An Erratum to this paper has been published: https://doi.org/10.1134/S1062873824110054

We develop a theory of composite Ramsey sequences of rf pulses interacting with the Zeeman structure at the long-lived atomic level, beyond the rotating wave approximation. Such sequences are proposed in experiments to detect the violation of local Lorentz invariance [R. Shaniv, et al., Phys. Rev. Lett. 120, 103202 (2018)]. Based on Fourier analysis, we have shown that taking into account non-resonant contributions leads to a radical change in the dynamics of the quantum system (with respect to the rotating wave approximation) in the case when the number of Ramsey pulses exceeds several tens. As a result, the effectiveness of using such rf pulses sequences to test local Lorentz invariance has not yet been fully determined and requires additional research.

The laser cooling and trapping of ${ }^{87} \mathbf{R b}$ atoms in pure-optical two frequency trap is studied in details. The parameter ranges in which optimal laser cooling is achieved were studied for the first time. The atoms can be simultaneously cooled and trapped by bichromatic laser field that opens up possibility to realize principally new type of pure optical trap. The depth of our trap is hundreds of spontaneous relaxation frequencies which corresponds to the depth of the magneto-optical traps used in the experiments.

In this report we describe shortly several modifications of the classical scheme of Ramsey spectroscopy developed by us and other authors to fight with unwanted probe-field induced shifts of the resonance position in atomic clocks (both optical and microwave) and interferometers.

In this work, we created a source of ultracold atoms for a quantum interferometer-gravimeter. A cloud of $10^{7}-10^{8}$ atoms with the temperature of around 6 uK was obtained. An effective selection of rubidium atoms in the nonmagnetic sub-state was carried out.

We develop a field-nonlinear theory of sub-Doppler spectroscopy in a gas of two-level atoms, based on a self-consistent solution of the Maxwell-Bloch equations in the mean-field and single-atom density-matrix approximations. This makes it possible to correctly take into account the effects caused by the free motion of atoms in a gas, which lead to a nonlinear dependence of the spectroscopic signal on the atomic density even in the absence of a direct interatomic interaction (e.g., dipole-dipole interaction). Within the framework of this approach, analytical expressions for the light field were obtained for an arbitrary number of resonant waves and arbitrary optical thickness of a gas medium. Sub-Doppler spectroscopy in the transmission signal for two counterpropagating and copropagating waves has been studied in detail. A previously unknown redshift of a narrow sub-Doppler resonance is predicted in a counterpropagating waves scheme, when the frequency of one wave is fixed and the frequency of the other wave is varied. The magnitude of this shift depends on the atomic density and can be more than an order of magnitude greater than the known shift from the interatomic dipole-dipole interaction (Lorentz-Lorenz shift). The found effects, caused by the free motion of atoms, require a significant revision of the existing picture of spectroscopic effects depending on the density of atoms in a gas. Apart from the fundamental aspect, obtained results are important for precision laser spectroscopy and optical atomic clocks.

The new two-stage scheme for deep laser cooling of ${}^{171} \mathbf{Y b}^{+}$ is suggested. This scheme apart from well-known approaches does not require application of magnetic field. The suggested approach opens up possibility for precise control of magnetic field for further progress in optical frequency standards and quantum computing.

We investigate dark-state resonances for alkali-metal atoms in a cell with buffer gases excited by frequency modulated elliptically polarized laser field. It is shown that all the resonance parameters depend on the ellipticity and that for some parameters this dependence is crucial for designing high-performance chip-scale atomic clocks.

A model was developed for laser cooling of alkali atoms in a polychromatic field, considering the real structure of atomic levels. The model was tested by the example of the 6Li atom. The minimum achievable temperatures of laser cooling of light alkali atoms were studied for different polarizations of the light field components, and the possibility of cooling below the Doppler limit was shown.

In this study, the Ramsey spectroscopy of coherent population trapping resonances excited on the D1 line of alkali metal atoms in miniature vapor cells has been studied theoretically and experimentally. The configuration of the field produced by two counterpropagating waves with opposite circular polarizations has been considered. A counterpropagating wave is formed as a result of reflection from a partially transmitting output mirror, while the signal from the initial wave transmitted through the mirror is detected. It is shown that such a scheme is characterized by the optimal mirror reflection coefficient, for which the short-term stability can be substantially improved relative to the standard scheme without the counterpropagating wave. The three-fold improvement of the short-term stability of the atomic clock based on the coherent population trapping resonance in a vapor cell with 87Rb atoms has been demonstrated experimentally.

We show the possibility of implementing a deep dissipative optical lattice for neutral atoms with a macroscopic period. The depth of the lattice can reach magnitudes comparable to the depth of the magneto-optical traps (MOT), while the presence of dissipative friction forces allows for trapping and cooling of atoms. The area of localization of trapped atoms reaches sub-millimeter size, and the number of atoms is comparable to the number trapped in MOT. As an example, we study lithium atoms for which the macroscopic period of the lattice $\Lambda=1.5$ cm. Such deep optical lattices with a macroscopic period open up possibility for developing effective methods for cooling and trapping neutral atoms without use of magnetic field as an alternative to MOT. This is important for developing compact systems based on cold atoms.

The kinetics of 6 Li atoms in a bichromatic laser field exciting transitions on D2 and D1 lines is investigated. The model takes into account the complex real structure of energy levels of 6 Li (including the Zeeman degeneracy) as well as the nonuniform spatial polarization of the laser field. It is found that detuning and the polarization configuration of the light field component of the resonant D2 line of the 6 Li atom are of fundamental importance for laser cooling. The possibility of cooling of atoms below the Doppler limit is demonstrated.

The work propose a scheme of deep laser cooling of ^171Yb^+. The cooling is based on the effect of electromagnetically induced transparency (EIT) in a polychromatic field with three frequency components are resonant to optical transitions of the ^2S_1/2→ ^2P_1/2 line. The deep cooling down to the ground motional state in a trap allows for a significant suppression of the second order Doppler shift in frequency standards. Moreover, there is no need to use a magnetic field, which is required for Doppler cooling of ^171Yb^+ in a field with two-frequency component. The cooling without use of magnetic field is important for deep suppression of quadratic Zeeman shifts of clock transitions from uncontrolled residual magnetic fields.

We report on a comparative analysis of quenched sideband cooling in trapped ions. We introduce a theoretical approach for time-efficient simulation of the temporal cooling characteristics and derive the optimal conditions providing fast laser cooling into the ion’s motional ground state. The simulations were experimentally benchmarked with a single 172 Yb + ion confined in a linear Paul trap. Sideband cooling was carried out on a narrow quadrupole transition, enhanced with an additional clear-out laser for controlling the effective linewidth of the cooling transition. Quench cooling was thus for the first time studied in the resolved sideband, intermediate and semi-classical regime. We discuss the non-thermal distribution of Fock states during laser cooling and reveal its impact on time dilation shifts in optical atomic clocks.

We propose a scheme of deep laser cooling of 171Yb+, which is based on the effect of electromagnetically induced transparency (EIT) in a polychromatic field with three frequency components resonant with optical transitions of the 2S1/2 -> 2P1/2 line. The deep cooling down to the ground motional state in a trap allows for a significant suppression of the second-order Doppler shift in the frequency standard. Moreover, in our scheme, there is no need to use a magnetic field, which is required for Doppler cooling of 171Yb+ in a field with a two frequency component. Cooling without the use of a magnetic field is important for the deep suppression of quadratic Zeeman shifts of clock transitions due to an uncontrolled residual magnetic field.

We study the field shift of coherent population trapping (CPT) resonance excited by a bichromatic field in an open Λ system with account for the Gaussian profile of the laser radiation intensity. Two methods for error signal formation are considered: the harmonic frequency modulation and the step phase modulation (phase jumps). It is shown that the spatial inhomogeneity of the light beam leads to an essentially nonlinear dependence of the error signal shift on the laser radiation intensity. We propose an approach for the linearization of this dependence, which is important for the development of methods for suppressing the field shift in atomic clocks based on CPT resonances.

We theoretically study the frequency shift in atomic clocks caused by the line-shape asymmetry of coherent population trapping (CPT) resonance in a bichromatic laser field. This asymmetry arises due to the inequality of the resonant spectral components and nonzero one-photon detuning. The line-shape-asymmetry-induced shift depends on the intensity of the resonant fields, which leads to a degradation in long-term stability due to fluctuations of the laser field parameters. A frequency stabilization based on the harmonic modulation of two-photon detuning is considered. It is shown that the use of a high-frequency modulation (compared to the CPT resonance width, i.e., the Pound-Drever-Hall regime) makes it possible to significantly suppress this shift (by one to two orders of magnitude).

We investigate the probe field induced shift for atomic lattice-based and ion-trap clocks, which can be considered as a near resonant ac-Stark shift, connected to the Zeeman structure of atomic levels and their splitting in a dc magnetic field. This shift arises from possible residual ellipticity in the polarization of the probe field and uncertainty in the magnetic field orientation. Such a shift can have an arbitrary sign and, for some experimental conditions, can reach the fractional value of the order of 10$^{-18}$-10$^{-19}$, i.e., it is not negligible. Thus, it should be taken into account in the uncertainty budgets for the modern ultra-precise atomic clocks. In addition, it is shown that when using hyper-Ramsey spectroscopy, this shift can be reduced to a level much lower than $10^{-19}$.

We develop a nonlinear theory of propagation of a monochromatic light wave in a gas of two-level atoms under the condition of inhomogeneous Doppler lineshape broadening, while considering a self-consistent solution of the Maxwell–Bloch equations in the mean-field approximation using a single atom density matrix formalism. Our approach shows a significant deformation of the Doppler resonant lineshape (shift, asymmetry), which depends on the atomic density. These effects are a consequence of only the free motion of atoms in a gas and is not associated with interatomic interaction. In particular, the frequency shift of the field-linear contribution to the transmission signal is more than an order of magnitude greater than the shift due to the interatomic dipole–dipole interaction, and the first nonlinear correction has an even stronger deformation, which exceeds the effect of the interatomic interaction by three orders of magnitude. The found effects caused by the free motion of atoms require a significant revision of the existing picture of spectroscopic effects, which depend on the atomic density in a gas.