Abstract For coherent population trapping (CPT) resonance excited by a bichromatic field in a closed Λ-system, we have obtained an analytical expression for the line shape in the case of a Gaussian profile of the radiation intensity distribution, taking into account the light shift of the reference transition frequency. Due to the spatial inhomogeneity of the light shift, the line shape is asymmetric. The dependence of the shift of the resonance peak position on the light intenisty is investigated.
State-of-the-art miniature atomic clocks (MACs) are based on the phenomenon of coherent population trapping (CPT) in alkali-metal atomic vapors (
Rb or
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 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.
In this comment, I demonstrate that an addition to the light shift of the coherent population trapping resonance’s frequency, shown in [V. I. Yudin, M. Yu. Basalaev, A. V. Taichenachev, O. N. Prudnikov, M. D. Radchenko, and V. G. Palchikov, JETP Lett. 122, 144 (2025)], is not due to a new physical effect but is consequence of the asymmetry. To do this, the following model is considered. The phase of a monochromatic optical field is harmonically modulated at the frequency corresponding to the interval between ground-state levels of the Λ-scheme. The carrier is tuned to the low-frequency transition, while the first-order sideband is resonant to the high-frequency transition. I present curves demonstrating the opposite asymmetry of the resonance for the cases of the shift deviating from the light one in different directions.