arXiv subjects

I. I. Beterov

Publications and source records attributed to I. I. Beterov.

At least 19 recordsLinked to original sources

arXiv2026

Three-dimensional three-photon Stark spectroscopy of a single Rb Rydberg atom in an ultrahigh-vacuum glass cell with eight electrodes

Quantum computing and quantum simulation with ultracold neutral atoms require Rydberg excitation of individual atoms in atomic arrays. Rydberg states are extremely sensitive to external electric fields, therefore precise three-dimensional control of the electric field is essential. We performed a spectroscopic study of three-photon Rydberg excitation of a single Rb atom in an optical dipole trap in the presence of an external DC electric field. The field was generated by eight electrodes deposited on the inner surfaces of an ultrahigh-vacuum glass cell. The used three-photon scheme of laser excitation of Rydberg \textit{nP} states allows the Stark shift and the splitting of the resonances to be observed simultaneously, which simplifies calibration of the electric field. In addition, in the commonly used two-photon Rydberg excitation schemes, the light shifts can complicate accurate determination of the DC Stark shift, particularly when the external electric field is scanned across different spatial directions, and different Stark components are excited. These shifts are absent in the three-photon excitation scheme used in our experiment. We demonstrated the ability to independently tune the electric field along all three spatial directions and to compensate for stray electric fields. The measured three-photon spectra exhibit Stark shifts and splittings of the three-photon resonance that are in good agreement with theoretical calculations. These results are also of interest for Rydberg electrometry.

physics.atom-ph↗

arXiv2026

Symmetric $C_Z$ gate for ultracold neutral atoms based on counterdiabatic driving at Rydberg excitation

We designed a scheme for a neutral atom Rydberg blockade $C_Z$ gate based on the double sequence of adiabatic pulses applied symmetrically to both atoms and using counterdiabatic driving for Rydberg excitation. This provides a substantial reduction in the quantum gate operation time compared to previously proposed double adiabatic schemes, and makes our scheme competitive with modern time-optimal protocols for high-fidelity entangling gates with neutral atoms. Our approach creates a bridge between fully adiabatic and time-optimal gate schemes. The use of adiabatic passage reduces the sensitivity of gate fidelity to variations in laser intensity, while counterdiabatic driving provides short gate times. The intensity and phase profiles of the laser pulse acting on the atoms are described analytically depending only on the gate duration. We demonstrated the applicability of this scheme for single-photon and two-photon schemes of Rydberg excitation in rubidium and cesium atoms, and, for the first time, discussed the implementation of a $C_Z$ gate using three-photon excitation of rubidium atoms. In contrast to many modern $C_Z$ gate protocols, our scheme does not generate intrinsic single-qubit phase shifts, although they still appear in two-photon configuration. We also designed a numerically optimized amplitude-robust gate with an analytically defined phase profile of the laser pulse and compared its performance with the counteradiabatic gate scheme.

quant-ph↗

arXiv2026

Numerically optimized amplitude-robust controlled-Z gate for ultracold neutral atoms with individual addressing capability

We numerically optimized a scheme for a neutral atom Rydberg blockade symmetric controlled-Z (CZ) gate to increase its robustness to variations in the Rabi frequency. This gate scheme uses analytically defined phase profiles of the laser pulse and demonstrates increased robustness to variations in the Rabi frequency almost by an order of magnitude compared to previous proposals. We demonstrate the applicability of our gate protocol to individual addressing in Rydberg excitation, taking into account the asymmetry of Rabi frequencies for two atoms that are individually excited by tightly focused laser beams. This allows for reducing the effects of residual thermal motion of trapped atoms and beam pointing instability on gate fidelities. We investigated the performance of our gate protocol for single-photon and two-photon Rydberg excitation schemes and showed its advantages for individual addressing at finite temperatures of trapped atoms.

quant-ph↗

arXiv2026

Splitting of the three-body Förster resonance in Rb Rydberg atoms as a measure of dipole-dipole interaction strength

Three-body Förster resonances controlled by a dc electric field are of interest for the implementation of three-qubit quantum gates with single atoms in optical traps using their laser excitation into strongly interacting Rydberg states. In our recent theoretical paper [Zh. Eksper. Teor. Fiz. 168(1), 14 (2025)] it was found that the proposed earlier three-body Förster resonance $3\times nP_{3/2} \to nS_{1/2} +(n+1)S_{1/2} +nP_{1/2} $ in Rb Rydberg atoms has a splitting, with one of the split components having weaker dependence of the resonant electric field (and the corresponding dynamic shift) on the distance $R$ between the atoms. Here we study this effect in more detail, since such a resonance is the most suitable for performing experiments on observing coherent oscillations of populations of collective three-body states and implementing three-qubit quantum gates based on them. For a linear spatial configuration of three interacting Rydberg atoms, the physical mechanism of this phenomenon is revealed and analytical formulas are obtained that describe the behavior of split structure of the Förster resonance depending on $R$. It is found that the splitting is a measure of the energy of the resonant dipole-dipole exchange interaction with an excitation hopping between neighboring Rydberg states $S$ and $P$.

physics.atom-ph↗

arXiv2025

Investigation of three-body Förster resonance for various spatial configurations of the three interacting Rubidium Rydberg atoms

Three-body Förster resonances controlled by a dc electric field are of interest for the implementation of three-qubit quantum gates with single atoms captured in optical traps and laser-excited into strongly interacting Rydberg states. In Ref. [P. Cheinet et al., Quantum Electronics 50(3), 213 (2020)], we proposed and analyzed a new type of three-body Förster resonance ${\rm 3}\times nP_{3/2} \to nS_{1/2} +(n+1)S_{1/2} +nP_{1/2}$ that can be realized with Rb Rydberg atoms for an arbitrary principal quantum number $n$. Its peculiarity is that the third atom goes into a state with a total angular moment $J=1/2$, which has no Stark structure, so two-body Förster resonances are completely absent. In the present work, an extended theoretical study of this three-body Förster resonance is performed for various spatial configurations of three interacting Rb Rydberg atoms and conditions for their experimental implementation are determined. It was found that one of the resonances has a weak dependence of the resonant electric field on the distance between atoms and is therefore most suitable for performing experiments to observe coherent oscillations of populations of collective three-body states and implement three-qubit quantum gates based on them.

physics.atom-ph↗

arXiv2025

Long-range $CCΦ$ gates via radio-frequency-induced Förster resonances

Registers of trapped neutral atoms, excited to Rydberg states to induce strong long-distance interactions, are extensively studied for direct applications in quantum computing. Here, we present a novel $CCΦ$ quantum phase gate protocol based on radio-frequency-induced Förster resonant interactions in the array of highly excited $^{87}$Rb atoms. The extreme controllability of interactions provided by RF field application enables high-fidelity and robust gate performance for a wide range of parameters of the atomic system, as well as it significantly facilitates the experimental implementation of the gate protocol. Taking into account finite Rydberg states lifetimes, we achieve an average theoretical gate fidelity of $99.27 \%$ under room-temperature conditions (improved up to $99.65 \%$ in a cryogenic environment), thus showing the protocol compatibility with modern quantum error correction techniques.

quant-ph↗

arXiv2024

High-Fidelity Individual Addressing of Single Atoms in Quantum Registers at Three-Photon Laser Excitation of Rydberg States

Precise individual addressing of single atoms in quantum registers formed by optical trap arrays is essential to achieve high-fidelity quantum gates in neutral-atom quantum computers and simulators. Two-qubit quantum gates are typically realized using coherent two-photon laser excitation of atoms to strongly interacting Rydberg states. However, two-photon excitation encounters challenges in individual addressing with tightly focused laser beams due to atom position uncertainty and the spatial inhomogeneity in both Rabi frequencies and light shifts. In this work, we theoretically demonstrate that the fidelity of individual addressing can be improved by employing coherent three-photon laser excitation of Rydberg states. For a specific example of $5s_{1/2}\!\xrightarrow{Ω_1}\!5p_{3/2}\!\xrightarrow{Ω_2}\!6s_{1/2}\!\xrightarrow{Ω_3}\!np$ excitation in $^{87}$Rb atoms, we find that upon strong laser coupling in the second step (Rabi frequency $Ω_2$) and moderate coupling in the first and third steps (Rabi frequencies $Ω_1$ and $Ω_3$), the three-photon Rabi frequency is given by $Ω\!=\!Ω_1Ω_3/Ω_2$. If the spatial distributions of $(Ω_1Ω_3)$ and $Ω_2$ are arranged to be identical, $Ω$ becomes independent of atom position, even within very tightly focused laser beams. This approach dramatically improves individual addressing of Rydberg excitation for neighboring atoms in trap arrays compared to conventional two-photon excitation schemes. Our findings are crucial for large-scale quantum registers of neutral atoms, where distances between adjacent atoms should be minimized to ensure stronger Rydberg interactions and compact arrangement of atom arrays.

quant-ph↗

arXiv2024

Rabi oscillations at three-photon laser excitation of a single rubidium Rydberg atom in an optical dipole trap

In an experiment on three-photon laser excitation $5S_{1/2} \to 5P_{3/2} \to 6S_{1/2} \to 37P_{3/2}$ of a single $^{87}$Rb Rydberg atom in an optical dipole trap, we have observed for the first time three-photon Rabi oscillations between the ground and the Rydberg states. The single atom was detected optically by measuring the signal of resonant fluorescence with a low-noise sCMOS video camera. Relative probability of the atom to remain in the trap after the action of three synchronized laser excitation pulses was measured for their durations varied in the range from 100 ns to 2 $μ$s. A specific feature of the experiment was the usage of intense laser radiation at the wavelength of 1367 nm on the second excitation step, which provided the single-photon Rabi frequency up to 2 GHz to control the effective detunings of the intermediate levels of the three-photon transition due to ac Stark effect. We have detected Rabi oscillations with frequency from 1 to 5 MHz depending on the intensities of the laser pulses on the first and the second excitation steps with the coherence time of 0.7-0.8 $μ$s. The ways to increase the coherence time and contrast of the three-photon Rabi oscillations for applications in quantum information processing with Rydberg atoms are discussed.

physics.atom-ph↗

arXiv2024

Generation of quantum phases of matter and finding a maximum-weight independent set of unit-disk graphs using Rydberg atoms

Recent progress in quantum computing and quantum simulation of many-body systems with arrays of neutral atoms using Rydberg excitation has provided unforeseen opportunities towards computational advantage in solving various optimization problems. The problem of a maximum-weight independent set of unit-disk graphs is an example of an NP-hard optimization problem. It involves finding the largest set of vertices with the maximum sum of their weights for a graph which has edges connecting all pairs of vertices within a unit distance. This problem can be solved using quantum annealing with an array of interacting Rydberg atoms. For a particular graph, a spatial arrangement of atoms represents vertices of the graph, while the detuning from resonance at Rydberg excitation defines the weights of these vertices. The edges of the graph can be drawn according to the unit disk criterion. Maximum-weight independent sets can be obtained by applying a variational quantum adiabatic algorithm. We consider driving the quantum system of interacting atoms to the many-body ground state using a non-linear quasi-adiabatic profile for sweeping the Rydberg detuning. We also propose using a quantum wire which is a set of auxiliary atoms of a different chemical element to mediate strong coupling between the remote vertices of the graph. We investigate this effect for different lengths of the quantum wire. We also investigate the quantum phases of matter realizing commensurate and incommensurate phases in one- and two-dimensional spatial arrangements of the atomic array.

quant-ph↗

arXiv2024

Toffoli gate based on a three-body fine-structure-state-changing Förster resonance in Rydberg atoms

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 Förster resonance we substantially simplified the scheme of laser excitation and phase dynamics of collective three-body states. This type of Förster 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.

quant-ph↗

arXiv2023

Parallel implementation of CNOT$^{N}$ and C$_2$NOT$^2$ gates via homonuclear and heteronuclear Förster interactions of Rydberg atoms

We analyze schemes of high-fidelity multiqubit CNOT$^{N}$ and C$_{2}$NOT$^{2}$ gates for alkali-metal neutral atoms used as qubits. These schemes are based on the electromagnetically induced transparency and Rydberg blockade, as proposed by M. Müller et al. [PRL 102, 170502 (2009)]. In the original paper, the fidelity of multi-qubit CNOT$^{\text{N}}$ gate based on Rydberg blockade was limited by the undesirable interaction between the target atoms, and by the coupling laser intensity. We propose overcoming these limits by using strong heteronuclear dipole-dipole interactions via Förster resonances for control and target atoms, while the target atoms are coupled by weaker van der Waals interaction. We have optimized the gate performance in order to achieve higher fidelity, while keeping coupling laser intensity as small as possible in order to improve the experimental feasibility of the gate schemes. We also considered optimization of schemes of C$_{2}$NOT$^{2}$ gates, where the fidelity is affected by the relation between the control-control, control-target and target-target interaction energies. Our numeric simulations confirm that the fidelity of CNOT$^4$ gate (single control and four target atoms) can be up to $99.3\%$ and the fidelity of C$_2$NOT$^2$ (two control and two target atoms) is up to $99.7\%$ for the conditions which are experimentally feasible.

quant-ph↗

arXiv2023

Mathematical problems and solutions of the Ninth International Olympiad in Cryptography NSUCRYPTO

Every year the International Olympiad in Cryptography Non-Stop University CRYPTO (NSUCRYPTO) offers mathematical problems for university and school students and, moreover, for professionals in the area of cryptography and computer science. The mail goal of NSUCRYPTO is to draw attention of students and young researchers to modern cryptography and raise awareness about open problems in the field. We present problems of NSUCRYPTO'22 and their solutions. There are 16 problems on the following topics: ciphers, cryptosystems, protocols, e-money and cryptocurrencies, hash functions, matrices, quantum computing, S-boxes, etc. They vary from easy mathematical tasks that could be solved by school students to open problems that deserve separate discussion and study. So, in this paper, we consider several open problems on three-pass protocols, public and private keys pairs, modifications of discrete logarithm problem, cryptographic permutations and quantum circuits.

cs.CR↗

arXiv2023

Scalable Heteronuclear Architecture of Neutral Atoms Based on EIT

Based on our recent paper [arXiv:2206.12176 (2022)], we propose a scalable heteronuclear architecture of parallel implementation of CNOT gates in arrays of alkali-metal neutral atoms for quantum information processing. We considered a scheme where we perform CNOT gates in a parallel manner within the array, while they are performed sequentially between the pairs of neighboring qubits by coherently transporting an array of atoms of one atomic species (ancilla qubits) using an array of mobile optical dipole traps generated by a 2D acousto-optic deflector (AOD). The atoms of the second atomic species (data qubits) are kept in the array of static optical dipole traps generated by spatial light modulator (SLM). The moving ancillas remain in the superposition of their logical ground states without loss of coherence, while their transportation paths avoid overlaps with the spatial positions of data atoms. We numerically optimized the system parameters to achieve the fidelity for parallelly implemented CNOT gates around $\mathcal{F}=95\%$ for the experimentally feasible conditions. Our design can be useful for implementation of surface codes for quantum error correction. Renyi entropy and mutual information are also investigated to characterize the gate performance.

quant-ph↗

arXiv2020

Searching optimal conditions for quantum gates application with the new 3-body Förster resonances in Rb and Cs Rydberg atoms

Three body resonant interactions between Rydberg atoms are considered in order to perform few-body quantum gates. So far, the resonances found in cesium or rubidium atoms relied on an adjacent two-body resonance which ceases to exist for principal quantum numbers above $n \simeq 40$. We have proposed recently a new class of 3-body interaction resonances in alkali-metal Rydberg atoms [P. Cheinet \textit{et al.}, Quant. Elect. \textbf{50}, 213 (2020)], which circumvienes this limit. We investigate here the relative strength between this new class of 3-body interaction resonance and quasi-forbidden 2-body interaction resonances in rubidium and cesium Rydberg atoms. We then identify the best case scenario for detecting and using this 3-body interaction.

physics.atom-ph↗

arXiv2020

Symmetric Rydberg controlled-Z gates with adiabatic pulses

We analyze neutral atom Rydberg $C_Z$ gates based on adiabatic pulses applied symmetrically to both atoms. Analysis with smooth pulse shapes and Cs atom parameters predicts the gates can create Bell states with fidelity ${\mathcal F}>0.999$ using adiabatic rapid passage (ARP) pulses. With globally optimized adiabatic pulse shapes, in a two-photon excitation process, we generate Bell states with fidelity ${\mathcal F}=0.997$. The analysis fully accounts for spontaneous emission from intermediate and Rydberg states, including the Rydberg lifetime in a room temperature environment, but does not include errors arising from laser noise. The gate protocols do not require individual addressing and are shown to be robust against Doppler shifts due to atomic motion.

quant-ph↗

arXiv2020

Observation of the Dipole Blockade Effect in Detecting Rydberg Atoms by the Selective Field Ionization Method

The dipole blockade effect at laser excitation of mesoscopic ensembles of Rydberg atoms lies in the fact that the excitation of one atom to a Rydberg state blocks the excitation of other atoms due to the shift in the collective energy levels of interacting Rydberg atoms. It is used to obtain the entangled qubit states based on single neutral atoms in optical traps. In this paper, we present our experimental results on the observation of the dipole blockade for mesoscopic ensembles of 1-5 atoms when they are detected by the selective field ionization method. We investigated the spectra of the three-photon laser excitation $ 5S_{1/2} \to 5P_{3/2} \to 6S_{1/2} \to nP_{3/2} $ of cold Rb Rydberg atoms in a magneto-optical trap. We have found that for mesoscopic ensembles this method allows only a partial dipole blockage to be observed. This is most likely related to the presence of parasitic electric fields reducing the interaction energy of Rydberg atoms, the decrease in the probability of detecting high states, and the strong angular dependence of the interaction energy of Rydberg atoms in a single interaction volume.

physics.atom-ph↗

arXiv2020

Three-body Förster resonance of a new type in Rydberg atoms

The three-body Förster resonances ${\rm 3}\times nP_{3/2} \to nS_{1/2} +(n+1)S_{1/2} +nP_{3/2}^{*} $ controlled by a dc electric field were realized earlier by the authors in an ensemble of several cold Rydberg Rb atoms. One of the drawbacks of such resonances for potential application in three-qubit quantum gates is the proximity of the two-body Förster resonance ${\rm 2}\times nP_{3/2} \to nS_{1/2} +(n+1)S_{1/2}, $ as well as the possibility of their implementation only for states with values of the principal quantum numbers $n\le 38$. In this paper we propose and analyze a three-body resonance of a new type ${\rm 3}\times nP_{3/2} \to nS_{1/2} +(n+1)S_{1/2} +nP_{1/2} , $ which can be realized for arbitrary $n$. Its specific feature is also that the third atom transits into a state with a different total angular moment $J=1/2$, which has no Stark structure, so that the two-body resonance is completely absent. Numerical calculations showed that for not too strong interaction, it is possible to observe coherent three-body oscillation of the populations of collective states, which is of interest for developing new schemes of three-qubit quantum gates controlled by an electric field.

physics.atom-ph↗

arXiv2020

Application of adiabatic passage in Rydberg atomic ensembles for quantum information processing

We review methods for coherently controlling Rydberg quantum states of atomic ensembles using Adiabatic Rapid Passage and Stimulated Raman Adiabatic Passage. These methods are commonly used for population inversion in simple two-level and three-level systems. We show that adiabatic techniques allow us to control population and phase dynamics of complex entangled states of mesoscopic atomic ensembles for quantum information processing with Rydberg atoms. We also propose several schemes of single-qubit and two-qubit gates based on adiabatic passage, Rydberg blockade and Förster resonances in Rydberg atoms.

quant-ph↗