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Abstract
We studied experimentally a left-right circularly polarized light feedback scheme. A vertical-cavity surface-emitting laser (VCSEL) and partial retroreflector formed an extended cavity, allowing ∼4% of the laser to enter the VCSEL. Such design helped to improve the microwave modulation efficiency. Comparing to the conventional circularly polarized light scheme, the resonance amplitude of this method was doubled while the noise was reduced five times because of the usage of the left-right circularly polarized light, which continuously interacted with atoms. The short-term instability was improved by one order of magnitude. This scheme can be applied to small or chip-scale atomic clocks.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Coherent Population Trapping (CPT) is a quantum interference phenomenon. The recent interest of small size and low power clocks resulted in increased CPT implementation into the optical fields modulated at a microwave frequency, which eliminates the requirement for microwave cavities [1–5]. CPT also has broad applicability in the global positioning system, network communication, underwater navigation, and other fields.
Current passive CPT atomic clocks generally use a vertical-cavity surface-emitting laser (VCSEL) as a light source. The crystal oscillator, as the local oscillator, provides microwaves to modulate the frequency of the current injected into the VCSEL to obtain a multichromatic and linearly polarized laser. The CPT state is prepared in a circularly polarized state using ± 1st sidebands of the laser [6]. However, the circularly polarized light fields optically pump a significant fraction of the atoms into the incoherent dark states (described as |F, mf=±F >), which are not coupled to any of the excited states by the incident light fields. These atoms do not contribute to the CPT resonance, which results in reduced detected signal strength.
Several schemes have been proposed and implemented that improve the signal strength, including lin//lin [7–10], lin⊥lin [2,11,12], push-pull optical pumping [13,14], σ+-σ- [15–19], and elliptically polarized beam [20]. The volume of lin//lin CPT is basically the same as the conventional circularly polarized light scheme, however, it requires that the excited state of hyperfine energy level must be resolvable.
Push-Pull is a scheme that can eliminate the incoherent dark state. The left-right circularly polarized lasers (described as σ- - σ+) interact with atoms periodically, yielding the constructive resonance. Jau’s group [14] used a thermal beam of potassium atoms positioned in the middle of the extended cavity to measure the hyperfine clock transition by CPT spectroscopy. The extended cavity in their case was formed by an edge-emitting laser and a grating. The cavity length was half of the microwave wavelength λ00 and corresponded to the frequency νhfs of the 39K ground state hyperfine energy levels, which was about 32.5 cm away from the oscillation frequency (νhfs) equal to 462 MHz.
VCSEL-based light feedback with the extended cavity mode spacing corresponding to the desired modulation frequency was also studied [21]. However, this study demonstrated that only a single interaction of light and atoms excited the corresponding CPT states. We also developed the co-propagating left and right circular polarization schemes [12,22], but discovered that σ- - σ+ bonds interacted with atoms only once.
We recently demonstrated usage of counter-propagation of the σ+-σ- optical feedback scheme with cavity length λ00 equal to 10.0 cm using of 85Rb atoms [23]. We called this method a left-right scheme. To obtain constructive interference the vapor cell was placed at a distance equal to ¼ of the cavity length. This study continues our research on CPT applicability to the atomic clock related field. Moreover, we focus on the research to improve short-term instability and it is suitable to small or chip-scale atomic clocks. We used 87Rb because its ground state hyperfine energy sublevels are less than of 85Rb. Comparing to our previous research, the cavity length and location of the vapor cell were changed in experiments performed in this work.
2. Experimental setup
The energy levels representing the interaction between light and 87Rb atoms are shown in Fig. 1. (b). The presence of both polarizations ensured that the incoherent dark states |F, mf=±F > are eliminated, allowing most atoms to contribute to the CPT resonance signal. However, this could not be achieved by using a linearly polarized light field propagating along the quantization axis because the dipole selection rules forbid an excitation of the CPT resonance.
Fig. 1. (a) Laser and optical feedback configuration. L - lens, A - adjustable attenuation plate, P - polarizer, λ/4 - a quarter-wave plate, PR - partial retroreflector, PD - photodetector, DC - direct current. (b) Energy level diagram of the D1 line in 87Rb showing the σ+-σ- transition used for CPT analysis.
This problem can be overcome by the introduction of a time or space delay between the σ+ and σ- components of the linearly polarized light fields [12,14,22,23]. By offsetting light field components by (2n+1)π (where n is an integer), the corresponding dark states can be aligned, allowing interference of the two CPT resonances.
To demonstrate this experimentally, we adopted a setup described from Ref. 23 (see Fig. 1(a)). In this configuration, a linearly polarized laser field was generated by a VCSEL (ULM795-01) with the linewidth about 100 MHz tuned to the D1 transition in 87Rb atom at 795 nm. The laser injection current was modulated at a frequency equal to one-half of the atomic hyperfine splitting frequency (equal to 6.834 GHz). Simultaneously, spectral components of VCSEL output were monitored using the Fabry-Perot interferometer. The laser frequency is stabilized with the Doppler-broadened absorption spectrum. The extended cavity was formed by a VCSEL and partial retroreflector (PR), which returned 50% of the power. To obtain the sidebands at 3.4 GHz, the PR was placed at a distance equal to (2n+1)λ00/2 (where n is an integer) from the VCSEL and mounted on a piezoelectric transducer for finer adjustments. Because the CPT signal varies as a sinusoidal function of phase difference [22], to achieve constructive interference, the atomic cell was placed in the center of the extended cavity. The CPT was observed from an atomic cell (2.5 cm in diameter and 0.8 cm long) filled with 87Rb and a 1:2 mixture of CH4 and N2 (stored in the cell at 27.5 torr pressure) acting as a buffer gas. The temperature of the vapor cell was maintained at 66 °C. A solenoid coil was placed outside of the vapor cell to provide a magnetic field, which also acted as a quantization axis of the interaction.
During polarization state studies, two λ/4 plates were inserted on both sides of the vapor cell. The horizontally polarized light was filtered by a Thorlabs LPVIS050 polarizer. It was converted into the left circularly polarized one (σ-) after the first λ/4 wave plate (which is Plate 1). After passing through the vapor cell, the laser beam was reflected back on itself using a partial retroreflector, which forced horizontal polarization of the laser light by Plate 1. This light was then projected back into the VCSEL. Another part of the laser was passed through the PR, after which the amplitude of the CPT resonance was measured by the photodetector (PD). To check the effect of the extended cavity, the light output was measured by a fast photodetector (ET-4000A) with 30 dB amplification, after which it was sent to the Agilent E4405B ESA-E spectrum analyzer.
After the CPT signal attained a maximum of the σ+ −σ− configuration for constructive interference produced by the counter-propagating beams, it was then changed its configuration to σ+ − σ+ one for further destructive interference. Under the presence of two λ/4 plates, the polarization state of the returned beam could be varied by changing the relative orientation of the waveplate optical axes, which were parallel to each other. Thus, their distance to the PR was maintained constant and equal to (2n+1)λ00/4 to achieve maximum CPT amplitude for the σ+ −σ− configuration. The whole system was installed on a horizontal platform. In another experiment PR was removed to compare our results with similar ones obtained using the conventional scheme.
3. Results and discussion
About 70% of the total light was absorbed by the vapor cell at 66 °C; thus, about 4% of the total light was reflected back into the VCSEL. The extended optical cavity length need not to be accurate since cavity mode cannot affect the output spectrum of VCSEL. The microwave power output obtained by the fast photodetector of the two schemes is shown in Fig. 2. The microwave power increased by ∼25 dBm under the presence of VCSEL as an extended cavity. At the microwave power equal to -14.5 dBm, the spectral components were the 0th and the ± 1st sidebands. However, over 96% of the optical power concentrated at the 0th sideband.
Fig. 2. The microwave spectrum measured by the fast photodetector with the 30 dB amplification. Spectrum analyzer: resolution/video bandwidth is equal to 1 Hz and span is equal to 100 Hz. The solid and dotted lines show VCSEL with and without an extended cavity.
The VCSEL and the partial retroreflector constituted an extended cavity with the length fixed to the microwave wavelength λ00, so that the laser output was a self-modulated spectrum with a frequency spacing of c/ (2n+1)λ00. Moreover, when the two-photon Raman resonance was satisfied, the 87Rb atoms absorb the least light of two sidebands with a frequency difference of 6.834 GHz, while the other off-resonance sidebands experienced more attenuation. There was self-injection locking when the light of the two sidebands with a frequency difference of 6.834 GHz was feed back to the VCSEL. A VCSEL, achieving the maximum gain of photons, would improve the microwave modulation efficiency.
The fractional transmission through the vapor cell near the CPT resonance signal was measured by a custom-build low response photodetector. The extended cavity length was set to 3λ00/2, which is equal to 6.6 cm. Figure 3 shows the response curve of the amplitude of the CPT resonance signal excited by the two schemes to the appropriate microwave power. The vapor cell acted as a a frequency filter and a microwave amplification was obtained with the extended cavity, thus the CPT resonance signal formed in the left-right scheme was still observed at the microwave power as low as -14.5 dBm. At the same time, the CPT signal in the conventional scheme was only detectable at -8.2 dBm. Thus, a CPT atomic clock with lower microwave power consumption can be constructed. Moreover, as the microwave power was increased, the resonance amplitude first increased, reached its maximum, and then decreased because of the optical sideband increase and reduction of the 0th sideband amplitude.
Fig. 3. The response curve of the CPT resonance amplitude to the microwave power of the two schemes at light intensity of 2.4 mW/cm2. The black squares represent the left-right scheme, and the red circle represents the conventional circular polarization scheme.
Figure 4 shows a comparison of the CPT resonance signal excited by the left-right scheme and the conventional circular polarization scheme. The top image shows the strongest CPT resonance signal obtained by a single interaction at -7.4 dBm microwave power and 2.4 mW/cm2 light intensity. The bottom image shows repeated interactions at -9.4 dBm microwave power. In this case, the amplitude reached its maximum with a left-right scheme. Because the counter-propagating σ+ and σ- polarized light differed from the optical path difference by (2n+1)λ00/2, the corresponding CPT states were thus constructive. Application of the left-right scheme resulted in a resonance amplitude of 11.8 mV, a line width of 1.16 kHz, while the conventional scheme yielded 4.8 mV resonance amplitude and 1.26 kHz line width (see Fig. 4). Because the right-left scheme can increase the interaction time between light and atoms, which is inversely proportional to the line width, the line width of the left-right scheme is slightly narrower.
Fig. 4. The CPT resonance signals excited by the conventional scheme (top image) and the left-right scheme (bottom image) at the 2.4 mW/cm2 light intensity. The application of the left-right scheme (bottom curve) resulted in 11.8 mV resonance amplitude and 1.16 kHz line width. Implementation of the conventional scheme (top curve) yielded 4.8 mV resonance amplitude and 1.26 kHz line width.
Figure 5 shows the noise spectrum for the two schemes. The short-term instability of the atomic clock described by the Allan deviation can be evaluated by Eq. (1) [4]:
Fig. 5. The noise spectra of the two schemes. The parameters are consistent with those shown in Fig. 4.
Chip-scale atomic clock or table-top apparatus are often realized using the conventional scheme [12,24]. The usage of the left-right scheme would result in the increased length of the optical path because of the polarization state reflection. However, the minimum optical path of the polarization state reflection is 22 mm for 87Rb and only 16 mm for 133Cs. Thus, the optical path increase is very limited. Our configuration (shown in Fig. 1) and configuration reported in Ref. 23 are identical to the original push-pull scheme. If the vapor cell can be miniaturized, the minimum extended cavity of our configuration is one half of the one published in [23] if the same atoms are used.
CPT atomic clocks need crystal oscillators to generate modulated microwaves for the VCSEL. If the optoelectronic oscillator (OEO) with the microwave output itself to modulate the carrier of VCSEL is implemented to induce self-oscillation of the vapor, the crystal oscillations can be canceled [25,26]. This solution can improve the microwave modulation efficiency. As a result, the lower microwave power can be used to excite the CPT resonance signal, which will help to obtain a lower power atomic clock. Using micro-electro-mechanical systems (MEMS), the left-right scheme physics package can be incorporated into the micro-chips on a large industrial scale.
4. Conclusion
The goal of this study was to cancel the influence of the incoherent dark state in the conventional scheme on the quality of the CPT resonance signal. To accomplish this, we studied a left-right circularly polarized light feedback scheme, which included an extended cavity consisted of a VCSEL and partial retroreflector. To achieve ± 1st sidebands, the extended cavity length was set to the odd multiples of half the microwave wavelength corresponding to the 87Rb hyperfine ground state splitting. For constructive interference of left-right circularly polarized light, the atomic cell was placed at the cavity center.
In this configuration, 4% of the light entered the VCSEL and resulted in achieving ± 1st VCSEL sidebands, which improved the microwave modulation efficiency. Under the same experimental conditions, the left-right scheme showed two times higher resonance amplitude and five times lower noise than the conventional scheme. Therefore, the short-term instability of the CPT atomic clock, using the left and right scheme, would be order of magnitude lower than if the conventional scheme is used. This scheme is not only suitable for the microchip-size atomic clock but can also be applied to fabricate high-performance, low power consumption CPT atomic clocks.
Funding
National Science Foundation for Cultivation of Bengbu University (2018GJPY05); Key Project of Natural Science of Bengbu University (2017ZR09zd); Natural Science Foundation of Bengbu University (2017ZR04).
Acknowledgments
One of the authors (S. Qu) is grateful to Sihong Gu, Yi Zhang, and Fan Zhang for for their help in the experiment.
Disclosures
The authors declare no conflicts of interest.
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