Jan 1, 1998 - 2S1/2 (7 # m # 12 for Rb; 5 # m # 7 for K) resonance transitions when a probe pulse ..... â Present address, Lockheed-Martin, 111 Lockheed.
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OPTICS LETTERS / Vol. 23, No. 1 / January 1, 1998
Interaction of atomic wave packets with four-wave mixing: detection of rubidium and potassium wave packets by coherent ultraviolet emission H. C. Tran,* P. C. John,† J. Gao, and J. G. Eden Everitt Laboratory, Department of Electrical and Computer Engineering, University of Illinois, Urbana, Illinois 61801 Received June 9, 1997 The observation of an atomic wave packet by use of a coherent, nonlinear-optical process is reported. Wave packets formed in K or Rb vapor by two-photon excitation of ns and sn 2 2dd states (n 8 for K; n 11, 12 for Rb) with red s,620-nmd, 80 – 100-fs pulses were detected by four-wave mixing in pump-probe experiments. The temporal behavior of the wave packet is observed by monitoring the coherent UV radiation generated near the alkali mp 2P ! 2 S1/2 (7 # m # 12 for Rb; 5 # m # 7 for K) resonance transitions when a probe pulse is scattered by the wave packet established by the earlier (identical) pump pulse. The spatial and spectral characteristics of the UV emission are well described by axially phase-matched four-wave mixing, and all the prominent frequency components of the wave packets are associated with energy differences between pairs of excited states for which Dl 0 or Dl 2. These results demonstrate that the wave packet modulates x s3d of the medium, thus rendering the wave packet detectable. 1998 Optical Society of America OCIS codes: 190.0190, 190.4380, 030.1670.
Wave packets result from the coherent superposition of two or more eigenstates and have been generated with pulsed, wide-bandwidth optical sources in both atoms and small molecules.1 – 4 In either case the temporal behavior of the wave packet is determined by the electronic, vibrational, or rotational states from which it is composed. As noted by Jones et al.,5 previous studies of wave packets in atoms and diatomic molecules in the gas phase generally relied on detecting the wave packet by photoionization—inferring the temporal history of the wave packet from the photoelectron current produced in pump– probe experiments —or ramped f ield ionization. Such experiments involve atomic or molecular beams and photoelectron detection or time-off light mass spectrometry capability. Although the observation of wave packets by f luorescence has been demonstrated, Alber et al.2 suggested in 1986 the detection of atomic wave packets by a coherent optical (Raman) process that, to our knowledge, had not been realized previously. Pump –probe experiments are reported here in which an atomic wave packet was detected optically by observation of the spatially and temporally coherent emission produced by parametric four-wave mixing. Wave packets are formed by two-photon excitation of ns and sn 2 2dd states of Rb and K (n 8 for K; n 10, 11 for Rb) with a red ,100-fs pulse and subsequently detected by means of monitoring the coherent UV or IR radiation produced when a second, identical laser pulse interacts with the wave packet. Spectral analysis of the temporal history of the UV emission demonstrates that the wave packet is modulated at terahertz frequencies associated with energy differences among the ns, sn 2 1dp, and sn 2 2dd states of the atom. These results represent what is believed to be the f irst demonstration of the observation of a wave packet by a coherent optical process and a nonlinear-optical technique in particular. The pump– probe experimental apparatus will be described in detail elsewhere. Brief ly, pulses produced 0146-9592/98/010070-03$10.00/0
by a colliding-pulse mode-locked oscillator and amplified (at 30 Hz) by four longitudinally pumped dye stages have energies of ,100 mJ, pulse widths of 80– 100 fs ssech2 d, and a peak wavelength of ,620 nm. After a beam splitter divides each pulse into two pulses of equal energy s,40 mJd, one pulse is delayed in time with respect to the other by a retroref lector mounted upon a computer-controlled translation stage. Both pulses are spatially filtered by diamond pinholes and focused with a 20-cm focal-length lens into a heat pipe containing Rb or K vapor at number densities of typically 101621017 cm23 . The peak intensity of the pump and probe pulses is ,1010 W cm22 , and the radiation is linearly polarized. The heat pipe includes a proportional counter (cylindrical diode) for measuring the relative photoelectron density produced by resonantly enhanced multiphoton ionization of the atom. All the data presented here were obtained for pumpprobe delay times sDtd , 8 ps. Figure 1 illustrates the 2S and 2D states of Rb that are accessible from ground by two-photon excitation with the optical pulses available for these experiments; note that two pairs of ns 2S 2sn 2 2dd 2D states lie within the bandwidth of the pump-pulse spectrum (11s29d and 12s210d). Irradiation of K or Rb vapor with a pair of femtosecond red pulses produces intense, spatially coherent UV emission in the vicinity of the K smp 2P ! 4s 2S, 5 # m # 7d and Rb smp 2P ! 5s, 7 # m # 12d resonance transitions at 321, 344, and 404 nm for K and 308, 311, 316, 323, 335, and 359 nm for Rb. As shown in Fig. 2 for Rb, the experimental spectrum consists of features that have spectral widths of ,0.1 nm (FWHM) located near the positions for the 7p211p ! 5s transitions.6 Note, however, that emission is observed only in the proximity of the 2P3/2 ! ground resonance line; with the exception of the 7p transitions, emission associated with the J 1y2 f ine structure component of the 2PJ ! ground transition is generally weak or undetectable. Measurements with a cooled InSb detector and two GaAs or Si wafers to 1998 Optical Society of America
January 1, 1998 / Vol. 23, No. 1 / OPTICS LETTERS
Fig. 1. Partial energy-level diagram for Rb, illustrating two-photon excitation of ns 2S and sn 2 2dd 2D states sn 11, 12d and subsequent emission in the IR and the UV. The hatched region indicates the 2S and 2 D states of Rb that are accessible with two pump photons, given the bandwidth of the available laser pulses.
Fig. 2. Emission spectrum in the 300– 360-nm region produced by two-photon excitation of Rb vapor with red slmax , 620 nmd, sub-100-fs pulses. Inset, expanded (and higher-resolution) view of the emission in the vicinity of the 11p 2PJ ! 5s transitions.
block visible radiation show that spatially coherent IR emission that corresponds to 2S, 2D ! 2P transitions is also produced. The upper limit on the duration of the UV emission was determined with a Si photodiode and a 1-GHz bandwidth oscilloscope to be 300 ps. All the spectral and spatial characteristics of the UV radiation are well described by axially phase-matched four-wave mixing.7,8 Calculations for Rb verify that satisfaction of the photon energy and momentum conservation relations9,10 occurs for the m 8211 terms ,0.123 cm21 to the blue side of only the mp 2PJ3/2 ! ground transition. Phase matching does occur close to the 9p 2P1/2 ! 5s 2S1/2 resonance but within the pressure and Doppler-broadened linewidth for the transi-
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tion. Also, numerical simulations demonstrate (and beam-intensity prof ile measurements confirm) that off-axis phase matching does not occur for angles of *1± . 17 mrad. Measurements of the UV and red beam cross-sectional intensity prof iles with a CCD camera reveal an elongation of the UV beam in the direction of the pump polarization. The pump and probe beams have divergences of 12 6 1 mrad, and their intensity prof iles are azimuthally symmetric. In contrast, the UV beam is elliptical, with a divergence along the pump polarization of 9 6 2 mrad s,0.5±d, which is a factor of 2.7 larger than that in the orthogonal direction. Peak intensity occurs on axis, which reinforces the conclusion that the four-wave-mixing process in Rb is axially phase matched. Measurements made for Rb of the dependence of the relative photoelectron number density and the UV intensity on the peak pump-pulse intensity sIp d reveal that, at the lowest red pulse intensities studied s108 , Ip , ,2 3 109 W cm22 d, the photoelectron production rate varies linearly with Ip . Since Rb is photoionized by a resonantly enhanced three-photon process (2 1 1 resonantly enhanced multiphoton ionization), a quadratic dependence of the photoelectron density on Ip is expected at low intensities, but for Ip * 108 W cm22 the two-photon process has saturated, and photoionization is limited by the final step. Production of UV emission, on the other hand, exhibits a sharp threshold at 7 2 8 3 109 W cm22 and, for 7 & Ip & 17 GW cm22 , varies as Ip 2 , which is also in accord with expectations. That is, the intensity of the UV (signal) radiation is given by I svs d ~ jP˜ s3d svs dj2 ~ jx s3d svs dEp 2Ei ds2vp 2 vi 2 vs d Å (1) 3 ds22bp 1 bi 1 bs d 2 ~ Ip 2 , where x s3d is the third-order nonlinear susceptibility and Ep and Ei are the pump and idler electric-field amplitudes, respectively. Varying the time delay sDtd between the pump and probe pulses while monitoring the intensity of coherent Rb (or K) emission serves as a convenient monitor of the temporal behavior of the wave packet. As illustrated by Fig. 3, a periodic signal having a nominal frequency of 2.8 THz (,350-fs periodicity) is observed for Rb, which is approximately what one would expect if the sinusoidal variation in the signal ref lected quantum beating between the 11s and 9d states (energy difference, 95 cm21 ). Also, the oscillatory response persists for Dt beyond tens of picoseconds, and yet the signal diminishes only slightly s,20%d in amplitude. It is well to point out that the amplitude f luctuations in Fig. 3 do not arise primarily from noise but rather are due to high-frequency contributions to the signal (discussed below). In these pump–probe experiments the medium polarization is modif ied by the term f1 1 expsivp Dtdg2 , and I svs d is, therefore, expressed as IUV svs d ~ h1 1 cosf2svp2 2 vp1 dDtgj 3 jx s3d svs dEp 2Ei j2 1 . . . ,
(2)
where hsv ¯ p2 2 vp1 d represents the energy difference between any two atomic states driven coherently by the
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OPTICS LETTERS / Vol. 23, No. 1 / January 1, 1998
Fig. 3. (a) Intensity of the coherent Rb emission near the 11p 2P ! 5s 2S1/2 (311-nm) line as a function of the time delay sDtd between the pump and probe laser pulses. The periodicity of the oscillations is ,350 fs and, although it is not shown here, the signal persists for tens of picoseconds. Inset, frequency spectrum (fast Fourier transform) associated with the emission-time delay scan. All the observed peaks are associated with differences in energy between states of the Rb atom; the feature at 459.4 6 1.6 cm21 can be assigned to either the 11p 2PJ 210p 2PJ sJ 1y2d or the 9d 2DJ 210s 2S1/2 sJ 3y2, 5y2d defects. ( b) Similar data obtained when coherent emission at ,316 nm (associated with the 10p ! 5s transition of Rb) was monitored.
pump f ield. Consequently the sinusoidal variation of the intensity with Dt unambiguously demonstrates the existence of an atomic wave packet. The inset in Fig. 3(a) shows the frequency spectrum (fast Fourier transform) of the 11p ! 5s time-domain scan (intensity versus Dt). Several frequency modes are reproducibly observed, all of which correlate with known energy differences between excited states of the atom. The feature at 94.1 6 1.6 cm21 , for example, is present in all the spectra obtained to date and is associated with the 11s 2S1/229d 2DJ energy defect in Rb, which is 94.67 cm21 for J 5y2 and 95.37 cm21 for J 3y2.8 Similarly, the peak at 66.8 6 0.8 cm21 corresponds well with the differences in energy between the 12s state and the fine structure levels of the 10d state s66.88 and 67.36 cm21 d. Figure 3(b) presents similar data acquired when the dependence on Dt of the relative UV emission intensity at 315.8 nm s10p ! 5sd was monitored. The general characteristics of the data shown in Fig. 3 can be described in terms of quantum beating between pairs of ns 2S and sn 2 2dd 2D states. However, the consistent presence of other features also reveals the involvement of the 2 P states. An interesting picture emerges in that all the prominent
modes in the spectra obtained to date are attributable to Dl 0, 2 pairs of states. Finally, similar results were obtained in potassium vapor but, because the limited bandwidth of the pump and the probe pulses is insuff icient to encompass the 7p state, only quantum beats between the 8s and 6d states were observed. On the basis of the experimental evidence, one concludes that (1) atomic wave packets that comprise low principal quantum number s, p, and d states are produced in Rb and K by two-photon transitions, (2) the spectral and spatial characteristics of the UV radiation are described by parametric four-wave mixing, and (3) the temporal behavior of the wave packet is ref lected in the variation of the relative UV intensity with Dt. The coupling of the wave packet with the four-wavemixing process occurs through modulation of the thirdorder nonlinear polarization of the medium by the wave packet. These results demonstrate the detection of a wave packet by a nonlinear-optical process and suggest that other x s3d processes will serve equally well in monitoring wave packet behavior. Conversely, it appears that wave packets can be exploited to study x s3d processes on the subpicosecond time scale. Therefore the approach reported here offers a new spectroscopic tool but also provides a window into the inf luence of wave packets on the nonlinear properties of a medium. Discussions with T. A. DeTemple and J. T. Verdeyen and the technical assistance of K. Voyles, A. Oldenburg, and Z. Figen are greatly appreciated. This study was supported by the U.S. Air Force Office of Scientific Research. *Present address, Northrop-Grumman, 600 Hicks Road, Rolling Meadows, Illinois 60008. †Present address, Lockheed-Martin, 111 Lockheed Way, Org. H1-B5, Sunnyvale, California 94088-3504. References 1. J. Parker and C. R. Stroud, Jr., Phys. Rev. Lett. 56, 716 (1986). 2. G. Alber, H. Ritsch, and P. Zoller, Phys. Rev. A 34, 1058 (1986). 3. M. Dantus, M. J. Rosker, and A. H. Zewail, J. Chem. Phys. 88, 6672 (1988). ¨ 4. T. Baumert, B. Buhler, R. Thalweiser, and G. Gerber, Phys. Rev. Lett. 64, 733 (1990); G. Rodriguez and J. G. Eden, Chem. Phys. Lett. 205, 371 (1993). 5. R. R. Jones, C. S. Raman, D. W. Schumacher, and P. H. Bucksbaum, Phys. Rev. Lett. 71, 2575 (1993). 6. C. E. Moore, Atomic Energy Levels (U.S. Government Printing Off ice, Washington, D.C., 1971), Vol. I. 7. D. M. Bloom, J. T. Yardley, J. F. Young, and S. E. Harris, Appl. Phys. Lett. 24, 427 (1974). 8. M. A. Moore, W. R. Garrett, and M. G. Payne, Phys. Rev. A 39, 3692 (1989). 9. The energy and momentum constraints are vs 2vp 2 vi and ns vs kˆ s 2np vp kˆ p 2 ni vi kˆ i , respectively, where s, p, and i denote parameters associated with the signal, pump, and idler, respectively, v is the frequency, kˆ represents a wave vector, and n is the index of refraction. 10. M.-H. Lu and Y.-M. Liu, Appl. Phys. B 54, 288 (1992).
