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Journal of Experimental and Theoretical Physics

Light Shift of Coherent Population Trapping Resonances in Cesium Vapor under the Laser Field with Dual Frequency–Amplitude Modulation

V. I. Vishnyakov, Denis V. Brazhnikov, Mikhail N Skvortsov

Published Jun 1, 2024• 3 citations
Publisher

Abstract

Abstract In this study, the light shift of coherent population trapping (CPT) resonances is studied in a miniature glass cell (~0.1 cm3) filled with 133Cs vapor. The atoms exposed to the radiation from a vertical-cavity surface-emitting laser (VCSEL). The laser current is modulated at a microwave frequency (≈4.6 GHz), which leads to the frequency modulation (FM) of output radiation. In addition, the light beam is transmitted through an electro-optic modulator (EOM), which is assembled as a Mach–Zehnder interferometer, acquiring amplitude modulation (AM). This dual (FM–AM) modulation leads to essentially nonlinear behavior of the function describing the light shift of the CPT resonance versus the total optical power in the cell. In particular, this function has an extremum that can be used to suppress the influence of small optical power variations in the cell on the stability of the CPT-based quantum frequency standard (QFS). The proposed scheme is characterized by a number of parameters such as the phase difference between the FM and AM signals as well as the bias voltage at EOM, which are additional degrees of freedom for controlling the behavior of the light shift of the CPT resonance. This can be used for the optimization of the QFS operation regime.

DOI
10.1134/s1063776125600254

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The light (ac Stark) shift of coherent population trapping (CPT) resonances in cesium vapor is studied under excitation by radiation from a vertical-cavity surface-emitting laser, whose current is modulated at a microwave frequency (≈ 4.6 GHz). This approach is used in some state-of-the-art microwave quantum frequency standards (QFS). One of the main factors leading to degradation of long-term frequency stability of QFS is associated with the light shift of the CPT resonance due to variations in optical power P in the vapor cell. In this work, it is shown that using an additional electro- optic modulator assembled as a Mach-Zehnder interferometer makes it possible to effectively control the amplitudes of sidebands in the radiation spectrum. This allows finding such an optimal optical power value near which the resonance shift is insensitive to its small changes. The results are of interest for the development of CPT-based QFS.

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State-of-the-art miniature atomic clocks (MACs) are based on the phenomenon of coherent population trapping (CPT) in alkali-metal atomic vapors ($\mathrm{Rb}$ or $\mathrm{Cs}$). Improving the stability of the clock frequency is a crucial issue; resolving it would result in significant progress in numerous applications. Here, we examine the configuration of the light field, which is composed of two bichromatic beams with opposing handedness of circular polarization. The beams are in resonance with optical transitions in the $\mathrm{Cs}$ ${D}_{1}$ line ($\ensuremath{\lambda}\ensuremath{\approx}895$ nm). This configuration has previously been shown to produce observed CPT resonances with higher contrast than a standard single-beam scheme; however, our scheme implements pump and probe beams that operate independently, with the transmission of the probe beam being monitored separately. This approach differs from previous studies. The experiments are carried out using a cubic $5\ifmmode\times\else\texttimes\fi{}5\ifmmode\times\else\texttimes\fi{}5\phantom{\rule{0.2em}{0ex}}{\mathrm{mm}}^{3}$ vapor cell filled with buffer gas. It is shown that the line shape of the resonance acquires an asymmetry that can be efficiently controlled by a microwave (Raman) phase between the beams. As a proof of concept, we study the way in which this asymmetry can help to mitigate the influence of the ac Stark (light) shift on the long-term frequency stability of CPT clocks based on vapor microcells ($V\ensuremath{\ll}1\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{3}$). Experimental verification is performed with both a distributed-Bragg-reflector laser and a vertical-cavity surface-emitting laser. The latter is of particular importance for the development of MACs. The experimental results are in qualitative agreement with the analytical theory based on a double-$\mathrm{\ensuremath{\Lambda}}$ scheme of atomic energy levels.

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In this paper we present our spectroscopic studies on Coherent Population Trapping (CPT) in micro-fabricated Caesium cells and our evaluation of its application in miniature atomic frequency standards (atomic clocks). We observe the CPT signal on the Cs D1-line by coupling two hyperfine ground-state Zeeman sub-levels to a common excited state using two coherent electromagnetic fields created with a modulated DFB laser. Contrarily to double resonance, CPT does not require any microwave cavity, which should facilitate the miniaturization of a future atomic clock device. We study and report here on the light shift phenomena at different cell temperatures and laser wavelength. We also present resonance shifts due to cell temperature variations and clock frequency stability measurements. To the best of our knowledge, this article is the first report on light shift with Cs D1 line in a CPT vapour-cell atomic clock.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Oct 8, 2010•1 citation
Abstract In this study, the light shift of coherent population trapping (CPT) resonances is studied in a miniature glass cell (~0.1 cm3) filled with 133Cs vapor. The atoms exposed to the radiation from a vertical-cavity surface-emitting laser (VCSEL). The laser current is modulated at a microwave frequency (≈4.6 GHz), which leads to the frequency modulation (FM) of output radiation. In addition, the light beam is transmitted through an electro-optic modulator (EOM), which is assembled as a Mach–Zehnder interferometer, acquiring amplitude modulation (AM). This dual (FM–AM) modulation leads to essentially nonlinear behavior of the function describing the light shift of the CPT resonance versus the total optical power in the cell. In particular, this function has an extremum that can be used to suppress the influence of small optical power variations in the cell on the stability of the CPT-based quantum frequency standard (QFS). The proposed scheme is characterized by a number of parameters such as the phase difference between the FM and AM signals as well as the bias voltage at EOM, which are additional degrees of freedom for controlling the behavior of the light shift of the CPT resonance. This can be used for the optimization of the QFS operation regime.
The light (ac Stark) shift of coherent population trapping (CPT) resonances in cesium vapor is studied under excitation by radiation from a vertical-cavity surface-emitting laser, whose current is modulated at a microwave frequency (≈ 4.6 GHz). This approach is used in some state-of-the-art microwave quantum frequency standards (QFS). One of the main factors leading to degradation of long-term frequency stability of QFS is associated with the light shift of the CPT resonance due to variations in optical power P in the vapor cell. In this work, it is shown that using an additional electro- optic modulator assembled as a Mach-Zehnder interferometer makes it possible to effectively control the amplitudes of sidebands in the radiation spectrum. This allows finding such an optimal optical power value near which the resonance shift is insensitive to its small changes. The results are of interest for the development of CPT-based QFS.
Previously, we have proposed a method to control the emission spectrum of the vertical-cavity surface-emitting laser (VCSEL) with the synchronized modulation of the injection current at single and doubled frequencies. In this work, the above method is used to improve the metrological characteristics of the coherent population trapping (CPT) resonance in 87 Rb. The dual-frequency (DF) modulation reduces the carrier power and suppresses the light shift of the resonance frequency, if it is unattainable with the single-frequency modulation. In addition, a higher resonance contrast is achieved by equalizing the powers of the resonant components of the spectrum.
State-of-the-art miniature atomic clocks (MACs) are based on the phenomenon of coherent population trapping (CPT) in alkali-metal atomic vapors (Rb\mathrm{Rb}Rb or Cs\mathrm{Cs}Cs). Improving the stability of the clock frequency is a crucial issue; resolving it would result in significant progress in numerous applications. Here, we examine the configuration of the light field, which is composed of two bichromatic beams with opposing handedness of circular polarization. The beams are in resonance with optical transitions in the Cs\mathrm{Cs}Cs D1{D}_{1}D1​ line ($\ensuremath{\lambda}\ensuremath{\approx}895$ nm). This configuration has previously been shown to produce observed CPT resonances with higher contrast than a standard single-beam scheme; however, our scheme implements pump and probe beams that operate independently, with the transmission of the probe beam being monitored separately. This approach differs from previous studies. The experiments are carried out using a cubic $5\ifmmode\times\else\texttimes\fi{}5\ifmmode\times\else\texttimes\fi{}5\phantom{\rule{0.2em}{0ex}}{\mathrm{mm}}^{3}$ vapor cell filled with buffer gas. It is shown that the line shape of the resonance acquires an asymmetry that can be efficiently controlled by a microwave (Raman) phase between the beams. As a proof of concept, we study the way in which this asymmetry can help to mitigate the influence of the ac Stark (light) shift on the long-term frequency stability of CPT clocks based on vapor microcells ($V\ensuremath{\ll}1\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{3}$). Experimental verification is performed with both a distributed-Bragg-reflector laser and a vertical-cavity surface-emitting laser. The latter is of particular importance for the development of MACs. The experimental results are in qualitative agreement with the analytical theory based on a double-$\mathrm{\ensuremath{\Lambda}}$ scheme of atomic energy levels.
We report the characterization of dark line resonances observed in Cs vapor microcells filled with a unique neon (Ne) buffer gas. The impact on the coherent population trapping (CPT) resonance of some critical external parameters such as laser intensity, cell temperature, and microwave power is studied. We show the suppression of the first-order light shift by proper choice of the microwave power. The temperature dependence of the Cs ground state hyperfine resonance frequency is shown to be canceled in the 77–80 °C range for various Ne buffer gas pressures. The necessity to adjust the Ne buffer gas pressure or the cell dimensions to optimize the CPT signal height at the frequency inversion temperature is pointed out. Based on such Cs–Ne microcells, we preliminary demonstrate a 852 nm vertical cavity surface emitted laser (VCSEL)-modulated based CPT atomic clock exhibiting a short term fractional frequency instability σy(τ)=1.5×10−10τ−1/2 until 30 s. These results, similar to those published in the literature by others groups, prove the potential of our original microcell technology in view of the development of high-performance chip scale atomic clocks.
We propose a model to reduce the influence that the light-shift induced frequency drift has on the long-term stability of coherent population trapping (CPT)-based low-power atomic clocks. We experimentally validated the proposed model using the chip-scale atomic clock architecture. The model considers both the drift of the dc-bias current to compensate for the wavelength aging of the vertical-cavity surface-emitting laser (VCSEL) and the variation in the modulation index of the light field generated by the VCSEL. We investigated the dc-bias-current-dependency of the frequency drift in an atomic clock module both theoretically and experimentally, confirming that the frequency drift can change as a function of the VCSEL basic parameters. When the atomic clock module was operated over a period of five months at the dc-bias current affording a zero-crossing of the clock frequency drift, the Allan standard deviation and clock frequency drift for long-term stability were 8.0×10−12 for averaging times of 4×106 s and 2.4×10−13/day, respectively. Our approach is promising to improve the long-term stability of CPT-based low-power atomic clocks.
In this paper we present our spectroscopic studies on Coherent Population Trapping (CPT) in micro-fabricated Caesium cells and our evaluation of its application in miniature atomic frequency standards (atomic clocks). We observe the CPT signal on the Cs D1-line by coupling two hyperfine ground-state Zeeman sub-levels to a common excited state using two coherent electromagnetic fields created with a modulated DFB laser. Contrarily to double resonance, CPT does not require any microwave cavity, which should facilitate the miniaturization of a future atomic clock device. We study and report here on the light shift phenomena at different cell temperatures and laser wavelength. We also present resonance shifts due to cell temperature variations and clock frequency stability measurements. To the best of our knowledge, this article is the first report on light shift with Cs D1 line in a CPT vapour-cell atomic clock.