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Журнал Экспериментальной и Теоретической Физики

KOMPENSATsIYa SVETOVOGO SDVIGA REZONANSOV KOGERENTNOGO PLENENIYa NASELENNOSTEY V PARAKh TsEZIYa PRI ISPOL'ZOVANII DVOYNOY ChASTOTNOY I AMPLITUDNOY MODULYaTsII LAZERNOGO IZLUChENIYa

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

Published Nov 1, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.31857/s0044451024100110

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The problem of developing control algorithms in quantum frequency standards based on the effect of coherent population trapping is considered. The development of such algorithms will make it possible to create frequency standards with metrological characteristics that are not inferior to the characteristics of rubidium frequency standards, with reduced power consumption and overall dimensions. A method for studying the dependence of the actual value and frequency instability of quantum frequency standards based on the effect of coherent population trapping on the operating modes of individual parts of the standards is presented. As a criterion for optimizing the laser injection current, the output power of the microwave generator, and the cell temperature, we chose to minimize the effect on the shift of the actual frequency of the standard. A comparative analysis of methods for changing the radiation intensity of a surface-emitting laser with a vertical resonator has been carried out and control algorithms have been developed that take into account the features of these methods. Based on these algorithms, software and tuning methods have been developed in quantum frequency standards based on the effect of coherent population trapping. For the prototype standard, the results of measuring the frequency instability are shown. It is shown that control algorithms and tuning methods can qualitatively change the metrological characteristics of quantum frequency standards based on the effect of coherent population trapping.

Izmeritel`naya Tekhnika•Jan 1, 2021•0 citations
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.
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.
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.
One of the important subjects in coherent-population- trapping-based (CPT-based) vapor cell frequency standards is the light shift (ac Stark shift). We calculate the light shift using a numerical method and perturbation approximation. Experimentally, we measure light shift using a pair of phase-locked diode lasers as well as a frequency-modulated diode laser. There is good agreement between theory and experiment. A method of controlling light shift in CPT-based frequency standards is proposed and implemented in Agilent Laboratories. The short-term stability of our CPT-based rubidium vapor cell frequency standard is measured as 1.3 x 10(-12) tau (-1/2), which is limited by the phase noise of the reference local oscillator used.
We have performed a series of experiments demonstrating the use of a vertical-cavity surface-emitting laser for nonlinear spectroscopy on the cesium D2 transition at 852 nm wavelength. Due to the high modulation efficiency of the VCSEL sufficiently strong modulation sidebands at 9.2 GHz frequency can be produced by direct modulation of the laser injection current. Using, the carrier and one of the modulation sidebands coherent population trapping (CPT) resonances in a buffered cesium vapor can be prepared with linewidths of only 60 Hz. For application of these narrow resonances to precision magnetometry we find a sensitivity of 10 pT in 0.3 s integration time. For the use of our setup as a frequency reference a relative stability of 1 • 10 − 11 / τ is predicted. In both applications of CPT resonances the use of VCSELs as light sources helps to build compact and reliable devices.
The active suppression of light shift of the reference coherent population trapping (CPT) resonance in87Rb vapor to improve the long-term stability of compact atomic clocks has been demonstrated experimentally. The approach is based on the phase jump technique used to synthesize an error signal, which is proportional to the light shift of the CPT resonance, from an optical transmission signal. The use of this error signal in an additional feedback loop allows one to stabilize the amplitude of a microwave signal for the phase modulation of laser radiation near a value at which the light shift of the CPT resonance is absent. This technique has made it possible to reduce the long-term instability of CPT atomic clocks in our experiments by a factor of 15 at an integration time of 10 000–20 000 s.
The problem of developing control algorithms in quantum frequency standards based on the effect of coherent population trapping is considered. The development of such algorithms will make it possible to create frequency standards with metrological characteristics that are not inferior to the characteristics of rubidium frequency standards, with reduced power consumption and overall dimensions. A method for studying the dependence of the actual value and frequency instability of quantum frequency standards based on the effect of coherent population trapping on the operating modes of individual parts of the standards is presented. As a criterion for optimizing the laser injection current, the output power of the microwave generator, and the cell temperature, we chose to minimize the effect on the shift of the actual frequency of the standard. A comparative analysis of methods for changing the radiation intensity of a surface-emitting laser with a vertical resonator has been carried out and control algorithms have been developed that take into account the features of these methods. Based on these algorithms, software and tuning methods have been developed in quantum frequency standards based on the effect of coherent population trapping. For the prototype standard, the results of measuring the frequency instability are shown. It is shown that control algorithms and tuning methods can qualitatively change the metrological characteristics of quantum frequency standards based on the effect of coherent population trapping.