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Mar 1, 2013 - absorption center obtained by modulation transfer spectroscopy in an iodine vapor cell. ... frequency is measured by an optical frequency comb.
Precise frequency measurements of iodine hyperfine transitions at 671 nm Yao-Chin Huang,1 Hsuan-Chen Chen,2 Shih-En Chen,1 Jow-Tsong Shy,1,2 and Li-Bang Wang1,3,* 1

Department of Physics and Frontier Research Center on Fundamental and Applied Sciences of Matters, National Tsing Hua University, Hsinchu 30013, Taiwan 2

Institute of Photonics Technologies, National Tsing Hua University, Hsinchu 30013, Taiwan 3

Golden-Jade Fellow, Kenda Foundation, Changhua 51064, Taiwan *Corresponding author: [email protected]

Received 20 December 2012; revised 28 January 2013; accepted 31 January 2013; posted 31 January 2013 (Doc. ID 182179); published 27 February 2013

We report absolute frequency measurements on the a1 , a10 , and a15 hyperfine components of the R(78) 4–6 line of 127 I2 . An external-cavity diode laser system at 671 nm is frequency-stabilized to the saturated absorption center obtained by modulation transfer spectroscopy in an iodine vapor cell. Its absolute frequency is measured by an optical frequency comb. The effect of pressure shift is investigated to obtain the absolute transition frequency at zero pressure. Our determination of the line centers reaches a precision of better than 40 kHz and will provide useful input for theoretical calculations. This frequency-stabilized laser can be used as a reference laser for the spectroscopy of lithium D lines. © 2013 Optical Society of America OCIS codes: 300.6320, 300.6390, 300.6460.

1. Introduction

Optical frequency standards are of great scientific importance not only for metrology applications [1,2] but also for high-resolution spectroscopy [3,4] and fundamental physics [5,6]. Diatomic iodine molecule provides more than 100,000 rovibrational lines in the visible and nearinfrared (NIR) regions. Iodine has a large nuclear quadrupole moment, which leads to hyperfine splittings up to 1 GHz for each rovibrational line and allows most of its hyperfine components to be easily resolved by Doppler-free saturated absorption spectroscopy. In addition, due to the long lifetime of the upper states, these hyperfine transitions have narrow natural linewidths [7,8]. These properties make iodine-stabilized laser an ideal easy-to-use frequency reference in the visible and NIR range. For example, 1559-128X/13/071448-05$15.00/0 © 2013 Optical Society of America 1448

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iodine transition lines around 730 nm are used as references in spectroscopy of muonium and hydrogen isotopes [9], and transitions around 548 nm provide suitable references for lithium ion spectroscopy [10]. Moreover, several iodine-stabilized laser systems are recommended by the Comité International des Poids et Mesures as the wavelength standards to define the length of a meter [11,12]. The frequencies of iodine transitions can be looked up in atlases by Gerstenkorn et al. [13–18] or by Katô et al. [19]. In addition, the iodine frequencies can be predicted by the IodineSpec program [20] based on model descriptions of the hyperfine and rovibronic structures [21–23]. The iodine transition frequencies can be predicted to be better than 2 MHz in the interval from 19; 000 cm−1 (526 nm) to 15; 000 cm−1 (667 nm) by the IodineSpec program. On the contrary, the current program has a relatively low precision in the region between 667 and 755 nm. The precision is on the order of 30 MHz due to lack of high-precision experimental data in this region.

In this paper we report our measurement on 127 I2 hyperfine transitions of R(78) 4–6 line at 671 nm. Our measurements are important for improving theoretical prediction of the iodine spectrum. Furthermore, this rovibrational line is very close to the 2S–2P transitions (D lines) of atomic lithium. Therefore, it can be used as a frequency reference for lithium spectroscopy. Lithium with only three electrons is a few-body quantum system whose electronic structures can be predicted precisely by QED atomic calculations. The important physical quantities that can be determined experimentally include relative nuclear charge radii of lithium isotopes, the QED corrections (Lamb shift) of the ionization energies of different states, and the fine and hyperfine structures, which can be compared with theoretical calculations to a very high precision [24]. In this work, we perform Doppler-free saturation spectroscopy in an iodine vapor cell using modulation transfer spectroscopy [25]. The saturated absorption signal is used to lock the laser frequency, and the absolute frequency of the transition is measured by an optical frequency comb. The effect of pressure shift is investigated to obtain the absolute transition frequency at zero pressure. To our knowledge, there are no precision measurements around this wavelength, and our measurements provide useful input for the theoretical predictions. 2. Experiment

The experimental setup is shown in Fig. 1. We use a home-made grating feedback external-cavity diode laser (ECDL) at 671 nm as the light source. The solitary laser diode has a wavelength of 664 nm at room temperature and can be tuned to 671 nm by increasing its temperature to approximately 52°C. The frequency of the ECDL is stabilized to a Fabry– Perot cavity to reduce its linewidth from 2 MHz to approximately 300 kHz by the Pound–Drever–Hall method [26,27]. The saturation spectroscopy of the hyperfine components of the R(78) 4–6 line at 671 nm is observed by modulation transfer spectroscopy.

Fig. 1. (Color online) Experimental setup. OI, optical isolator; λ∕2, half-wave plate; PBS, polarizing beam splitter; BS, beam splitter; F–P cavity, Fabry–Perot cavity; PD, photodiode; PI, electronic servo loop; EOM, electro-optic modulator; AOM, acousto-optic modulator.

A polarizing beam splitter (PBS) and a half-wave plate (λ∕2) are used to adequately distribute the power of the pump beam and the probe beam. The pump beam is phase-modulated by an electro-optic modulator (EOM), which produces a modulation depth of 0.8 rad at 4.5 MHz. The pump beam is shifted up in frequency by 85 MHz and is amplitude modulated at 10.47 kHz by an acousto-optic modulator (AOM). The pump beam and probe beam are overlapped in the iodine cell. The power of the pump and probe beams incident in the iodine cell are 1.54 mW and 400 μW, respectively. Both beams have a beam radius of approximately 1 mm inside the iodine cell. After the iodine cell, the probe beam is detected by a fast photodiode (New Focus 2051), and the signal is demodulated with a balanced mixer whose local oscillator is referenced to the same modulation source of the EOM. To obtain a background-free saturation signal, the mixer output is processed further by a lock-in amplifier (Stanford Research System SR830) with the 10.47 kHz chopping frequency of the AOM as the reference. Typical time constant of the lock-in amplifier is 30 ms. The output from the lock-in amplifier is then used as an error signal and fed back into a proportional and integral (PI) servo loop to lock the Fabry–Perot cavity to the molecular transition. A 58 cm long iodine vapor cell with plane windows fused to the cylindrical body at a slightly tilted angle to avoid interference effects is used and has a cold finger for controlling the iodine vapor pressure inside the cell. The cold finger temperature is typically stabilized at 20°C and is allowed to change to other temperatures to study the effect of pressure shift. The iodine vapor pressure is calculated by the following empirical formula [28]: logP 

−3512.830 − 2.013 · logT  18.37971; (1) T

where P is the iodine vapor pressure in pascals and T is the cold finger temperature in degrees Kelvin. The cell body is wrapped with a tape heater, and the temperature of the cell body is maintained at 220°C to increase thermal population in the lower level of the rovibrational transitions that we are interested in. In order to increase the available laser power for frequency measurement, we set up a second diode laser by the method of optical injection lock as shown in Fig. 2. We obtain the best efficiency by creating an optical system based on a Faraday rotator, a halfwave plate, and a PBS. The power of the slave laser is about 10.4 mW. A partial beam from the slave laser is coupled into a polarization-maintaining single-mode fiber to transfer the light to an optical frequency comb for frequency measurements. The beat note between the injection-locked laser and the comb laser is detected by an avalanche photodiode (Menlo Systems APD 210), and the beat frequency is recorded by a frequency counter (HP 53132A). 1 March 2013 / Vol. 52, No. 7 / APPLIED OPTICS

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Fig. 2. (Color online) Injection-locked laser system for measuring the absolute frequency. λ∕2, half-wave plate; PBS, polarizing beam splitter; BS, beam splitter; F–P cavity, Fabry–Perot cavity; and PD, photodiode. The F–P cavity is used to monitor the mode structure of the slave laser and ensure it is injection-locked to the master laser.

When the ECDL is locked to the iodine hyperfine transition, its frequency is measured by an optical frequency comb, which is based on a femtosecond Ti:sapphire laser with a repetition rate f rep of approximately 1 GHz and an offset frequency f offset set at 817.024 MHz. The accuracy of the optical comb is achieved by referencing it to an Rb atomic clock calibrated by GPS signal. The accuracy of the frequency comb is better than 1 × 10−12 for a 1000 s measurement time [29]. The iodine transition frequency f iodine can then be derived by the following relation: f iodine 

f pump  f probe 2

 Nf rep  f offset  f beat 

f AOM ; 2

(2)

where f beat is the beat frequency between the 671 nm laser and the comb laser, and f AOM is 85 MHz in our case. Due to the frequency shift in the pump beam by the AOM, the laser is locked at a frequency that is 42.5 MHz lower than the actual transition frequency of the hyperfine transition. N is a large integer to be determined. In order to accurately determine the value of N, we measure the frequency difference between this iodine spectroscopy laser and the D1 line of atomic lithium. This is achieved by having a separate laser system that is tuned to the lithium D1 transition observed in a collimated atomic beam. A fast photodiode (Newport 1434-50) and a highfrequency counter (Agilent A53150) are used to precisely measure the beat frequency (∼6.2 GHz) between the two lasers. We also scan the frequency of the iodine spectroscopy laser over several gigahertz to identify all the transitions according to the patterns predicted by the IodineSpec program. Because the absolute frequency of the lithium D1 line and the predicted frequencies from the IodineSpec program both have uncertainties much smaller than the repetition rate of the frequency comb, we can confidently determine the value of N.

Fig. 3. (Color online) Hyperfine structure pattern of the R(78) 4–6 line. The S/N of the a1 component is about 70.

The signal-to-noise ratio (S/N) of these three components is about 70 at a time constant of 30 ms. To measure the transition frequency, a partial beam of the slave laser is coupled into a single-mode fiber and sent to an optical frequency comb. To investigate the frequency stability of our laser system, we record the beat frequency using different gate times for the frequency counter. The calculated Allan deviation is shown in Fig. 4. The laser frequency has a fractional Allan deviation of 5 × 10−11 at an integration time of 3 s. When the laser is locked to the selected iodine hyperfine transition, we measure the beat frequency between the spectroscopy laser and the frequency comb. The gate time of the counter is set to be 100 ms. The results of the absolute frequency measurements are shown in Fig. 5. Each data point consists of 600 measurements at a vapor pressure of 26.9 Pa. The mean value and the standard error of the 600 measurements are plotted as one data point in the figure. During the measurements, the laser is unlocked and relocked again to ensure good experimental conditions. In order to accurately determine the transition frequency at zero pressure, the pressure-dependent shift must be carefully studied. We vary the cold

3. Results and Discussions

We perform measurements on the a1 , a10 , and a15 hyperfine components of the R(78) 4–6 line of 127 I2. Figure 3 shows the hyperfine structures when the laser frequency is scanned across the R(78) 4–6 line. 1450

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Fig. 4. (Color online) Fractional Allan deviation of the laser frequency. The system reaches its best stability at an averaging time of 3 s.

Fig. 6. (Color online) Pressure shift of the transition frequency for the a1 component. The negative slope shows that the interaction due to collision is attractive.

found some possible systematic effects that may limit the accuracy of the measurement. A small DC drift is present in the iodine signal. Several attempts have been tried to reduce this effect, such as careful shielding of RF sources and cables, checking ground-loop problems, and finally adding an offset voltage to the lock-in signal to null this effect. A pulling effect from the PI feedback loop is also observed. Depending on the settings of the PI gain of the feedback loop, the error signal is not completely kept at zero position. This causes systematic effects, which are investigated and listed in Table 1. Table 2 shows our final results of the three measured transition frequencies. Our results of the absolute frequencies differ from the predicted values by approximately 3 MHz, while the hyperfine splittings between the lines have much better agreement with the theoretical predictions. Fig. 5. (Color online) Measurements at the iodine vapor pressure of 26.9 Pa. Each data point represents the mean value of 600 measurements. The standard deviation of the measurements divided by the square root of 600 is assigned as the error bar of each point. The results for the three transitions a1 , a10 , and a15 are 446,806,191,649(23), 446,806,778,709(33), and 446,807,072,397 (22) kHz, respectively.

finger temperature to change the vapor pressure according to Eq. (1). In order to see the effect of pressure shift, we measure the beat frequency between the iodine spectroscopy laser and another laser tuned to the D1 line of lithium. Typical data are shown in Fig. 6. The result shows great linearity in the pressure range between 25 and 65 Pa. We do not observe differences in the slopes among the three components (a1 , a10 , and a15 ). A linear fit of the combined data points of a1 component shows a pressure shift of −8.95  0.39 kHz∕Pa. We then use this pressure shift coefficient to correct all the measured results to obtain the zero-pressure transition frequencies. The sources of measurement uncertainties are summarized in Table 1. Besides the statistical errors and the uncertainty from the pressure shift, we have

Table 1.

Sources of Uncertainties (kHz)

Source

Correction

Uncertainty

241

11 11

Pressure shift System stabilitya

a This effect is from the DC drift of the error signal and the pulling effect of the PI feedback circuit.

Table 2. Results and Comparison to the Calculated Values (kHz); Uncertainty of the Calculated Value is Approximately 30 MHz as Reported in the IodineSpec 5 Program

Measureda 446,806,191,890(25) a1 446,806,778,950(35) a10 a15 446,807,072,638(24) 880,748(35) a15 − a1 a15 − a10 293,688(42) 587,060(43) a10 − a1

Calculated

Measured − Calculated

446,806,194,569 446,806,781,526 446,807,075,266 880,697 293,740 586,957

−2; 679 −2; 576 −2; 628 51(35) −5242 103(43)

a The uncertainty is the combined error of the value in Fig. 5 and the uncertainties listed in Table 1.

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4. Conclusion

In summary, we have measured the absolute transition frequencies of the a1 , a10 , and a15 hyperfine components of the R(78) 4–6 line of 127 I2. Our measurements reach a precision of approximately 30 kHz and are important for theoretical calculations around this wavelength. This laser system is useful for laser cooling and trapping of lithium atoms. This laser system can be used as a reference laser for precision spectroscopy of the D lines of lithium after improving its stability and reproducibility. We gratefully acknowledge the financial support from National Science Council of Taiwan under Contract No. NSC 99-2112-M-007-010-MY3. We also thank Dr. H. Knöckel for fruitful discussions and providing the IodineSpec5 program. References 1. J.-M. Chartier, S. Fredin-Picard, and L. Robertsson, “Frequency-stabilized 543 nm He–Ne laser systems: a new candidate for the realization of the metre?,” Opt. Commun. 74, 87–92 (1989). 2. T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002). 3. H. C. Chui, M. S. Ko, Y.-W. Liu, J.-T. Shy, J. L. Peng, and H. Ahn, “Absolute frequency measurement of rubidium 5S–7S two-photon transitions with a femtosecond laser comb,” Opt. Lett. 30, 842–844 (2005). 4. S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb,” Nature 445, 627–630 (2007). 5. P. Cancio Pastor, G. Giusfredi, P. De Natale, G. Hagel, C. de Mauro, and M. Inguscio, “Absolute frequency measurements of the 23 S1 → 23 P0;1;2 atomic helium transitions around 1083 nm,” Phys. Rev. Lett. 92, 023001 (2004). 6. A. Huber, T. Udem, B. Gross, J. Reichert, M. Kourogi, K. Pachucki, M. Weitz, and T. W. Hänsch, “Hydrogen-deuterium 1S–2S isotope shift and the structure of the deuteron,” Phys. Rev. Lett. 80, 468–471 (1998). 7. C. J. Bordé, G. Camy, and B. Decomps, “Measurement of the recoil shift of saturation resonances of 127 I2 at 5145 Å: a test of accuracy for high-resolution saturation spectroscopy,” Phys. Rev. A 20, 254–268 (1979). 8. W.-Y. Cheng, L. Chen, T. H. Yoon, J. L. Hall, and J. Ye, “SubDoppler molecular-iodine transitions near the dissociation limit (523–498 nm),” Opt. Lett. 27, 571–573 (2002). 9. S. L. Cornish, Y.-W. Liu, I. C. Lane, P. E. G. Baird, G. P. Barwood, P. Taylor, and W. R. C. Rowley, “Interferometric measurements of 127 I2 reference frequencies for 1S–2S spectroscopy in muonium, hydrogen, and deuterium,” J. Opt. Soc. Am. B 17, 6–10 (2000). 10. Y.-C. Hsiao, C.-Y. Kao, H.-C. Chen, S.-E. Chen, J.-L. Peng, and L.-B. Wang, “Absolute frequency measurement of the molecular iodine hyperfine transitions at 548 nm,” J. Opt. Soc. Am. B 30, 328–332 (2013). 11. T. J. Quinn, “Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards (2001),” Metrologia 40, 103–133 (2003).

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