We give a brief review of the current status of world research in the field of creating quantum sensors of DC and RF electric fields based on highly excited Rydberg atoms with principal quantum number n ≫ 1. Such atoms have large dipole moments, which increase as n2 with increasing n. Due to this fact, electric polarizabilities of Rydberg levels increase as n7 and exceed the polarizabilities of low-excited atoms by many orders of magnitude. This forms the basis for creating highly sensitive quantum sensors. For their implementation, alkali-metal atoms in compact optical vapor cells are excited to Rydberg states. When microwave radiation with a frequency above 1 GHz should be detected, splitting of a single resonance of electromagnetically induced transparency (EIT), which appears under two-photon laser excitation of Rydberg states, into two resonances due to the Autler-Townes (AT) effect in a microwave radiation field is measured. With Rydberg sensors, it is possible to construct both metrological standards for measuring electric field strength and highly sensitive detectors of RF fields for various applications. Our first experimental results on the observation of EIT resonances under two-photon laser excitation 5S1/2 → 5P3/2 → nS1/2 of 85Rb Rydberg states in an optical cell and on the observation of AT splitting in the field of microwave radiation with a frequency of 58.17 GHz, which was in resonance with 41S1/2 → 41P3/2 transition between the neighboring Rydberg states, are also presented.

In this study, we investigate the conductivity of a two-dimensional (2D) system in HgTe quantum well comprising two types of carriers with linear and quadratic spectra, respectively. The interactions between the two-dimensional Dirac holes and the heavy holes lead to the breakdown of Galilean invariance, resulting in interaction -limited resistivity. Our exploration of the transport properties spans from low temperatures, where both subsystems are fully degenerate, to higher temperatures, where the Dirac holes remain degenerate while the heavy holes follow Boltzmann statistics, creating a partially degenerate regime. Through a developed theory, we successfully predict the behavior of resistivity as rho similar to T2 and rho similar to T3 for the fully degenerate and partially degenerate regimes, respectively, which is in reasonable agreement with experimental observations. Notably, at elevated temperatures, the interaction -limited resistivity surpasses the resistivity caused by impurity scattering by a factor of 5-6. These findings imply that the investigated system serves as a versatile experimental platform for exploring various interaction -limited transport regimes in two component plasma.

The resistivity of two-dimensional (2D) metals generally exhibits insensitivity to electron -electron scattering. However, it is worth noting that Galilean invariance may not hold true in systems characterized by a spectrum containing multiple electronic branches or in scenarios involving electron -hole plasma. In the context of this paper, we focus on 2D electrons confined within a triple quantum well (TQW) based on HgTe. This system displays a coexistence of energy bands featuring both linear and paraboliclike spectra at low energy and, therefore, lacks the Galilean invariance. This paper employs a combined theoretical and experimental approach to investigate the transport properties of this two -component system across various regimes. By manipulating carrier density and temperature, we tune our system from a fully degenerate regime, where resistance follows a temperature -dependent behavior proportional to T 2 to a regime where both types of electrons adhere to Boltzmann statistics. In the nondegenerate regime, electron interactions lead to resistance that is weakly dependent on temperature. Notably, our experimental observations closely align with the theoretical predictions derived in this paper. In this paper, we establish the HgTe-based TQW as a promising platform for exploring different interaction -dominant scenarios for the massless -massive Dirac system.

The microwave photoconductivity of a system of gapless Dirac fermions in HgTe quantum wells with a critical thickness has been experimentally and theoretically investigated. It has been found that the photoconductivity fluctuates depending on the gate voltage near the Dirac point, and the fluctuation amplitude increases with an increase in the conductor size and a decrease in temperature. A theoretical explanation of the microwave response based on the assumption of the existence of a percolation two-dimensional fractal network of helical edge current states induced by fluctuations in the well thickness near the critical value has been proposed. It has been shown that the microwave photoconductivity of this network fluctuates with a change in the Fermi energy and the behavior of the fluctuation amplitude is in qualitative agreement with the corresponding experimental data.

We theoretically study the photogalvanic effect in a strained two-dimensional transition-metal dichalcogenide monolayer due to deformation-induced lowering of the monolayer symmetry and electron-density difference in opposite valleys. This effect arises as a system response to a scalar nonequilibrium perturbation (electron-density difference in the valleys), which is in contrast with the conventional photogalvanic effect, represents the secondorder response to an external electromagnetic radiation. Using the description of linear and nonlinear interband recombination, we develop a theory for a p-type and an intrinsic monolayer semiconductor. We show that at low temperatures, the photogalvanic current is caused by the impurity relaxation processes controlling the valley population imbalance.

The semimetal quantum well (QW) based on HgTe structures exhibiting unusual transport properties at low temperature is examined experimentally. It demonstrates either a linear or quadratic growth of resistance with temperature at different top-gate voltages in the semimetal regime. We develop a theoretical model of HgTe-based semimetal QW resistance temperature dependence based on electron-hole scattering processes at low temperatures. We apply the Boltzmann transport equation approach to study the effect of electron-hole scattering in a semimetal QW. The calculated temperature behavior of 2D semimetal resistivity demonstrates an excellent agreement with experimental findings.

Diffusion currents are theoretically examined in two-dimensional Dirac materials, such as those of the transition metal dichalcogenides (TMD) family. The transversal effects are analogues of the valley Hall (VHE) and photogalvanic (PGE) transport phenomena in case when the electron driving force is not an electric field but a gradient of electron density distribution in the sample. The latter can be created by a finite-sized laser spot or by the injection of electrons from other materials. We develop the theory of diffusive VHE effect assuming the anisotropic electron-short-range-impurity skew scattering. The electron PGE-like transport caused by higher electron-density derivatives is analyzed assuming the trigonal warping anisotropy of electron valleys in a TMD monolayer. The nonlinear responses on electron-density gradient are studied as well. The isotropic processes of electron scattering off the short-range and Coulomb centers are taken into account in the PGE-like transport theory.

Three-photon laser excitation of single rubidium atoms in an optical dipole trap (ODT) into the 37 P Rydberg state by laser radiation with wavelengths of 780, 1367, and 743 nm has been experimentally demonstrated. The excitation to Rydberg states is detected by an optical method using the losses of atoms in the ODT. The laser excitation spectra of single Rydberg atoms in the ODT are recorded, and the dependence of the excitation probability on the laser pulse duration is measured. The measured spectrum width was 2 MHz. Experiments on fluorescence quenching spectroscopy of a cloud of cold atoms in a magneto-optical trap during the three-photon laser excitation of atoms to Rydberg states are also carried out. The experimental results are compared with a numerical calculation. Methods for increasing the accuracy of the coherent three-photon laser excitation of Rydberg atoms in the ODT are considered.

Spin states of two-dimensional Wigner clusters are considered at low temperatures, when all electrons are in ground coordinate states. The spin subsystem behavior is determined by antiferromagnetic exchange integrals. The spin states in such a system in the presence of a magnetic field are described in terms of the Ising model. The spin structure, correlation function, and magnetic susceptibility of the cluster are found by computer simulations. It is shown that the spin susceptibility experiences oscillations with respect to the magnetic field, owing to the magnetoinduced spin subsystem rearrangements.

Mesoscopic conductance fluctuations were discovered in a weak localization regime of a strongly disordered two-dimensional HgTe-based semimetal. These fluctuations exist in macroscopic samples with characteristic sizes of 100 μm and exhibit anomalous dependences on the gate voltage, magnetic field, and temperature. They are absent in the regime of electron metal (at positive gate voltages) and strongly depend on the level of disorder in the system. All the experimental facts lead us to the conclusion that the origin of the fluctuations is a special collective state in which the current is conducted through the percolation network of electron resistances. We suppose that the network is formed by fluctuation potential whose amplitude is higher than the Fermi level of electrons due to their very low density.

The absorption of a light wave interacting with optical transitions in the D 1 line of an alkali metal atom subjected to microwave radiation that is in resonance with magnetic dipole transitions between hyperfine ground-state components, has been investigated. It is known that when scanning a longitudinal magnetic field ( B || k , where k is the wavevector), one may observe a magneto-optical resonance due to the ground-state Hanle effect. In addition, the effect of double radio-optical resonance takes place because of the presence of the resonance microwave field. The joint influence of these effects on the formation of a narrow magneto-optical resonance in light wave absorption has been studied theoretically and experimentally. It has been shown analytically that the effects compete with each other and destructively act on the resonance formation. As a result, the amplitude of the resonance is small and its shape is complicated. However, in the presence of a buffer gas the pressure of which is such that the hyperfine splitting of the ground state remains spectrally unresolved, it becomes possible to observe a magneto-optical resonance with a relatively large amplitude. Experiments have been carried out with the use of a miniature glass cell ( V ~ 0.1 cm 3 ) filled with 87 Rb vapor and a buffer gas argon (a pressure of about 95 Torr). In particular, the theoretically predicted resonance narrowing with increasing light field intensity has been experimentally observed. A configuration for magneto-optical resonance excitation suggested here may be applied in quantum magnetometry to measure weak permanent magnetic fields and resonance microwave fields using cells filled with alkali metal vapor.

We present our experimental results of two-photon laser excitation 5S1/2→5P3/2→nS1/2 of Rb atoms to Rydberg nS1/2 states with a homemade 480 nm laser in the second excitation step. In an experiment with cold Rb atoms, we excited the 42S1/2 state and detected Rydberg atoms with a selective-field-ionization (SFI) detector that provides single-atom resolution. The resonance line shapes well agreed with numerical simulations in a three-level theoretical model. We also studied the multiatom spectra of Rydberg excitation of mesoscopic atom ensembles which are of interest to quantum information processing. In the experiment with hot Rb atoms, we first excited the 30S1/2 state and observed a narrow Rydberg EIT resonance. Its line shape also agreed well with theory. Then, we performed a similar experiment with the higher 41S1/2 state and observed the Autler–Townes splitting of the EIT resonance in the presence of a microwave field, which was in resonance with the microwave transition 41S→41P3/2. This allowed us to measure the average strength of the microwave field and, thus, demonstrate the operation of a Rydberg microwave sensor. We may conclude that the developed homemade laser at 480 nm substantially extends our capabilities for further experiments on quantum information and quantum sensing with Rydberg atoms.

Illumination of a two-dimensional system by a twisted light beam is considered in order to find specific effects caused by twisting. Direct interband transitions between the valence and conduction bands are supposed. The generation rates of the electron orbital momentum is found. A kinetic equation for an orbital momentum distribution function is formulated and solved. The mean electron orbital momentum is found.

Experimental results demonstrating long-term stability of the operation of our atmospheric quantum cryptography setup using the BB84 protocol and polarization coding are presented. It was shown that the “sifted” quantum key distribution rate and the quantum bit error rate in the key remained constant for 1 hour and were equal to 10 kbit/s and 6.5 %, respectively, at a distance between the transmitter and the receiver equal to 20 cm. Theoretical dependences of the secret quantum key generation rate on a quantum channel transmission coefficient for single-photon detectors, which were used in this experiment, and for new detectors with a reduced level of dark pulses are given.

Topological insulators (TIs) represent a new quantum state of matter which is characterized by edge or surface states and an insulating band gap in the bulk. In a two-dimensional (2D) system based on the HgTe quantum well (QW) of critical width random deviations of the well width from its average value result in local crossovers from zero gap 2D Dirac fermion system to either the 2D TI or the ordinary insulator, forming a complicated in-plane network of helical channels along the zero-gap lines. We have studied experimentally the transport properties of the critical width HgTe QWs near the Dirac point, where the conductance is determined by a percolation along the zero-gap lines. The experimental results confirm the presence of percolating conducting channels of a finite width. Our work establishes the critical width HgTe QW as a promising platform for the study of the interplay between topology and localization.

We have developed an improved scheme of a three-qubit Toffoli gate based on fine structure state changing three-body Stark-tuned Rydberg interaction. This scheme is a substantial improvement of our previous proposal [I.I.Beterov et al., Physical Review A 98, 042704 (2018)]. Due to the use of a different type of three-body F\"orster resonance we substantially simplified the scheme of laser excitation and phase dynamics of collective three-body states. This type of F\"orster resonance exists only in systems with more than two atoms, while the two-body resonance is absent. We reduced the sensitivity of the gate fidelity to fluctuations of external electric field and eliminated the necessity to use external magnetic field for fine tuning of the resonant electric field value, compared to the previous scheme of Toffoli gate based on Rydberg atoms. A gate fidelity of >99% was demonstrated in the calculations.

The temporal dynamics of three-photon 5S(1/2) -> 5P(3/2) -> 6S(1/2) -> 39P(3/2) laser excitation of mesoscopic ensembles of cold Rb atoms to Rydberg states in a magneto-optical trap is studied using cw single-frequency lasers at each stage. The ensembles comprise N = 1-5 atoms and are detected by the method of selective field ionisation with postselection with respect to the number of atoms. The dependence of the excitation probability on the duration of the exciting laser pulses and the number of detected Rydberg atoms is investigated. At short interaction times, a linear increase in probabilities is observed, and at large times, the probabilities reach saturation, while each number of atoms has its own characteristic features. The experimental dependences are compared with the results of numerical calculations in the framework of a four-level model, and their good agreement is obtained. The conditions necessary for observing Rabi population oscillations are determined. The obtained results are important for the application of Rydberg atoms in quantum information.

A two-dimensional Wigner cluster (2DWC) with the number of electrons up to 200 in a parabolic potential well has been studied numerically and analytically. It has been shown that the inner part of the 2DWC in the axisymmetric potential well is polycrystalline, whereas electrons in outer layers form pronounced circular shells. The scaling of the cluster under the variation of the stiffness of the potential well has been considered. The threshold of the free rotation of the solid cluster in the axisymmetric potential well has been determined. The action of an alternating magnetic field generated by a coaxial solenoid on the 2DWC has been examined. It has been shown that the initially immobile solid 2DWC subjected to a weak vortex electric field begins to rotate at an angular velocity equal to half the cyclotron frequency. Furthermore, in a stronger vortex field, the cluster not only rotates but also begins to be periodically compressed, holding its structure. A further increase in the vortex field can lead to the total collapse of the cluster accompanied by the destruction of its structure. A sufficiently strong vortex electric field can also result in the differential rotation of the shells of the 2DWC. The rotational friction coefficient caused by ohmic losses in the gate, which can restrict the free rotation of the 2DWC, has been determined.

We develop a theory of circular photogalvanic effect in nongyrotropic two-dimensional transition metal dichalcogenide monolayers under interband optical transitions. Oblique incidence of circularly polarized electromagnetic field or normal incidence of elliptically polarized electromagnetic field is assumed. In contrast to the linear-in-intensity conventional photogalvanic effect, the effect considered here arises in the second intensity order. The effect is conditioned by (i) the predominant population of the valleys by the circular in-plane electromagnetic field component and (ii) the direct drift of the photoexcited carriers by the linear-polarized in-plane electromagnetic field component in the presence of trigonal valley asymmetry.

2D topological insulator edge states are considered within the Volkov-Pankratov Hamiltonian. A smooth transition between a topological and ordinary insulator is assumed. The edge states are formed in the total gap of homogeneous 2D material. We found the energy spectrum, wave functions, together with the matrix elements of the impurity potential, and the velocity operator between these states. A pair of states have linear dispersion (the Weyl states), others have gapped Dirac spectra. Optical selection rules are found. It is stated that the Weyl states do not experience the backscattering, while the elastic scattering is permitted between the Dirac states or between the Weyl and Dirac states.