. Phys. Rev. Lett. 106, 185301 (2011). [4] A. Cetoli, J. Brand, R. G. Scott, F. Dalfovo, L. P. Pitaevskii, Snake instability of dark solitons in fermionic superfluids, arXiv:1307.3717 (2013). [5] A. Bulgac, M. M. Forbes, K. J. Roche, G. Wlazłowski, Quantized Superfluid Vortex Rings in the Unitary Fermi Gas, arXiv:1306.4266 (2013).
∗ Contact email:
[email protected]
21
A PPROXIMATING M ETAL /I NSULATOR T RANSITION C. Danieli, K. Rayanov, S. Flach ∗ New Zealand Institute for Advanced Study, Centre for Theoretical Chemistry and Physics, Massey University, Auckland, New Zealand
From Anderson localisation, discovered in 1958 [1] in a tight-binding linear model ¡ ¢ ˙ n = H ψ l = ²l ψl + ψl +1 + ψl −1 , ιψ
l ∈Z;
(1)
with random potential ²l ∈]−W /2,W /2[ of finite strength W < +∞, the study of wave localisation in discrete systems has been an active research topic. In this research area, the study of quasiperiodic systems has become a really stimulating field when in 1989 Aubry and Andre’ [2] studied the model (1) with a quasiperiodic potential ²l = λ cos(2π(αl + β)) α ∈ R \ Q , l ∈ Z , (2) and proved the existence of a transition upon the strength of potential λ ∈ R∗+ , between the metallic regime (with λ > 2) and the insulating regimes (0 < λ < 2). This first case has introduced a new class of quasiperiodic models, obtained introducing an incommensurate parameter α ∈ R\Q to periodic potential ²l := f (αl ). The potential applicability of such class of model to recent experimental activities with ultracold atoms in optical lattices increased the interest in corresponding theoretical studies. From the study of the spectral properties (mainly the Cantor structure of the spectrum [3] and the spectral decomposition [4]) and its correspondences with the understanding of the wave dynamics and the localisation phenomena, the Aubry-Andre’ model was hotly debated, leaving open a huge number of questions. Starting from the analysis of the fractal structure of the spectrum, an iterative construction of a periodic potential ²l from a family of increasingly periodic potentials {E k }Kk=1 ²l :=
K X
E k (l ) ,
∀l ∈ Z .
(3)
k=1
has been done for reconstruct its self-similar spectral structure of the Aubry-Andre’ model. This new potential reveals not only the claimed self-similar structured spectrum, but in particular present an approximated metal/insulator transition upon the change of the potential strength. The spectral and dynamical properties shown by this new potential (3) allows us not only to study and have better understanding of properies of AA model, for which some properties can only be numerically approximated or are not even defined (as for example the group velocity), but also introduce a new class of quasiperiodic models. The limit to infinity of this method of construction (i.e. superposing a well-defined infinite family of periodic potentials {E k }+∞ ) yields to the property of quasiperiodic of the new potentials (3). This construck=1 tion can also be generalized (changing the periodicities and the basis of functions) defining a new class of quasiperiodic potentials which exhibit self-similar spectrum and transition between metallic and insulating regime.
References [1] [2] [3] [4]
P. W. Anderson, Phys. Rev. 109, 1492 (1958). S. Aubry, G. André , Ann. Israel Phys. Soc., vol. 3, Hilger, Bristol, 1980, pp. 133-164 A. Avila, Svetlana Jitomirskaya. Annals of Mathematics 170 , 303-342 (2009) A. Gordon, S. Ya. Jitomirskaya, Y. Last, B. Simon, Acta Math 178 (2), 169-183 (1997)
∗ Contact email:
[email protected];
[email protected];
[email protected]
22
H EAT CAPACITY OF A B OSE -E INSTEIN CONDENSATE S. K. Ruddell† , D. H. White, and M. D. Hoogerland Department of Physics, University of Auckland, New Zealand
We experimentally investigate the relationship between the energy and the temperature of a trapped Bose-Einstein condensate (BEC). While fundamental properties of a BEC such as the number of condensed atoms as a function of temperature are well known, the temperature dependence of energy has proven more difficult to discern with any useful degree of accuracy. For our experiments, we use a BEC of 87 Rb atoms held in a dipole trap formed at the intersection of two focussed CO2 beams. We consider two methods to transfer a known amount of energy to the BEC, which we then relate to the resulting temperature of the system. The first uses a method proposed by Blakie et al. [1], whereby the trapped atoms are released and allowed to fall under the influence of gravity. The BEC will undergo a self-similar expansion before the trap is reinstated and the atoms are caught. The system is then allowed to rethermalize before undergoing the process of absorption imaging so that the final temperature can be determined. By summing the different contributions to the energy we are able to build an energy-temperature curve, and compare this to theory. The second method to transfer energy to the BEC involves applying a single short pulse from a onedimensional standing wave to the atoms while they are in the trap. This imparts quantised momenta to the atoms in the same way as the atom-optics implementation of the delta-kicked rotor (e.g. see [2]). We are able to calibrate this energy by immediately extinguishing the trap and allowing the atoms to expand. This allows the fraction of atoms in each momentum state to be easily discerned, and hence the imparted energy can be measured. Once we know what these energies are the experiment can be repeated, however now the atoms remain trapped after the kick, and are able to rethermalize. The final temperature of the system is then obtained from a time-of-flight absorption image. Using these two methods we are able to study the energy dependence of BEC thermodynamics, including the effect of differing interaction strengths, and compare this to theory.
References [1] P. B. Blakie, E. Toth and M. J. Davis, J. Phys. B: At. Mol. Opt. Phys. 40, 16, 3273 (2007). [2] A. Ullah, S. K. Ruddell, J.-A. Currivan and M. D. Hoogerland, Eur. Phys. J. D. 66, 315 (2012).
† Contact email:
[email protected]
23
DYNAMICS OF TWO ATOMS UNDERGOING COLLISIONS AND MOLECULE FORMATION IN AN OPTICAL MICROTRAP Y. H. Fung ∗ , A. V. Carpentier, and M. F. Andersen Jack Dodd Centre for Quantum Technologies, Department of Physics, University of Otago, New Zealand
Photo association provides a promising route to the ability to construct individual molecules in particular quantum states. We study the dynamics of atoms in optical traps when exposed to laser light that induces molecule formation and light-assisted collisions [1, 2]. We experimentally prepare individual atom pairs and observe their evolution when exposed to the light. Due to the simplicity of the system (just two atoms in a microtrap) we can directly simulate the pair’s dynamics, thereby revealing detailed insight into it. We find that collision often often results in only one of the partners getting expelled from the optical trap. This finding highlights the importance of studying microscopic processes at the individual event level as it allows us to discriminate between different outcomes of events. Finally, our work marks an initial step towards the ability to photo-associate individual molecules atom by atom.
Figure 1: Experimental sequence. (I) We count the number of atoms to ensure that we have exactly two in our optical trap. (II) We induce collisions or molecule formation using light. (III) we count the number of remaining atoms.
References [1] A. V. Carpentier, P. Sompet, Y. H. Fung, T. G. Walker, and M. F. Andersen Preparation of a single atom in an optical microtrap, Laser Phys. Letters in press. [2] P. Sompet, A. V. Carpentier, Y. H. Fung Dynamics of two atoms undergoing light-assisted collisions in an optical microtrap, Phys. Rev. A. in press.
∗ Contact email:
[email protected]
24
N ONLINEAR WAVES IN DISORDERED LATTICES WITH BROKEN TIME REVERSAL SYMMETRY Xiaoquan Yu ∗ , Sergej Flach † New Zealand Institute for Advanced Study, Centre for Theoretical Chemistry and Physics, Massey University, Auckland 0745, New Zealand
I will present some recent progress on wave spreading dynamics in disordered nonlinear systems in the absence of time reversal symmetry. We consider a disordered discrete nonlinear Schrödinger model on a two-leg ladder in the presence of a magnetic field which breaks the time reversal symmetry. On a mean field level, this model mimics interacting bosons in disordered quasi-1D optical lattices exposed to synthetic gauge fields. We launch a single site excitation. We find that the wave packet exhibits universal sub-diffusive behavior in the long time limit, namely the second moment of the wave packet m 2 grows as m 2 ∼ t α with the universal exponent α ' 1/3. This universal sub-diffusive behavior has already been observed in the presence of time reversal symmetry [1]. However the prefactor is modified by the strength of the magnetic field. For weak magnetic field, the prefactor is enhanced and for strong magnetic field the prefactor is reduced. This is related to the fact that for the corresponding linear system, the localization length is enhanced for almost all the energy levels in weak magnetic field, however in strong magnetic field the localization length is strongly reduced.
References [1] S. Flach, D. O. Krimer and Ch. Skokos, Phys. Rev. Lett. 102, 024101 (2009).
∗ Contact email: † Contact email:
[email protected] [email protected]
25
A P HASE E NGINEERED QUANTUM R ATCHET D. H. White∗ , S. K. Ruddell, and M. D. Hoogerland† Department of Physics, Private Bag 92019, University of Auckland, New Zealand
Ratchet behaviour is of great relevance to many disciplines of science. The phenomenon allows motion only in a single direction, despite the potential being unbiased. How is it possible for a noisy system such as Brownian motion or chaos to produce directed transport and do work? The answer lies in a requirement for broken symmetry. In a classical system, symmetry must be broken through, for example, a temperature gradient. Ratchet systems are present in a wide variety of settings, such as classic, thermodynamical settings, and biological motors and membranes. Here, we consider a set of ultracold atoms undergoing ratchet behaviour. We prepare approximately 30000 ultracold 87 Rb atoms in a state of Bose-Einstein condensation in an all– optical setup. We then apply a series of kicks, generated by two counterpropagating laser beams forming a pulsed standing wave. The required broken symmetry is induced by changing the phase of this standing wave every kick in a controlled, asymmetric way. The system is a ‘ratchet’ as the potential is periodic both in space and in time. The delta-kicked rotor is a classic example of a chaotic system and is therefore perfectly analogous to a noisy system, such as Brownian motion. Although our system is distinctly quantum mechanical, epsilonclassical theory allows us to take a fictitious classical limit, forming classical phase space portraits. The critical thing about the phase modulation is that within the classical phase space, islands of stability are present within a chaotic sea. Moreover, these islands produce acceleration in only a single direction, providing an opportunity for ratchet behaviour to occur. We observe directed transport, with approximately 20% of the atoms in a clear accelerator mode (see Fig. 1). The accelerator mode is found to obey the predicted k² scaling theory, and its behaviour agrees strongly with simulations.
1
2
3
4
5
6
7
8
9 10 11 12
Figure 1: Experimental images of momentum distribution as a function of number of kicks. Note the linearly accelerated atoms on the accelerator mode.
References [1] D. H. White, S. K. Ruddell and M. D. Hoogerland, Experimental Realization of a Quantum Ratchet through Phase Modulation, arXiv:1308.6008 (2013).
∗ Contact email:
[email protected]
† Group URL: http://qilab.phy.auckland.ac.nz
26
F LUCTUATIONS IN U NIFORM S PIN -1 B OSE -E INSTEIN C ONDENSATES L. M. Symes1∗ , D. B. Baillie1 , and P. B. Blakie1 1 Jack Dodd Centre for Quantum Technologies, Department of Physics,
University of Otago, New Zealand
Spinor Bose-Einstein condensates (BECs) have a spin degree of freedom, which produces extensive physics beyond that of scalar BECs [1]. A spin-1 condensate has three spin components coupled together by spin exchange collisions, with total atom number and F z magnetization of the system being dynamically conserved. In the presence of a magnetic field, the linear and quadratic Zeeman effects break the degeneracy of the energy levels. For a uniform system, the resulting phase diagram has five distinct phases [2]. The F z magnetization, quadratic Zeeman strength q, and spin-dependent interaction c 1 determine which phase is the ground state.
Figure 1: Visualization of the symmetry of the spinor order parameter, using spherical harmonics. Surface plots are of magnitude, while shading is the phase. The sign of the spin-dependent interaction parameter c 1 determines which of these phases appear on the ground state phase diagram. Phase III only appears for c 1 > 0 and q < 0, while Phase V only appears for c 1 < 0 and q > 0. We are interested in phases III and V because here the fluctuations in spin densities are coupled to multiple spin excitation modes. Figure from [1].
Experiments can use Stern-Gerlach separation and absorption imaging [3], or phase-contrast imaging [4], to measure number densities in each spin level. Fluctuations of observables can then be analyzed within finite cells. We are investigating various spin density observables such as F z , F x and F y in the low temperature regime. Two regions of the phase diagram that are most interesting are the ones where multiple spin components coexist (phases III and V in Figure 1). To calculate the fluctuations of our observables, we construct static structure factors and expand them in terms of the low-lying collective excitations. Different observables are sensitive to specific spin mode excitations. The nature of these spin modes determines how fluctuations change within each phase and over different cell sizes.
References [1] Y. Kawaguchi, and M. Ueda. “Spinor Bose-Einstein condensates". Physics Reports (2012). [2] Y. Kawaguchi, N. T. Phuc, and P. B. Blakie. “Finite-temperature phase diagram of a spin-1 Bose gas." Phys. Rev. A 85, 053611 (2012). [3] J. Stenger, S. Inouye, D. M. Stamper-Kurn, H-J. Miesner, A. P. Chikkatur, and W. Ketterle. “Spin domains in ground-state Bose-Einstein condensates". Nature 396, 6709 (1998). [4] J. M. Higbie, L. E. Sadler, S. Inouye, A. P. Chikkatur, S. R. Leslie, K. L. Moore, V. Savalli, and D. M. Stamper-Kurn. “Direct nondestructive imaging of magnetization in a spin-1 Bose-Einstein gas". Phys. Rev. Lett. 95, 050401 (2005).
∗ Contact email:
[email protected]
27
A B ORN -O PPENHEIMER- INSPIRED APPROACH TOWARDS THE STABILISATION OF VORTICES AND SOLITONS M.W.J. Bromley∗ , H.L. Nourse, D. Preece, A.B. Stilgoe, and H. Rubinsztein-Dunlop School of Mathematics and Physics, The University of Queensland, Brisbane, Queensland, Australia.
y (osc. units)
The engineering of complicated phase and amplitude structures into wavefunctions is interesting for fundamental reasons such as understanding turbulent flow in the non-linear dynamics of superfluids, but also for a range of applications such as orbital angular momentum-based laser tweezers. We present an algorithm that can imprint arbitrary phase and amplitude structures into wavefunctions and then smooth them out to remove any unwanted excitations. By varying the distance between these structures that we impose we are able to adiabatically map out a Born-Oppenheimer-like energy landscape which indicates the regions of stability. We also present laser-based experiments demonstrating both the production and dynamics of the resulting wavefunctions. The algorithm uses internal boundary condition/s to fix the wavefunction at certain points on a spatial grid, followed by a melding algorithm that projects the desired phase structures around those points. The optimisation of 1-D, 2-D, and 3-D wavefunctions has been implemented using the Crank-Nicolson finite-difference method with imaginary time evolution. An example of the result of a 2-D Schrödinger wavefunction is shown in Fig. 1(a), wherein a single particle has been confined in a harmonic trap with three singly-charged vortices imprinted into it in a triangular configuration (with length of sides being 2 oscillator units). In addition, the rotation of the phase of one of the vortices is chosen here to be different to the other two. We are then able to map out the energy landscape of the system by varying the location of the imprinted structures. This is similar to a previous approach by Möttönnen et al. [1], however, our optimisation algorithm is entirely different, and we can easily apply it to non-stationary reference frames, eg. for the optimisation of dark and grey solitons. We have experimentally also used a spatial light modulator to create beams of light with vortex structures. We have, for example, demonstrated that the equivalent of Fig. 1(a) can be imprinted onto optical beams as shown in the intensity picture shown in Fig. 1(b). Note that this particular wavefunction shown in Fig. 1 is not a stationary state. Thus as the beam is imaged at various distances from the focal length, the vortices experience a wavefunction revival reminiscent of vortex knots [2], but here they will be shown to undergo even more complicated dynamics including vortex fusing.
4 3 2 1 0 -1 -2 -3 -4
2π π 0
-4 -3 -2 -1 0 1 2 3 4 x (osc. units) Figure 1: (a) Optimised three vortex wavefunction with imprinted charges +1,+1, and −1. The local wavefunction phase is given as the colour gradient, while the amplitude is given as contours that denote equi-probability densities (at |Ψ(x, y)|2 = 0.0001, 0.01, 0.03, 0.05, 0.07). (b) The experimental image of the intensity of an nearly identical laser beam generated by a spatial light modulator with the same phase and amplitude encoded onto it as that shown in (a), albeit the vortices have rotated.
References [1] “Stationary vortex clusters in nonrotating Bose-Einstein condensates", M. Möttönnen, S. M. M. Virtanen, T. Ishoshima, M. M. Salomaa, Phys. Rev. A 71, 033626 (2005). [2] “Isolated optical vortex knots", M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, M. J. Padgett, Nat. Phys. 6 118 (2010).
∗ Bromley Group URL: http://www.smp.uq.edu.au/people/brom
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PATH INTEGRAL M ONTE C ARLO S TUDY OF THE H ANBURY B ROWN T WISS EFFECT IN A FINITE - SIZED B OSE GAS SYSTEM S. A. Oh∗ , J. Towers, D. A. W. Hutchinson, and D. Schumayer Jack Dodd Centre for Quantum Technologies, Department of Physics, University of Otago, New Zealand
Using the Path Integral Monte Carlo (PIMC) method, we investigate the Hanbury-Brown Twiss (HBT) effect in an ideal homogeneous ultracold bosonic gas. The pair correlation function g(r) was computed for a range of temperatures above and below the Bose condensation critical temperature, and compared to analytical results for systems in the thermodynamic limit. The bunching effect is evident in the form of a “bump" at small interatomic distances, with the bump decreasing with lower temperatures as the system approaches a coherent state (pure condensate). In general, the shape and temperature-dependent trend of the g(r) curves agree with the analytical results. However, some deviations exist and we attribute this to finite size effects. We also find that the presence of repulsive interaction suppresses bunching of the bosons, as expected. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
R. Hanbury Brown and R. Q. Twiss, Nature (London) 177, 27 (1956). M. Yasuda, F. Shimizu, Phys. Rev. Lett. 77, 3090 (1996). M. Schellekens, et al., Science 310, 648 (2005). T. Jeltes, et al., Nature (London) 445, 402 (2007). T. Muller, et al., Phys. Rev. Lett. 105, 040401 (2010). S. Sanner, et al., Phys. Rev. Lett. 105, 040402 (2010). A. Perrin, et al., Nature Physics 8, 195 (2012). J. Bosse, K. N. Pathak, and G. S. Singh, Phys. Rev. E. 84, 042101 (2011). D. M. Ceperley, Rev. Mod. Phys. 67, 279 (1995). M. Boninsegni, J. Low Temp. Phys. 141, 27 (2005). L. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Clarendon Press, Oxford, 2003). P. Grüter, D. Ceperley, and F. Laloë, Phys. Rev. Lett. 79, 3549 (1997).
∗ Contact email:
[email protected]
29
Photonics and Quantum Optics
Longdell group, Otago
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T HE OPEN D ICKE MODEL WITH LINEAR AND NONLINEAR ATOM - PHOTON INTERACTIONS Scott Parkins1∗ and Arne Grimsmo1,2 1 Department of Physics, University of Auckland, New Zealand 2 Department of Physics, The Norwegian University of Science and Technology, Trondheim, Norway
A scheme in optical cavity QED based upon cavity-assisted Raman transitions in multilevel atoms has been proposed for the simulation of the Dicke model and the associated (dissipative) quantum phase transition it undergoes for sufficiently strong atom-field coupling strength [1]. At the level of a single atom, this scheme also offers the possibility of simulation of atom-field dynamics in the ultra-strong coupling regime [2]. Arguably more interesting, however, is the possibility offered by the scheme of simulating a generalised model in which a nonlinear (or dispersive) atom-field coupling can occur on an equal footing with the effective dipole (linear) coupling strength, and can in fact give rise to critical-type behavior even at the single-atom level [2]. A semiclassical analysis (corresponding to the “thermodynamic limit” of a very large number of atoms) for this generalised model predicts an exceedingly rich dynamical phase diagram for the steady state of the system with fundamentally new behaviour and phases, such as a new superradiant phase, regions of co-existent superradiant and normal phases, and regimes with oscillatory long-time attractors [3, 4]. We explore these predictions in a fully quantum model of the system with finite, but possibly large, atom number, focussing on when and how these various regimes, and the transitions between them, manifest themselves in the spectral, statistical, and entanglement properties of the system [5]. This also allows us to identify possibilities for the preparation of novel and potentially useful quantum states of both atoms and light fields.
References [1] F. Dimer, B. Estienne, A. S. Parkins, and H. J. Carmichael, “Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system,” Phys. Rev. A 75, 013804 (2007). [2] A. L. Grimsmo and S. Parkins, “Cavity-QED simulation of qubit-oscillator dynamics in the ultrastrong-coupling regime,” Phys. Rev. A 87, 033814 (2013). [3] J. Keeling, M. J. Bhaseen, and B. D. Simons, “Collective dynamics of Bose-Einstein condensates in optical cavities,” Phys. Rev. Lett. 105, 043001 (2010). [4] M. J. Bhaseen, J. Mayoh, B. D. Simons, and J. Keeling, “Dynamics of non-equilibrium Dicke models,” Phys. Rev. A 85, 013817 (2012). [5] A. L. Grimsmo and A. S. Parkins, “Dissipative Dicke model with nonlinear atom-photon interaction,” J. Phys. B: At. Mol. Opt. Phys., in press.
∗ Contact email:
[email protected]
33
B REAKDOWN OF P HOTON B LOCKADE : A D ISSIPATIVE QUANTUM P HASE T RANSITION IN Z ERO D IMENSIONS H. J. Carmichael∗ Department of Physics, University of Auckland, Private Bag 92019, Auckland, New Zealand The year 2013 marks the 50th anniversary of the Jaynes-Cummings model [1], a cornerstone of the quantum mechanical description of light, the unifier of cavity/circuit QED, and the starting point of much work on the manipulation of qubits. There is irony in its prominence, however, since Jaynes and Cummings placed more emphasis on the semiclassical version of their model than its quantum counterpart. In this paper we revisit their interest in the semiclassical versus quantum theories of radiation, while at the same time demonstrating a novel dissipative quantum phase transitions for photons [2, 3]. We start from the notion of photon blockade, where, for sufficiently strong dipole coupling, vacuum Rabi resonances behaves as two-state systems [4]: absorption of one photon blocks absorption of a second, in a striking parallel with Coulomb blockade for quantum-well electrons [5]. Recent experiments with superconducting qubits provide remarkable demonstrations of the blockade effect [6, 7]. Photons are not electrons, however, and this leads to generalizations and limitations. Most notably, the blockade is not fundamental but the result of detuning, and at high drive it may be broken through. We explore the “breaking through” and show that it occurs by way of a dissipative quantum phase transition (see Fig. 1). 30
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References [1] E. T. Jaynes and F. W. Cummings, Comparison of quantum and semiclassical radiation theories with application to the beam maser, Proc. IEEE 51, 89-109 (1963). [2] K. Baumann, C. Guerlin, F. Brennicke, and T. Esslinger, “Dicke quantum phase transition with a superfluid gas in an optical cavity,” Nature 464, 1301-1306 (2010). [3] J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, “Bose-Einstein condensation of photons in an optical microcavity,” Nature 468, 445-448 (2010). [4] L. Tian and H. J. Carmichael, “Quantum trajectory simulations of two-state behavior in an optical cavity containing one atom,” Phys. Rev. A 46, R6801-R6804 (1992). [5] A. Imamo˘glu, H. Schmidt, G. Woods, and M. Deutsch, “Strongly interacting photons in a nonlinear cavity,” Phys. Rev. Lett. 79, 1467-1470 (1997). [6] L. V. Bishop, J. M. Chow, J. Koch, A. A. Houck, M. H. Devoret, E. Thuneberg, S. M. Girvin, and R. J. Schoelkopf, “Nonlinear response of the vacuum Rabi resonance” Nature Physics 5, 105-109 (2009). [7] C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. M. Fink, A. A. Abdumalikov Jr., M. Baur, S. Filipp, M. P. da Silva, A. Blais, and A. Wallraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243606-1-4 (2011).
∗ Contact email:
[email protected]
34
P HOTONIC CRYSTAL NANOFIBERS : A WORKBENCH FOR QUANTUM OPTICS M. Sadgrove∗ , R. Yalla, K. P. Nayak, and K. Hakuta Center for Photonic Innovations, The University of Electro-communications, Chofu City, Tokyo, Japan We detail recent progress made at the Center for Photonic Innovations in the implementation of photonic crystal properties in optical nanofibers (PhCNF) and towards the combination of quantum emitters and atoms with PhCNFs. Specific attention is paid to recent integrated optics methods of creating a PhCNF where a nanofiber is reversibly combined with a nanofabricated grating in order to create Bragg mirrors and cavities on the nanofiber. PhCNFs, which are fiber analogs of photonic crystal nanobeams [1] rather than photonic crystal fibers, have been created by three different methods at the Center for Photonic Innovations as shown in Fig. 1. In all cases, we begin by manufacturing a ∼ 500nm diameter nanofiber in-house using heat and pull techniques. The focussed ion beam technique (Fig 1(a)) produces PhCNFs by cutting rectangular grooves in the nanofiber surface [2]. A second technique, which is performed entirely in-house, uses femto-second laser ablation to produces thousands of nano-craters on the nanofiber surface (Fig. 1(b)) [3]. The most recent method we have employed to produce PhCNFs uses a nanofabricated grating to which the fiber is reversibly attached [4]. The grating has a period Λg = 305 nm, a depth of 2 µm and is comprised of 200 individual slats of thickness 80 nm. We use nanopositioning stages to bring the fiber into contact with the grating, giving rise to an effective 1D PhC with a transmission stop-band of width several nm, a reflectivity of > 95% and optical loss < 5%. This method has the advantages of great design flexibility along with the ability to position the grating precisely with respect to a quantum dot deposited on the nanofiber [5]. Simulation results suggest that with a suitably designed cavity, the combination of a PhCNF and cold atoms or quantum dots can provide an efficient, fiber-coupled single photon source. Furthermore, theoretical studies suggest additional applications for PhCNFs for the observation novel electro-magnetic transparency and super-radiance type phenomena [6, 7].
Figure 1: Scanning electron microscope images of photonic crystal nanofibers made by (a) Ion-beam milling, (b) femto-second laser ablation and (c) external grating methods.
References [1] [2] [3] [4] [5] [6] [7]
Eichenfield, Matt, et al. Nature 459 550 (2009). K. P. Nayak et al. Opt. Express 19, 14040 (2011). K. P. Nayak and K. Hakuta, Opt. Express 21, 2480 (2013). M. Sadgrove, R. Yalla, K.P. Nayak and K. Hakuta, Opt. Lett. 38, 2542 (2013). R. Yalla, Fam Le Kien, M. Morinaga, and K. Hakuta, Phys. Rev. Lett.¢a109, 063602 (2012) F. L. Kien and K. Hakuta, Phys. Rev. A 79, 013818 (2009). F. L. Kien and K. Hakuta, Phys. Rev. A 77, 013801 (2008).
∗ Contact email:
[email protected]
35
C ONTROL OF T EMPORAL C AVITY S OLITONS . Stuart Murdoch, Jae Jang, Miro Erkintalo and Stephane Coen Physics Department, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
Temporal cavity solitons (CS) are localized nonlinear optical pulses that exist in passive driven Kerr cavities [1-2]. Our Kerr cavity consists of an optical coupler and 100m of single-mode fiber formed into a fiber ring with a finesse of 20. The cavity is driven by an external CW pump, referred to as the holding beam. We demonstrate cavity solitons written into the ring by the application of short (100 ps) pulses of phase modulation imprinted onto the holding beam, Fig. 1(a). These pulses of phase modulation need several (5 10) cavity roundtrips to write a CS and so need to be synchronous with the cavity. Once written a CS is attracted to the nearest peak of the phase modulation. This lets us target individual solitons and translate them around the cavity, Fig. 1(b). We use this translation to demonstrate the merging of two CS when they are brought together, Fig. 1(c). Finally we show that strong pulses (amplitude 1.5 Rad) of synchronous phase modulation can both write new CS and erase existing CS, mimicking the operation of an all-optical toggle flip-flop, Fig. 1(d). Together these techniques allow us to individually address any soliton in the cavity and represent a remarkable demonstration of the control of light by light.
Figure 1: (a) Cavity solitons written by synchronous pulses of phase modulation; at t = 20 s the phase modulation is extinguished and the CS evolve freely via an acoustic interaction (b) a CS translated around the cavity through phase modulation of the holding beam, (c) the merging of two CS, (d) CS written, held, and erased by controlled phase modulation of the holding beam (strong phase modulation pulses are indicated by the black dots).
References [1] F. Leo et al, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer” Nature Photonics 4, 471-476 (2010) [2] J. Jang et al, “Ultraweak long-range interactions of solitons observed over astronomical distances”, Nature Photonics 7, 657-663 (2013)
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U LTRA - WEAK LONG - RANGE ACOUSTIC INTERACTIONS OF TEMPORAL CAVITY SOLITONS ∗
Jae K. Jang , Miro Erkintalo, Stuart G. Murdoch, and Stéphane Coen Department of Physics, The University of Auckland, Private Bag 92019, Auckland 1142
Solitons are ubiquitous nonlinear waves that manifest themselves across a plethora of physical systems. Soliton interactions can be either short-range or long-range, the latter being mediated by the coupling of light with a non-local material response. Here we report what we believe is by far the weakest interaction between solitons ever observed. Our experiment utilizes temporal cavity solitons (CSs) recirculating in a coherently-driven optical fiber loop [1, 2]. We observe two such CSs, separated by up to 8000 times their width, changing their temporal separation by a few attoseconds per round-trip of the 100 m-long resonator. The acoustically-mediated [3] interactions are so weak that they require an effective propagation distance of the order of an astronomical unit to truly manifest themselves [2]. The interactions were studied by writing a single pair of CSs in the fiber cavity and by observing how the temporal separation of the two pulses evolve using an ultra-high-sampling-rate real-time digital oscilloscope triggered on the leading soliton [2]. In Fig. 1 we summarize four distinct measurements obtained with different initial separations. Note that we omit showing the leading pulse, located at zero delay, for clarity. The trailing soliton can be either repelled away or attracted towards the leading soliton, eventually settling at one of two stable separations (19.78 ns or 22.05 ns). The timescales over which the interactions occur are incredibly slow for an optical system. During the 300 second interval shown in Fig. 1, the CSs travel around the cavity 600 million times, for a total distance of 60 million kilometers, or 0.4 astronomical units. Yet over that vast distance the solitons only shift their temporal separation by 1 ns; less than two attoseconds (corresponding to much less than a wavelength of the soliton carrier wave) per cavity-roundtrip. In order to highlight the acoustic origin of the interaction, we have calculated the acoustic perturbation to the fiber refractive index due to the CSs and incorporated it into the mean-field model describing the system. Simulation results (with no free parameters) are superimposed as red curves in Fig. 1 and show excellent agreement with experiments. In conclusion, we report what we believe is the weakest interaction ever observed between solitons. Mediated by transverse acoustic waves, the interaction couples two solitons separated by up to 8000 times their width and is only detectable after millions of kilometers of effective propagation.
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References [1] F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, and M. Haelterman, Temporal cavity solitons in one-dimensional Kerr media as bits in an alloptical buffer, Nat. Photon. 4, 471-476 (2010). [2] J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, Ultraweak long-range interactions of solitons observed over astronimical distances, Nat. Photon. 7, 657-663 (2013). [3] E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, and A. M. Prokhorov, Long-range interaction of picosecond solitons through excitation of acoustic waves in optical fibers, Appl. Phys. B 54, 175-180 (1992).
∗ Contact email:
[email protected]
37
S ENSITIVITY O PTIMIZATION OF P ORTABLE A MMONIA S ENSOR K. Wu1∗ , J. Harvey1 , D. Hirst2 , S. Murdoch1 1 Department of Physics, University of Auckland, New Zealand 2 Southern Photonics, New Zealand
The design of a portable gas sensor used for detecting ammonia concentrations in the atmosphere is being optimized, aiming for sub-ppm sensitivity. A prototype was previous created by Southern Photonics which is capable of detecting ammonia concentration with ppm sensitivity. It uses a tunable diode laser that scans an absorption feature of ammonia. The laser is wavelength modulated so when the signal demodulated at the receiver end is subject to lower levels of 1/f noise. The diode laser scans across the absorption line at 1531.7nm. In that infrared region there are absorption lines of up to twice as strong while still staying away from the absorption features of other particles present in the atmosphere. By switching the laser wavelengths to scan the stronger absorption lines, the detection sensitivity can be increased, in theory, by the same amount. Select strongest, interference-free feature
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Figure 1: Main areas to optimize the sensitivity of gas sensor.
The optical path of the laser is formed by a double pass between the detector and a retro-reflector. Lengthening the optical path allows more ammonia molecules to absorb the laser light and create stronger absorption signals. The sensitivity can be increased by lengthening the optical path as long as the power received is high enough so the signal is distinguishable from background noise. The received signal is recovered by two lock-in amplifier circuits at the modulation and second harmonic frequency. Various signal processing techniques such as matched filtering are investigated to increase the sensitivity of ammonia concentration reading. The lock-in amplifiers themselves can be digitized to recover the signals for better filter properties and ease of data manipulation. Absorption signal at modulated frequency
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∗ Contact email:
kwu036@@aucklanduni.ac.nz
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L ASER FABRICATION OF S INGLE - MODE A MORPHOUS P OLYCARBONATE WAVEGUIDES Xinjie Song, Rainer Leonhardt and Stuart Murdoch Department of Physics, University of Auckland,New Zealand
Fast fabrication of single mode Amorphous Polycarbonate (APC) waveguides is achieved by using an Excimer Laser machining system running at a 500Hz repetition rate. A numerical simulation program (MODE) is used to determine the dimensions for single-mode operation. The machining system operates at a wavelength of 248nm with a pulse duration of 5ns. ESEM pictures indicate a good surface quality for both end-faces and sidewalls of the waveguides. We obtain a coupling efficiency of about 20% with a lensed single-mode fiber for the input coupling and an aspheric lens for the output. For the propagation loss measurement of the waveguides, we propose a novel but simple method. Waveguides with different lengths are fabricated on one substrate with a trapezoidal shape and thus we are able to plot a curve of the output power for waveguides with different lengths [Fig. 1 (left)]. Our waveguides are patterned to be several different waveguide structures. We directly cut normal straight APC waveguide on glass and the attenuation is measured to be 1.8dB/cm at 1550nm. Polyurethane and PMMA are proved to be good undercladding material for reversed APC waveguide [Fig. 1 (right)]. We also fabricate Mach-Zehnder (MZ) structures, the two arms of which are separated by 100um with a splitting angle of 1o . Visible light is used to demonstrate the coupling, splitting, and propagation of light for these APC waveguides.
Figure 1: (Left) Plot of the output powers of waveguides of different lengths. (Right) ESEM picture of reversed APC waveguide with Polyurethane as the undercladding.
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D ISPERSIVE WAVE G ENERATION BY F OUR-WAVE M IXING C ASCADES K. E. Webb∗ , M. Erkintalo, Y. Q. Xu, and S. G. Murdoch Department of Physics, University of Auckland, Private Bag 92019, Auckland, New Zealand
Dispersive wave (DW) emission is a central process in nonlinear fiber optics. While conventionally described in the context of a temporal soliton perturbed by higher-order dispersion [1], the process is more general with equivalent radiation observed from non-solitonic pulses in the normal dispersion regime [2, 3]. Recently, a frequency domain description of DW emission has been given, with cascaded four-wave mixing (FWM) identified as the underlying mechanism [4]. This theory establishes a direct link between phasematched cascaded FWM by two continuous wave (CW) lasers, and the emission of DWs by single cycles of the temporal beat signal. Here, we investigate the efficiency of cascaded FWM in driving DW emission as the detuning ∆ between the two pumps is changed. While the efficiency initially decreases with detuning, a near perfect recovery is observed below a given detuning. In Fig. 1(a) and 1(b) we plot the simulated spectral evolution of two 5 W CW pumps centered at 1580.46 nm with detunings (a) ∆/2π = 1.09 THz (n = 9) and (b) ∆/2π = 0.30 THz (n = 34) propagating in 100 m of dispersion shifted fiber (ZDW= 1553.5 nm). Values of ∆ are chosen to phasematch the n t h order sideband at the DW frequency. Fig. 1(c) and 1(d) show the corresponding experimental output spectra, displaying excellent agreement with the simulations. (a)
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Vast differences are seen in the evolution as the pump detuning (cascade order) is changed. When n = 9, the coherence length of the individual non-phasematched processes is short, and inefficient transfer to the DW occurs. When n = 34, the coherence length of each process is long, resulting in more efficient power transfer. The evolution in Fig. 1(b) bears a striking resemblance to that of high order solitons emitting DWs. Finally in Fig. 1(e) we show the simulated and experimental conversion efficiency to the DW as a function of cascade order n. Three distinct regions can be explained in terms of the effective soliton order N of individual cycles of the bichromatic field. While the conversion efficiency initially drops since N < 1 (region 1), dramatic improvement is seen when N > 1 (region 2) as individual field cycles can temporally compress (spectrally broaden) to emit radiation at the DW frequency. In region 3, the length at which temporal compression occurs is larger than the fiber length, and DW emission drops quickly. These results give a guideline for efficient DW generation, and provide further insight into the frequency domain description of DWs.
References [1] [2] [3] [4]
P. K. A. Wai, C. R. Menyuk, Y. C. Lee, and H. H. Chen, Opt. Lett. 11, 464 (1986). K. E. Webb, Y. Q. Xu, M. Erkintalo, and S. G. Murdoch, Opt. Lett. 38, 151 (2013). M. Conforti and S. Trillo, Opt. Lett. 38, 3815 (2013). M. Erkintalo, Y. Q. Xu, S. G. Murdoch, J. M. Dudley, and G. Genty, Phys. Rev. Lett. 109, 223904 (2012).
∗ Contact email:
[email protected]
40
S TABILITY AND COHERENCE OF MICRORESONATOR- BASED OPTICAL FREQUENCY COMBS Miro Erkintalo1∗ and Stéphane Coen1 1 Physics Department, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
The generation of optical frequency combs (OFCs) in monolithic microresonators has attracted considerable interest during the past few years [1]. Owing to the device’s microscopic footprint, power efficiency and CMOS-compatibility, this technology represents a promising route towards on-chip OFC generators. So far the intractable computational complexity of dominant numerical models has restricted microresonator studies to pure experiments. However, the microscopic device footprint makes it difficult to obtain insights using experiments alone. As a consequence, several characteristics critical for the performance of any OFC, such as stability, remain poorly understood in the microdomain. We have recently shown that microresonator frequency combs can be realistically modeled in a matter of seconds using a generalized Lugiato-Lefever equation (LLE) [2]. Here, we use numerical simulations based on the generalized LLE to examine the stability and coherence characteristics of microresonator frequency combs. We observe universal regimes of comb stability, whose spectral signatures are in excellent agreement with past experiments. We model an octave-spanning OFC generated in a silicon nitride resonator whose diameter d = 200 µm [3]. Figure 1 shows the simulated OFC for four different values of the cavity detuning. The red curves represent the mean spectrum averaged over 1 million roundtrips; the black lines show a snapshot of the OFC over a single roundtrip. We identify four different regimes. For low cavity detunigs [Fig. 1(a)] the comb lines are separated by multiple free-spectral ranges (FSRs). Here the mean spectrum is identical with a snapshot over a single roundtrip: the comb is stable. In contrast, increasing the cavity detuning results in a chaotic comb in which the comb lines are separated by a single FSR [Fig. 1(b)]. The mean spectrum is smooth, and differs from the structured snapshot. The comb fluctuates from roundtrip-to-roundtrip, which causes the fine-structure to be washed out on ensemble averaging. When the cavity detuning is further increased the comb exhibits gradual stabilization. Indeed, the mean spectrum shown in Fig. 1(c) displays fine-structure, yet the comb exhibits breathing and recurs only periodically. Finally, for the largest cavity detuning [Fig. 1(d)] the comb is perfectly stable, and the mean spectrum shows identical fine-structure as a snapshot of an arbitrarily selected roundtrip. Our simulations are in excellent agreement with experiments, and the comb reported in [3] is nearly indistinguishable from the simulation in Fig. 1(b). A time-domain analysis reveals that the observed regimes of comb stability represent different branches of solutions of the underlying LLE, extending the applicability of our results to arbitrary resonator configurations. To conclude, we have numerically investigated the stability of microresonator OFCs. We have identified universal regimes of comb stability, linked to the solutions of the underlying LLE. Methods to experimentally quantify comb coherence will be discussed. Spectrum (dB)
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References [1] T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, Science 332, 555–559 (2011). [2] S. Coen, H. G. Randle, T. Sylvestre, and M. Erkintalo, Opt. Lett. 38, 37–39 (2013). [3] Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, and A. L. Gaeta, Opt. Lett. 36, 3398–3400 (2011).
∗ Contact email:
[email protected]
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C OHERENCE AND SINGLE - SHOT SPECTRA OF NOISE - LIKE PULSES A. F. J. Runge∗ , C. Aguergaray, N. G. R. Broderick, and M. Erkintalo 1 Physics Department, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
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Mode-locked lasers epitomize stability, with the output pulse trains being sufficiently regular to facilitate frequency metrology with unprecedented precision. In this context, it is surprising that several passively mode-locked fiber oscillators can sustain an operation regime that manifests as a seemingly regular train of output pulses whose closer scrutiny reveals to resemble bursts of noise-like (NL) fluctuations [1]. So far characteristics of NL pulses such as their spectral stability and phase coherence have not been assessed using direct experiments. Here we correct this deficiency, reporting on experimental studies of coherence and fluctuations in NL ultrafast fiber oscillators. In particular, we use real-time spectral measurements to show that the smooth spectrum characteristic for NL pulses arises from ensemble averaging. Our experiments use a 1.1 MHz, Er-doped fiber laser mode-locked using the nonlinear polarization evolution. Because the oscillator allows us to excite both the soliton and NL regimes, we are able to compare and contrast the two. To gain insights into the coherence properties of the field we propagate the pulse train through a Michelson interferometer with a path difference of one cavity roundtrip between the arms of the device. Typical spectral interferograms are shown as solid black curves in Figs. 1(a) and (b) for the soliton and the NL regimes, respectively. Superimposed on the interference patterns is the oscillator output spectrum before the interferometer (dashed red line). In the soliton regime we can observe fringes with visibility close to unity, indicating total pulse-to-pulse phase stability. When the laser is switched to the NL regime the fringes vanish, and cannot be recovered. This indicates total lack of phase coherence across the NL pulse train. Pulse-to-pulse phase fluctuations also suggest the existence of shot-to-shot spectral fluctuations. To overcome the slow response time of optical spectrum analyzers we employ a photonic time-stretch technique, and map the pulse spectra into the temporal domain using a highly dispersive fiber [2]. This allows us to measure the single-shot spectra of the megahertz pulse train in real-time using a fast oscilloscope. Single-shot results are shown as the bottom density maps of Figs. 1(c) and (d) for the soliton and the NL regimes, respectively. The spectra in the soliton regime are nearly indistinguishable, and the variation between the ensemble-averaged mean and an arbitrarily chosen realization (top graphs) is negligible. To the contrary, the NL regime is associated with significant shot-to-shot fluctuations. Yet, when an ensemble average is computed, the variations are washed out, yielding a smooth spectrum as reported for NL pulses. To conclude, we have experimentally investigated the phase coherence and shot-to-shot spectral fluctuations of NL fiber lasers. In particular, we have presented direct experimental evidence that the smooth spectrum characteristic for noise-like pulses arises from the ensemble averaging of a multitude of highly structured and fluctuating elementary spectra. −2.1 −1.2 1 (d) 0.8 0.6 0.4 0.2 200
Time (ns) −0.2 0.8
1.7
150 100 50 1540 1550 1560 1570 1580 Wavelength (nm)
Figure 1: (a,b) Spectra at the output of the interferometer (black solid line) and at the output of the oscillator (red dashed line). (c,d) Single-shot results. Bottom graphs show 200 consecutive spectra while top graphs compare the ensemble average (black solid line) with an arbitrary single realization (red dashed line). In (a,c) the laser is soliton mode-locked while in (b,d) the operation is noise-like.
References [1] M. Horowitz, Y. Barad, and Y. Silberberg, Opt. Lett. 22, 799–801 (1997). [2] K. Goda and B. Jalali, Nature Photon. 7, 102–112 (2013).
∗ Contact email:
[email protected]
42
P USHING THE LIMITS OF ENVIRONMENTALLY STABLE FIBRE LASERS : 120 FS , 4.2 N J, ALL -PM ALL - FIBRE Claude Aguergaray, Antoine Runge, Miro Erkintalo, and Neil G. R. Broderick Physics Department, University of Auckland, Private Bag 92019, Auckland, New Zealand
As research and industrial applications of laser systems get more advanced, the pressure to enhance the performance of the front-end oscillators becomes more intense. In the past decade a huge leap in the improvement of the stability and overall environmental robustness has come from fibre-based lasers. Using new designs for the fibre geometry and the laser cavities, this technology is now on par with, or even surpasses in some cases, bulk lasers. However, the majority of the proposed fibre-based oscillators are limited in energy or do not fully profit from the benefits of the waveguide medium such as alignment-free operation and environmental stability since they host free space elements. The laser cavity holding the record for the shortest pulse duration from a fibre-based oscillator is a good illustration of the aforementioned trend [1]. Indeed, these pulses were generated in a dispersion-managed cavity consisting mostly of free-space components and their energy was restricted to 0.7 nJ. The limited scalability of pulse energy in fibre-based lasers has recently been overcome thanks to the use of cavities built exclusively of normal-dispersion elements (ANDi lasers), and several mode- locking techniques have been successfully demonstrated with this design [3]-[6]. So far, however, each have failed in delivering extremely short pulses with several nJ pulse energy while simultaneously maintaining the environmental robustness innate for all-fiber all-polarization maintaining (PM) cavities. In this contribution, we present the first laser architecture [see Fig. 1(a)] that combines all the key features that the fibre technology has to offer and simultaneously delivers extremely short pulses with an energy of several nJ. In particular, we demonstrate, to the best of our knowledge, the shortest pulse duration combined with the highest pulse energy out of an all-fibre PM laser which is naturally stable, versatile, robust against peak power fluctuations, and does not require any tuning or include any components susceptible to life-time degradation issues such as saturable absorber mirrors. Compared to other ANDi lasers, the crucial feature of our cavity is the inclusion of a nonlinear amplifying loop mirror (NALM). The laser outputs linearly polarized 4.2 nJ pulses at a repetition rate of 10 MHz. With a spectral bandwidth of 20 nm [see Fig. 1(b)], the output pulses can be de-chirped to a duration as short as 120 fs [see Fig. 1(c)]. The NALM of the laser provides a reliable and flexible tool for self-starting mode-locked operation while the integrated all-PM design makes the laser insensitive to temperature variations and mechanical vibrations. These results represent a notable improvement in comparison to previous results. Indeed, compared to our latest work [6], we obtain pulses twice as short at a higher repetition rate. But above all, compared to the most performing all-fibre PM ANDi laser based on a different mode-locking technique [4], we demonstrate a threefold increase of the output pulse energy and nearly four times shorter pulses, corresponding to more than one order of magnitude gain in the peak power. Numerical modelling suggests that even shorter pulses could be obtained using a broader band-pass filter in the cavity, and we hope to demonstrate this in the near future.
Figure 1: (a) Laser cavity. (b) Linear Spectrum (insert on a log plot) and (c) Measured autocorrelation trace of the laser output.
References [1] X. Zhou, D. Yoshitomi, Y. Kobayashi, and K. Torizuka, “Generation of 28-fs pulses from a mode-locked ytterbium fiber oscillator,” Opt. Express 16, 7055-7059 (2008). [2] W. Renninger, A. Chong, and F. Wise, “Self-similar pulse evolution in an all-normal-dispersion laser,” Phys. Rev. A 82, 021805 (2010). [3] D. Mortag, D. Wandt, U. Morgner, D. Kracht, and J. Neumann, “Sub-80-fs pulses from an all-fiber-integrated dissipative-soliton laser at 1 ?m,” Opt. Express 19, 546-551 (2011). [4] J. Lecourt, C. Duterte, F. Narbonneau, D. Kinet, Y. Hernandez, and D. Giannone, “All-normal dispersion, all-fibered PM laser mode- locked by SESAM”, Opt. Express 20, 11918-11923 (2012). [5] C. Aguergaray, N. G. R. Broderick, M. Erkintalo, J. S. Y. Chen, and V. Kruglov, “Mode-locked femtosecond all-normal all-PM Yb- doped fiber laser using a nonlinear amplifying loop mirror,” Opt. Express 20, 10545-10551 (2012). [6] M. Erkintalo, C. Aguergaray, A. Runge, and N. G. R. Broderick, “Environmentally stable all-PM giant chirp oscillator,” Opt. Express 20, 22669-22674 (2012).
43
D ELAY EFFECTS IN A SEMICONDUCTOR LASER WITH OPTICAL FEEDBACK FROM TWO FILTER LOOPS Bernd Krauskopf1∗ , P. SŁowinski ´ 2 , and S. Wieczorek3 1 Department of Mathematics, The University of Auckland,
Private Bag 92019, Auckland 1142, New Zealand 2 Mathematics Institute, Zeeman Building, University of Warwick,
Coventry CV4 7AL, United Kingdom 3 Mathematics Research Institute, CEMPS, University of Exeter,
North Park Road, Exeter EX4 4QF, United Kingdom
This talk will give a glimpse of the complicated solution and stability structure of a semiconductor laser receiving time-delayed and frequency-filtered optical feedback (FOF) from two external filters. This system is referred to as the 2FOF laser, and it has been used as pump laser in optical telecommunication and as light source in sensor applications. The 2FOF laser is modeled by rate equation in the form of delay differential equations [1]. Our analysis of the 2FOF laser focuses its the basic solutions, known as external filtered modes (EFMs), which correspond to laser output with steady amplitude and frequency. We consider the EFM-surface in the space of steady frequency, the corresponding steady population inversion, and the feedback phase difference. The EFM-surface emerges as the natural object for the study of the 2FOF laser, and we classify its possible types in dependence on the two detunings of the filter, for different but fixed values of the filter width and the two delay times. Moreover, we consider how the stability regions of EFMs are related to the type of the EFM-surface. From a viewpoint of practical interests, we find various bands and islands of stability on the EFM-surface that may be accessible experimentally; see Figure 1. This work can also be seen as a case study that demonstrates how delay effects in lasers and other devices can be analysed with the help of tools from dynamical system.
Figure 1: Example of stability regions on the EFM-surface
References [1] P. Slowinski, B. Krauskopf and S. M. Wieczorek, Solution structure and dynamics of a semiconductor laser subject to feedback from two external filters, Proceedings of SPIE Europe 7720 (2010).
∗ Contact email:
[email protected]
44
N UMERICAL INVESTIGATIONS FOR A HOLLOW CORE TERAHERTZ WAVEGUIDE WITH EMBEDDED METAL WIRES Nurfina Yudasari1∗ , Rainer Leonhardt† Physics Department, University of Auckland, Private Bag 92019, Auckland, New Zealand
Advanced applications of Terahertz (THz) radiation have attracted much attention for developing and optimizing the transmission through THz waveguides. However, this is challenging as low-loss materials (like glass in the IR) do not exist in this frequency range. We demonstrate numerical investigations of a hollow core THz waveguide where the cladding consists of a dielectric material with embedded metal wires. The waveguide is designed with a core of 4mm diameter that is surrounded by 12 small holes with 0.35 mm of the diameter. These holes allow us to put different numbers of metal wires in the cladding, Fig. 1 (left) and Fig. 1 (right) show the case of 2 wires while we investigate also larger number of wires. Two different boundary conditions are applied for this investigation, with and without a metal coating on the outside surface of the waveguide. The numerical investigation is conducted by running a simulation using the 2D Lumerical MODE Solution program to obtain the physical properties of the waveguide. The hybrid mode can be guided in the core region, for both conditions. These simulations also determine the effective refractive index that turns out to be close to the expected value for vacuum. Both samples show about the loss values of less than 1dB/cm. It is predicted that the metal coating enables a broader frequency range for single- mode operation.
Figure 1: Left: Cross section of a hollow core dielectric terahertz waveguide with two embedded metal wires. Right: Simulated mode profile at 0.75 THz
∗ Contact email:
[email protected]
† Group URL: http://www.physics.auckland.ac.nz/uoa/home/about/our-research/research-by-area/laser-physics#s2c2
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C O - LINEAR WIRE WAVEGUIDE FOR THE TERAHERTZ REGION Najma Zia, Rainer Leonhardt Department of Physics, University of Auckland,New Zealand
Terahertz (THz) radiation bridges the gap between infrared and microwave in the electromagnetic spectrum, and offers significant technological potential in various fields. For many applications it is vital to develop waveguides with minimal transmission loss. This is a challenge because almost all materials are absorbent in the terahertz region. Here we present an experimental investigation for single-mode THz waveguides that have a hollow core where the boundary conditions are mainly determined by two wires that are embedded in the cladding. For this purpose, two copper wires of 0.4 mm diameter were imbedded in commercially available PVC hose which has an inner and an outer diameter of 3 mm and 5 mm respectively. The cross-section of the waveguide is shown in Fig. 1 (left). For the first time, this design based on a plastic hose should enable THz single-mode waveguides that are easily bendable. A THz time domain spectroscopy setup with a frequency range from 0.2 to 1.2 THz is used to record the transmitted pulses and compare them with the reference pulses. Figure 1 (right) shows the spectral power density for the reference pulses as well as for pulses that have propagated through a 45mm-long waveguide. Overall we get a transmission efficiency of 5% but this is clearly frequency dependent as can be seen in Fig. 1 (right). Further investigations will focus on separating the coupling efficiency from the waveguide losses, and establishing the cut-off frequency as a function of the core diameter.
Figure 1: (Left) Cross section of the waveguide with core diameter of 3mm. (Right) Power spectral density of the reference and sample signal.
46
S ELF - TESTING AND INTERACTIVE PROOFS FOR QUANTUM EXPERIMENTS Matthew McKague∗ Jack Dodd Centre for Quantum Technologies, Department of Physics, University of Otago, New Zealand
As we build more and more complex quantum experiments we will eventually run into a problem of computation. The state space of the quantum apparatus will grow exponentially with the number of subsystems and so computing predictions on the outcomes of large experiments will be infeasible. As well, tools such as tomography which are used for characterizing quantum experiments also require an exponential amount of computational resources. Hence as experiments reach higher complexity we will need to develop new tools to allow us to make use of the quantum formalism. Self-testing is a concept of testing a quantum experiment where we do not start with any trusted devices. Instead, by examining the outcome statistics of the experiment for various measurement settings, we can certify that the entire apparatus is behaving close to some specification. As an example, using CHSH correlations we can verify that an experiment creates maximally entangled pairs of qubits and then measures them in the X , Z , and X ± Z bases. We can also test certain families of large states using only a linear number (in the number of subsystems) of measurement settings and a similar amount of computational resources. Moreover, these self-testable states and measurements are universal for quantum computation. An interactive proof is a computation involving a powerful but untrustworthy computer (a quantum computer, for example) and a less powerful but trustworthy computer. The two computers communicate with each other and either agree on the output, which must be correct with high probability, or they abort. Interactive proofs allows us to make use of untrustworthy computing resources and still have confidence in the outcome. Using self-tested resources, we can construct interactive proofs that allow a classical computer to tap into quantum resources and perform quantum computations, without first trusting these quantum resources. For example, this would allow us to use a quantum computer to compute predictions for a quantum experiment, and we can trust these predictions without first needing to characterize the quantum computer itself. As well, these interactive proofs certify the correct operation of the quantum computer.
References [1] Matthew McKague. Interactive proofs for BQP via self-tested graph states. September 2013.
EPRINT
arxiv:1309.5675.
[2] Ben W. Reichardt, Falk Unger, and Umesh Vazirani. A classical leash for a quantum system: Command of quantum systems via rigidity of CHSH games, September 2012. EPRINT arXiv:1209.0448.
∗ Contact email:
[email protected]
47
E XPLORING THE H YPERFINE S TRUCTURE OF 167 Er : Y2 SiO 5 VIA S PECTRAL H OLE B URNING X. Fernandez-Gonzalvo1∗ , and J. Longdell1 1 Department of Physics, University of Otago, New Zealand
Laser Detuning (GHz)
In order to incorporate superconducting qubits into the quantum optical network we aim to find a material in which we can perform a lambda system coupling microwave and telecom frequency photons. A promising candidate is erbium embedded in an yttrium orthosilicate crystal (Er:Y2 SiO5 ). Er:Y2 SiO5 presents a natural transition at 1536 nm, from the 4 I15/2 ground state to the 4 I13/2 excited state. We aim to find the microwave transition inside the hyperfine structure of either state. 167 Er is the only stable isotope with nonzero nuclear spin (I=7/2). Knowledge of hyperfine splittings in both excited and ground states is needed in order to calculate the different transition strengths involved in the pursued lambda system. The hyperfine structure of the 4 I15/2 ground state was determined by Baldit et al. in 2010 [1], but the hyperfine structure of the 4 I13/2 excited state remains unknown. This work aims to determine the hyperfine structure of the 167 Er excited state in a spectral hole burning (SHB) experiment The SHB technique starts by shining a spectrally narrow laser pulse on the sample inside of the inhomogeneously broadened absorption line. For a given class of atoms this promotes population from a particular hyperfine level of the ground state to a particular level of the excited state. The ground state level is therefore emptied, thus generating a transmission window at the burning laser frequency since there will be no atoms to absorb its light. A series of side-holes and antiholes will also appear as a consequence of this population reorganization. If one is able to read such features with a frequency scanned probe pulse, the spectral separation between them can then be translated into energy differences between hyperfine levels. In our laboratory we use a tunable telecom laser to burn and read holes into an Er:Y2 SiO5 sample cryogenically cooled to temperatures around 3∼4 K. To do so, we send into the sample a long and pulse (tens of ms) in order to burn a spectral hole with its accompanying side-structure, and then we shine a short and weak read pulse (a few µs), synchronized with a scan of the laser frequency produced by a piezoelectric component in the laser (a few hundreds of MHz wide). We perform these measurements for different burning frequencies that we scan with a fiber electro-optic modulator from d.c. to up to 8 GHz. Finally we repeat this operation for several laser wavelengths that we tune in an interval of a few GHz around the central absorption line. Figure 1 shows an example of the experimental data acquired. We believe this multiple frequency scan will allow us to read over an interval sufficiently wide as to get enough information to reconstruct the hyperfine structure of the 4 I13/2 excited state of erbium, and this will in turn provide us with the necessary knowledge to find a suitable lambda system coupling microwave to telecom frequency photons.
0.5 0.4 0.3 0.2 0.1 800
1000 1200 Scan Freq. (MHz)
1400
Figure 1: Absorption spectra for different laser frequencies (vertical axis), far from the central absorption line. Absorption is also plotted in the vertical axis in arbitrary units.
References [1] E. Baldit et al., Identification of Λ-like systems in Er3+ :Y2 SiO5 and observation of electromagnetically induced transparency, Phys. Rev. B 81, 144303 (2010).
∗ Contact email:
[email protected]
48
S HAPING THE LIGHT FROM A TINY HOLE Yu-Hui Chen∗ Jack Dodd Centre for Quantum Technologies, Department of Physics, University of Otago, New Zealand
Light emerging from a tiny hole in an opaque plate is a long-established subject in optics. It is well known in geometrical optics that a pinhole can form an inverted image as a consequence of the rectilinear propagation of light rays. When the size of such a hole goes to subwavelength scale, the light is expected to be diffracted into all directions. However patterning periodic grooves on a metallic film can collimate or focus the light from a subwavelength hole [1]. In this work we show that, when a subwavelength hole in a metal thin film is surrounded by well-designed patterns of grooves, the wavefront of the light through it can be shaped into a preset complicated pattern at a given position [2] instead of being diffracted in all directions. Specifically, we shaped the 1064 nm light from a 180-nm-radius circular hole on a 240-nm-thick silver film into the shape of a Latin letter "L" or an "O" by patterning some 100-nm-width grooves on the output surface. The method used to design such structures are named the surface-wave-holography(SWH) method, which brings the concepts of holography and surface electromagnetic wave together. The SWH method uses computer to calculate the holographic structures and then uses micro/nano-fabrication techniques to pattern a metallic surface. Because the SWH method does not involve any exposure process and is free of transmitted background, it makes the holographic technique more feasible in a micro-optical system. We expect that this method may find applications in steering the optical wavefront in a micro scale.
Figure 1: (a1) and (a2) designed patterns. (b1) and (b2) scanning-electron-microscope images. (c1) and (c2) simulated field distributions. (d1) and (d2) experimental data.
References [1] H.J. Lezec et al, Beaming light from a subwavelength aperture, Science 297, 820 (2002). [2] Y.H. Chen et al, Wavefront shaping of infrared light through a subwavelength hole, Light Sci. Appl. 1, e26 (2012).
∗ Contact email:
[email protected]
49
ATOMIC FREQUENCY COMBS AND THE OPTICAL DETECTION OF ULTRASOUND Luke R. Taylor, Jevon J. Longdell Jack Dodd Centre for Quantum Technologies, Department of Physics, University of Otago, New Zealand
Optical imaging techniques suffer from high scattering in biological tissues (limiting penetration depth) yet enable multi-scale morphological distinction and high resolution, whereas purely ultrasound-based techniques have the advantage of being able to image deep into tissue without significant scattering. A combination of these techniques would be ideal for highly sensitive deep tissue imaging. Ultrasoundmodulated optical tomography (UMOT) is one such technique combining light and ultrasound for softtissue imaging. Photons interacting with an acoustic wave will be frequency shifted by the ultrasound frequency, typically eight to nine orders of magnitude smaller than the optical frequency in question. This can make the detection of the ultrasound ’tagged’ photons difficult. Techniques for detecting such small shifts in optical frequency do exist, yet they remain limited by a small étendue or response times significantly longer than the decorrelation time in biological tissues. We present results from a novel method combining quantum memory techniques with the optical detection of ultrasound, providing a solution to the described problem- as well as displaying both large étendue and a micro-second response time as required for in-vivo biological tissue imaging. The atomic frequency comb (AFC), a spectral filter generated via holeburning in a cryogenically cooled rare-earth-iondoped crystal (Pr3+:Y2SiO5), is our quantum memory of choice. We create a pair of AFCs (tooth separation ∆ = 150 kHz, comb finesse f c ∼ 2 and optical depth αL ∼ 2) separated by twice the ultrasound modulation frequency (1MHz) on either side of a broad spectral pit, itself centred at the frequency of the carrier. The AFCs are prepared simply via optical pumping without any need for external fields. The ultrasound ’tagged’ sidebands are then absorbed in the AFCs, to be re-emitted as a photon echo later in time (as defined by the comb parameters, and with 10-20% efficiency). In contrast, the carrier passes unimpeded through the sample- in fact, any light not interacting with the AFC appears in the carrier temporal window and does not pollute the (delayed) signal. In this manner we are able to temporally separate the carrier and sidebands, enabling a record level of discrimination between the two (49dB). Both an effective quantum memory and the sensitive detection of ultrasound benefit from the associated high storage efficiencies and low noise levels. We further show that the technique does not rely on the spatial quality of the beam, as required for the imaging of highly scattering biological samples. Current work is aimed at the detection of photons scattered from an acoustic (ultrasound) wave propagating through a turbid medium, and is progressing towards the imaging of an immersed phantom. In particular, and as we understand and quantify the signal contributions from scattering off the compression wave and from moving particles, we focus on the detection of scattering inclusions gelled into this scattering phantom. Results will be presented.
50
M APPING OF CANCER ON THE P OINCARÉ S PHERE C.M. Macdonald1 , A. Doronin1 , M. Eccles2 , and I. Meglinski1∗ 1 Jack Dodd Centre for Quantum Technologies, Department of Physics,
University of Otago, Dunedin, New Zealand 2 The Centre for Translational Cancer Research, Pathology Department,
Dunedin School of Medicine, University of Otago, New Zealand
Cancer is often a fatal disease. Modern medicine has developed many modes of treating cancer, including surgery, chemotherapy, and radiation therapy. However, the key to effective treatment is early detection. Currently, the ‘gold-standard’ and most widely used methodology for precise cancer diagnosis is histological analysis that utilizes exhaustive microscopy investigation. Despite best laboratory practices the rate of conclusive diagnosis by histological analysis for a range of cancers, including cervical, prostate, bladder, skin and oral cancer, is only 65 − 75% [1]. Here we show that circularly polarized light scattered within the biological tissues is highly sensitive to the presence of cancer cells and their aggressiveness. In particular, we found that the position of Stokes vector of scattered light on the Poincaré sphere displays the successive stages of colorectal cancer. Abnormalities induced in tissues by cancerous changes include an increased nucleus to cytoplasm ratio and an overall increase in the volume density of cells. These two effects impact greatly on the state of polarization of light propagated through the tissue. An increase of nuclear size leads to a higher forward scattering of incident circularly polarized light that keeps its original helicity. Therefore, if position of the Stokes vector at the Poincaré sphere is closer to the state of incident light, then the tissue is either neoplastic potentially malignant or neoplastic malignant. For normal tissues the ellipticity of scattered light is changed towards linear polarization and the Stokes vector becomes closer to the equator of the Poincaré sphere. Our results demonstrate that navigating by the Poincaré sphere provides an opportunity to monitor the condition of biological tissues and grading cancerous stage. In the bigger picture, the proposed approach has the strong potential to revolutionize the current practice of real-time detection of cancer in living tissues before metastasis.
Figure 1: Position of Stokes vector on the Poincaré sphere (center) correlates with successive grades (grade I - green; grade II - yellow; grade III - red) of colorectal cancer confirmed by microscopy studies (left). The changes of elipticity of circularly polarized light predicted by Monte Carlo modeling (right).
References [1] K. Nouri, Skin Cancer, The McGraw-Hill Companies Inc. (2008).
∗ Contact email:
[email protected], Group URL: http://www.biophotonics.ac.nz
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T OWARDS PROPAGATION OF CIRCULARLY POLARIZED LIGHT IN MULTIPLE - SCATTERING MEDIUM I. Meglinski1∗ , C.M. Macdonald1 , A. Doronin1 , and M. Eccles2 1 Jack Dodd Centre for Quantum Technologies, Department of Physics,
University of Otago, Dunedin, New Zealand 2 The Centre for Translational Cancer Research, Pathology Department,
Dunedin School of Medicine, University of Otago, New Zealand
We exploit the directional awareness of circularly polarized light, propagating in the media exhibiting strong multiple scattering, and by tracking Stokes vector of detected light on the Poincaré sphere investigate its applicability for characterization of anisotropy of scattering. A phenomenological model is shown an excellent agreement with the experimental data and with the results obtained by the polarization tracking Monte Carlo modeling. By analogy to the diffusing-wave spectroscopy [1] we call this approach diffusingwave polarimetry, and illustrate its utility in probing cancerous and non-cancerous tissue samples in vitro.
Figure 1: The Stokes vector of light scattered from healthy kidney tissue (lower green circle with the error bars) and cancerous kidney tissue (upper red circle with the error bars) plotted on the Poincaré sphere (a) with corresponding microscope images (b) and tissue sample (c). Squares on the Poincaré sphere (a) show the results of experiment of light scattering by polystyrene microspheres of 3 different diameters dispersed in water; respectively, circles present the results of Monte Carlo modeling.
References [1] D.J. Pine, D.A. Weitz, P.M. Chaikin, and E. Herbolzheimer, Diffusing wave spectroscopy, Phys. Rev. Lett. 60, 1134 (1988).
∗ Contact email:
[email protected], Group URL: http://www.biophotonics.ac.nz
52
P ROPAGATION OF COMPLEX STRUCTURED VECTOR LIGHT BEAMS IN TURBID MEDIUM A. Doronin∗ and I. Meglinski† The Jack Dodd Centre for Quantum Technologies, Department of Physics, University of Otago, New Zealand Polarization is one of light’s most salient features, even more so than its spectral or coherence properties. When light interacts with the matter its state of polarization is changed. The state of polarization of “simple" linearly, elliptically or circularly polarized light has long (since 1800s) been used to characterize material surfaces, thin films and transparent media. The structure of light can be more“complex" in addition to the conventional state of polarizations, the light beams can be radially or azimuthally polarized and carry orbital angular momentum. When complex structured light propagates in a homogeneous transparent medium, both spin and orbital angular momentum are conserved. In the medium with anisotropic scattering the spin or angular momentum are changed that leads to spin-orbit interaction. Such a spin-orbit interaction leads to the mutual influence of the polarization and the trajectory of the light propagation. A Monte Carlo based model [1] is presented and the results of simulation of complex structured light propagation in turbid tissue-like media with a primary goal to proof the concept of using structured light for tissue diagnosis. The propagation of various beams are considered and compared, including linear, elliptically and circularly polarized, as well as radial and azimuthally polarized cylindrical vector beams on the higher order Ponicare sphere (HOPS) [2].
Figure 1: Example of surface distribution of the intensity of right- and left-handed components of circularly polarized light scattered within the highly anisotropic scattering medium (scattering coefficient µs = 30 mm −1 , anisotropy factor g = 0.98), counted for incident laser light of different coherence length l c (from left to right l c = 0, 0.1, 0.3, 1 and 100 mm, respectively.
References [1] A. Doronin and I. Meglinski, Online object oriented Monte Carlo computational tool for the needs of biomedical optics, Biomed. Opt. Express 2, 2461 – 2469 (2011). [2] G. Milione, H.I. Sztul, D.A. Nolan, and R.R. Alfano, Higher-Order Poincaré Sphere, Stokes Parameters, and the Angular Momentum of Light, Phys. Rev. Lett. 107, 053601 (2011).
∗ Contact email: † Contact email:
[email protected] [email protected] Group URL: http://www.biophotonics.ac.nz
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I MAGING OF THE INTERACTION OF LOW FREQUENCY ELECTRIC FIELDS WITH BIOLOGICAL TISSUES BY O PTICAL C OHERENCE T OMOGRAPHY J. Devine, A.F. Pena, A. Doronin, and I. Meglinski∗ The Jack Dodd Centre for Quantum Technologies, Department of Physics, University of Otago, New Zealand Low frequency electric fields propagating in ex vivo biological tissues have been observed by using double correlation optical coherence tomography (OCT) before and during the optical clearing. Optical clearing has been used as a technique to reduce tissue scattering by matching refractive index between tissue components, causing tissue dehydration and thickness reduction. The results present the direct observation of the scope of the electric field influencing biological tissues with OCT. The results show that variation in voltage and frequency of the applied electric field relates exponentially to the magnitude of its influence on biological tissue in vitro. The magnitude of influence is about twice more for fresh tissue samples in comparison to non-fresh ones. In addition, this study has partially been focused on the evaluation of the thickness reduction in tissues during the application of optical clearing agent. The obtained results suggest that OCT can be used for observation and quantitative evaluation of the electro-kinetic changes in biological tissues under different physiological conditions.
References [1] A.F. Pena, J. Devine, A. Doronin, and I. Meglinski, Imaging of the interaction of low frequency electric fields with biological tissues by Optical Coherence Tomography, Opt. Lett., 38, 2629 – 2631 (2013).
∗ Contact email:
[email protected] Group URL: http://www.biophotonics.ac.nz
54
