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We have developed and experimentally studied a coherent population trapping (CPT) state preparation scheme for atomic clock application with co-propagating left and right circularly polarized lasers. With realization of constructive interference and spin-polarized dark state free in CPT state preparation, we have obtained CPT resonance signal 3 times larger than that of the conventional scheme used in atomic clock. Polarization fluctuations and CPT signal sensitivity to laser power behaviors are both improved with the scheme. Our study reveals that it is a promising candidate for both normal-size and chip-scale CPT atomic clocks.
© 2012 Optical Society of America
1. Introduction
Since Alzetta et al. first observed Coherent Population Trapping (CPT) phenomenon through laser-atom interaction using a dye laser [1], CPT resonance has been widely studied, and obtained many applications. In 1982 J. E. Thomas et al. proposed to realize CPT atomic clock using CPT resonance signal as microwave frequency discriminating signal [2], the CPT atomic clock has been widely studied and developed, and the products of the CPT atomic clock have been commercially available [3].
In conventional scheme of CPT atomic clocks [4–7], the CPT state is prepared with either a pure left or a right circularly polarized laser. The scheme suits for small size clock, however, the circularly polarized laser pumps certain atoms into the spin-polarized dark states thus non-contributing to CPT state preparation. In order to overcome the problem, different schemes, lin ⊥ lin [8, 9], lin ∥ lin [10, 11], push-pull optical pumping [12, 13], left and right circular polarizations [14–17] etc, have been proposed and studied. This paper presents our developed Left and Right Circularly Polarized Lasers (LRCPL) CPT state preparation scheme, and the experimental studied results.
2. Experiment
As shown in Fig. 1(b), in conventional scheme either the right circularly polarized dichromatic laser (σ+) or the left circularly polarized (σ−) one interacts with atoms to prepare CPT state in a Λ-type configuration. As both σ+ and σ− lasers interact with atoms, there will be quantum interference. When ΔΦ, a microwave phase difference between two polarized lasers, satisfies ΔΦmax = (2n+1)π (n = 0,±1,±2,...), the prepared CPT resonance reaches its maximum due to constructive interference, while when ΔΦmin = 2nπ, destructive interference makes it reach minimum. In general, the CPT resonance changes as a sinusoidal function of ΔΦ.
Fig. 1 (a) Experimental setup for LRCPL scheme. Mirror1 and mirror2 are mounted on a single-axis platform. ND filter: Neutral Density filter, PBS: Polarizing Beam Splitter, FM: Frequency Modulation, DC servo: Direct Current servo. (b) Working energy levels related to D1 line transition in 87Rb atoms, with which two Λ-type configurations can be realized.
Our LRCPL scheme experimental setup is illustrated as Fig. 1(a). The cylindrical vapor cell (diameter ϕ = 25 mm, and length L = 8 mm) is filled with enriched 87Rb atoms accompanied by a buffer-gas mixture of methane and nitrogen in the pressure radio of 0.5 at 28.2 Torr and temperature stabilized at about 75 °C. A uniform magnetic field of 0.2 μT produced by a solenoid defines the quantization axis and selects out the mF = 0 clock states. Outside the cell and solenoid a permalloy shell shields stray fields from the environment. A Vertical Cavity Surface Emitting Laser (VCSEL) is used to provide 794.7nm 100MHz-bandwidth linearly polarized laser. A microwave at ν = Δhfs/2 ≈ 3.417 GHz is mixed into the DC current supply of the VCSEL, which subsequently outputs a frequency modulated laser beam. The ±1st sidebands of the laser are utilized to prepare CPT state [18].
A convex lens turns VCSEL’s output into a parallel beam of 1mm diameter, and a neutral density filter is arranged for adjusting beam intensity. With the first Polarizing Beam Splitter (PBS1), the horizontal linearly polarized beam is selected out, and it is then transformed into the σ− one by the first λ/4 plate (Plate1). The σ− laser then enters the vapor cell to prepare 87Rb atoms into CPT state. Exiting the cell, the beam is turned into the vertical linearly polarized one by the second λ/4 plate (Plate2). Then it is reflected by the second PBS (PBS2), two mirrors and PBS1 in turn, and overlaps with the horizontal linearly polarized one at PBS1. The vertical linearly polarized component of the overlapped beam is then turned into right circularly polarized one by Plate1 to prepare CPT state one more time, and is converted into the horizontal linearly polarized one by Plate2 after interacting with atoms. The horizontal linearly polarized beam, carrying the information of laser-atom interaction, passes through PBS2 and reaches the photo detector.
By means of polarization reflection, the laser prepares CPT state twice in left and right circularly polarization states separately. In the process, actually the σ± lasers interact with atoms simultaneously, so that there will be quantum interference between the two CPT states. In the experimental setup, the two mirrors in Fig. 1(a) are mounted on a single-axis platform so that the ΔΦ can be adjusted by varying optical path length of the vertical polarized component through fine turning the platform.
The frequency stabilizations are arranged to both laser and microwave frequencies in the experimental setup. In Fig. 1(a), DC current servo loop is for laser frequency stabilization, which stabilizes laser frequency with a Doppler-broadened atom transition signal as frequency discriminating signal [18]. Microwave servo loop is for microwave frequency stabilization, which stabilizes microwave frequency with the CPT resonance signal as microwave frequency discriminating signal. In order to stabilize microwave frequency, the microwave is frequency modulated at 500 Hz with modulation depth of 80 Hz, and the CPT resonance signal is differentiated into a frequency correction signal through phase sensitive detection with a lock-in amplifier. In the experiment, the amplitude and differential signals were both monitored and recorded with a data acquisition system.
3. Result and discussion
We have experimentally studied the dependence of CPT resonance signal on ΔΦ by changing optical path length of the vertical linearly polarized laser through turning platform, and observed the interference effect. Figure 2 shows the experimentally recorded result of CPT contrast verse ΔΦ. The CPT contrast is defined as the amplitude of CPT resonance signal divided by the amplitude of background laser signal at off CPT resonance. It is seen that the periodical dependence of the contrast on ΔΦ is in good agreement with the prediction of quantum interference. The minimum interference of the curve is not zero mainly due to both cell windows are not antireflection coated, and the no ideal flatness of the vapor cell windows. it could also be because of the imperfect parallel laser beam which causes the unequal intensity in the σ+ and σ− light.
Fig. 2 The dependence of contrast on phase difference ΔΦ. The experimental data were recorded by adjusting ΔΦ from −π to π with increment of 2π/11, the increment corresponds to moving the platform by 2 mm. The experimental laser intensity is 15 μW/mm2.
At the same experimental conditions, we have experimentally studied with both schemes, in which conventional scheme experiment was carried out by removing PBS2. Fixing ΔΦ at ΔΦ ≈ ΔΦmax, the typical recorded CPT resonance spectral lines from both schemes are presented in Fig. 3(a). It is seen that the contrast by conventional scheme is 3.1 %, while it is 9.7 % by LRCPL scheme, 3 times larger than that by the former.
Fig. 3 (a) Typical CPT resonances produced by the two schemes. The top panel shows prevail scheme signal. The contrast obtained with LRCPL scheme in the bottom panel is 3 times larger than that with conventional one. The laser intensity is 29μW/mm2 (measured right after ND filter in Fig. 1(a)). (b) Correction slope versus laser intensity for two schemes. In comparison with conventional scheme, correction slope for LRCPL scheme is obviously larger.
In the conventional scheme the amplitude of CPT resonance signal grows with increasing laser intensity at first but then saturates or deceases at higher intensities. Using LRCPL scheme we find that the signal amplitude is proportional to laser intensity over a wider range, in agreement with previous observations. As the line width of the CPT resonance signal increases along with laser intensity, and the frequency correction effect depends on both amplitude and line width of the discriminating signal, the best discriminating signal can’t be determined by discriminating signal amplitude alone, we further investigated behavior of the correction signal.
In a CPT atomic clock, the microwave frequency is locked at ν= Δhfs/2, where the slope of correction signal is at its maximal value. The larger the correction slope is, the better quality of the clock will be. We have investigated the potential of correction slope with both schemes in certain laser intensity range, and the experimental results are presented in Fig. 3(b). It is seen that the correction slope of conventional scheme reaches maximum at 10 μW/mm2, and declines with further increase of laser intensity. However, the correction slope of the LRCPL scheme increases monotonously along with laser intensity in the whole experimental range, though saturated symposium appears starting from 20 μW/mm2.
As the atoms in spin-polarized dark state increase along with laser intensity in conventional scheme, there won’t be a problem in LRCPL scheme benefited from eliminating those dark states by LRCPL pumping, that shall be the reason that the correction slopes change in opposite directions after certain laser intensity.
Different from counter-propagating LRCPL scheme [14, 15] in which constructive and destructive interferences happen alternatively along laser propagation due to spatial interference, co-propagating lasers in our scheme keeps the same interference, and the best constructive interference can be realized by setting ΔΦ at ΔΦmax. Using two VCSELs is another approach of co-propagating LRCPL [16], while it is difficult to control the phase difference ΔΦ between two independent VCSEL outputs, and the fluctuation of ΔΦ will affect the quality of atomic clock output frequency.
The polarization fluctuations of VCSEL are a problem of CPT atomic clocks [19], by eliminating of unwanted polarized components with PBS1, better performance of output frequency can be expected with LRCPL scheme.
In order to achieve better frequency stability, the largest correction slope, corresponding to a laser intensity of 10 μW/mm2 in the curve of Fig. 3(b), is usually chosen for stabilizing microwave frequency in conventional scheme. From Fig. 3(b) it is seen the slope around its maximum changes sharply with laser intensity, thus the behavior of atomic clock is sensitive to laser intensity. However, with LRCPL scheme, it allows to choose the slope in the slow changing range, corresponding to 25∼58 μW/mm2 in Fig. 3(b). Though the power of semiconductor laser’s output generally decays, the less sensitive dependence on laser density will result in the better long-term performance and the longer lifetime of CPT atomic clocks.
Chip-scale atomic clock has been realized with the conventional scheme [6, 7]. With LRCPL scheme, the polarization reflection will increase the size of optical setup. However, to satisfy ΔΦ = ΔΦmax, the minimum optical path length of the polarization reflection is 22 mm for 87Rb, and only 16 mm for 133Cs, the increase to optical setup is indeed very limited. Through Micro-Electro-Mechanical Systems (MEMS), the LRCPL scheme physics package still can be micro-fabricated into chip scale.
In order to provide enough interacting atoms, the vapor cell is heated to relative high temperature in chip-scale atomic clock applying conventional scheme [5–7], while with LRCPL scheme the same amount of interacting atoms will be obtained at considerable lower temperature. Therefore, even lower power consumption chip-scale atomic clocks can be achieved with this scheme.
4. Conclusion
We have developed and experimentally studied the co-propagating left and right circularly polarized laser (LRCPL) CPT state preparation scheme. The spin-polarized dark state atoms are eliminated by left and right circularly polarized laser pumping, and constructive interference is realized by controlling the phase difference between two co-propagating circularly polarized laser components. The LRCPL scheme has been experimentally compared with conventional scheme applied in CPT atomic clocks, and 3 times stronger CPT resonance signal has been obtained with LRCPL scheme. Moreover, the polarization fluctuations problem is avoided and laser intensity sensitivity behavior is improved by LRCPL scheme. All of those will improve performance of CPT atomic clocks. LRCPL scheme is also suitable for the chip-scale atomic clock. In summary, our study reveals that the better performance atomic clocks based on CPT in normal size and chip scale can be achieved with LRCPL scheme.
Acknowledgments
One of the authors (Y. Z.) is grateful to Peter Yun for his help in the experiment and Guobin Liu for his helpful discussion. This work is supported by the National Natural Science Foundation of China (NSFC) under grant No. 10927403 and the Program of the Chinese Academy of Sciences under Grant No. KGCX2-YW-143.
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