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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 $5s_{1/2}\!\xrightarrow{\Omega_1}\!5p_{3/2}\!\xrightarrow{\Omega_2}\!6s_{1/2}\!\xrightarrow{\Omega_3}\!np$ excitation in $^{87}$Rb atoms, we find that upon strong laser coupling in the second step (Rabi frequency $\Omega_2$) and moderate coupling in the first and third steps (Rabi frequencies $\Omega_1$ and $\Omega_3$), the three-photon Rabi frequency is given by $\Omega \!=\!\Omega_1\Omega_3/\Omega_2$. If the spatial distributions of $(\Omega_1\Omega_3)$ and $\Omega_2$ are arranged to be identical, $\Omega$ 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., Comment: 7 pages, 4 figures

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 $\mu$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 $\mu$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., Comment: 14 pages, 6 figures

Fourier transform spectra of Nd Penning and hollow cathode discharge lamps were recorded within the region 32,500-54,000 cm$^{-1}$ (3077-1852 {\AA}) and grating spectra of Nd vacuum sliding sparks were recorded within the regions 820-1159 {\AA} and 1600-3250 {\AA}. New energy levels were found using the observed wavelengths measured accurate to a few parts in $10^8$ in Fourier transform spectra and to a few parts in $10^7$ in grating spectra. Atomic structure and transition probability calculations of Nd III were made using the Cowan codes by adjusting energy parameters to fit all known Nd III levels. Nd-rich stellar spectra were also used to evaluate the new calculations. In total, 355 transitions were classified from observed spectra involving 116 previously experimentally unknown energy levels of the 4f$^3$7s, 4f$^3$6d, and 4f$^3$5f configurations of Nd III, all reported here for the first time. One newly identified level of the 4f$^3$5d configuration is also reported. Typical level energy uncertainties are 0.01 cm$^{-1}$ for the 4f$^3$7s and 4f$^3$6d levels and 0.3 cm$^{-1}$ for the 4f$^3$5f levels. In addition, calculated energy levels up to 130,936 cm$^{-1}$ are presented, including eigenvector composition and calculated level lifetimes. Calculated transition probabilities and wavelengths between 1900-50,000 {\AA} are also presented. Using newly established levels of the 4f$^3$7s configuration and the recently established levels of the 4f$^3$6s configuration, the ionisation energy of Nd III was estimated at $178,090\pm330$ cm$^{-1}$, doubling the accuracy of the previously published value.

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., Comment: 13 pages, 9 figures

We investigated the absence of certain bright peaks in Autler-Townes laser excitation spectra of alkali metal atoms. Our research revealed that these dips in the spectra are caused by a specific architecture of adiabatic (or ``laser-dressed'') states in hyperfine (HF) components. The dressed states' analysis pinpointed several cases where constructive and destructive interference between HF excitation pathways in a two-photon excitation scheme limits the available two-photon transitions. This results in a reduction of the conventional two-photon selection rule for the total angular momentum $F$, from $\Delta F= 0,\pm 1$ to $\Delta F\equiv 0$. Our discovery presents practical methods for selectively controlling the populations of unresolvable HF $F$-components of $ns_{1/2}$ Rydberg states in alkali metal atoms. Using numerical simulations with sodium and rubidium atoms, we demonstrate that by blocking the effects of HF interaction with a specially tuned auxiliary control laser field, the deviations from the ideal selectivity of the HF components population can be lower than $0.01\%$ for Na and $0.001\%$ for Rb atoms., Comment: 20 pages, 14 figures, to be submitted to PRA. Changelog: * added missing ORCID iDs; * Notation used in figures 4,6 is now consistent with the rest of the manuscript: Pump paser -> S-laser; * corrected typos, more precise language througout the paper; * improved legibility of labels in figures 4-8

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 $CC\Phi$ quantum phase gate protocol based on radio-frequency-induced F\"{o}rster 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 and atomic position control imperfections, we achieve theoretical gate fidelities of up to $99.7 \%$ in a cryogenic environment, thus showing the protocol compatibility with modern quantum error correction techniques., Comment: 11 pages, 6 figures, 1 table

Emission spectra of neodymium (Nd, Z=60) were recorded using Penning and hollow cathode discharge lamps in the region 11500-54000 cm$^{-1}$ (8695-1852 \r{A}) by Fourier transform spectroscopy at resolving powers up to 106. Wavenumber measurements were accurate to a few 10$^{-3}$ cm$^{-1}$. Grating spectroscopy of Nd vacuum sliding sparks and stellar spectra were used to aid line and energy level identification. The classification of 433 transitions of doubly-ionised neodymium (Nd III) from the Penning lamp spectra resulted in the determination of 144 energy levels of the 4f$^4$, 4f$^3$5d, 4f$^3$6s, and 4f$^3$6p configurations of Nd III, 105 of which were experimentally established for the first time. Of the 40 previously published Nd III levels, 1 was revised and 39 were confirmed. New Nd III atomic structure calculations were made using the Cowan code parameterised by newly established levels. These results will not only benchmark and improve future semi-empirical atomic structure calculations of Nd III, but also enable more reliable astrophysical applications of Nd III, such as abundance analyses of kilonovae and chemically peculiar stars, and studies of pulsational wave propagation in these stars.

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., Comment: 8 pages, 6 figures

The spectrum of eight-times ionized iron, Fe IX, was studied in the 110-200 {\AA} region. A low inductance vacuum spark and a 3-m grazing incidence spectrograph were used for the excitation and recording of the spectrum. Previous analyses of Fe IX have been greatly extended and partly revised. The numbers of known lines in the 3p^53d - 3p^54f and 3p^53d - 3p^43d^2 transition arrays are extended to 25 and 81, respectively. Most of the identifications of the Fe IX lines from the 3p^53d - 3p^43d^2 transition array in the solar spectrum have been confirmed and several new identifications are suggested., Comment: Accepted by ApJ, 24 pages, 7 figures, 5 tables

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. M\"{u}ller 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 F\"{o}rster 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., Comment: 15 pages, 13 figures. Supplementary datasets are available from here: https://doi.org/10.5281/zenodo.8154008

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.

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., Comment: 5 pages, 3 figures, 2 tables

The identifications of Fe VII emission lines in the wavelength range 193-197 {\AA} are discussed in the light of new measurements of laboratory spectra and atomic data calculations. This region is of importance to studies of solar spectra from the EUV Imaging Spectrometer (EIS) on board the Hinode spacecraft, which has its peak sensitivity at these wavelengths. Ten lines are measured, arising from seven fine structure levels in the $3p^53d^3$ configuration. Two lines have not previously been reported and lead to new experimental energies for the $(a^2D)^3F_{2,3}$ levels. Updated experimental energies are obtained for the remaining levels. The new atomic model is used to compute theoretical values for the two density diagnostic ratios $\lambda$196.21/$\lambda$195.39 and $\lambda$196.21/$\lambda$196.06, and densities are derived from EIS spectra of coronal loop footpoints., Comment: Accepted by ApJ; 10 pages; 4 figures

We introduce a real-time, high-resolution background replacement technique which operates at 30fps in 4K resolution, and 60fps for HD on a modern GPU. Our technique is based on background matting, where an additional frame of the background is captured and used in recovering the alpha matte and the foreground layer. The main challenge is to compute a high-quality alpha matte, preserving strand-level hair details, while processing high-resolution images in real-time. To achieve this goal, we employ two neural networks; a base network computes a low-resolution result which is refined by a second network operating at high-resolution on selective patches. We introduce two largescale video and image matting datasets: VideoMatte240K and PhotoMatte13K/85. Our approach yields higher quality results compared to the previous state-of-the-art in background matting, while simultaneously yielding a dramatic boost in both speed and resolution.

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., Comment: 16 pages, 7 figures

In this paper, we consider the conjugate gradient method for solving the problem of minimizing a quadratic function with additive noise in the gradient. Three concepts of noise were considered: antagonistic noise in the linear term, stochastic noise in the linear term, and noise in the quadratic term, as well as combinations of the first and second with the last. It was experimentally obtained that error accumulation is absent for any of the considered concepts, which differs from the folklore opinion that, as in accelerated methods, error accumulation must take place. The paper gives motivation for why the error may not accumulate. The dependence of the solution error both on the magnitude (scale) of the noise and on the size of the solution using the conjugate gradient method was also experimentally investigated. Hypotheses about the dependence of the error in the solution on the noise scale and the size (2-norm) of the solution are proposed and tested for all the concepts considered. It turned out that the error in the solution (by function) linearly depends on the noise scale. The work contains graphs illustrating each individual study, as well as a detailed description of numerical experiments, which includes an account of the methods of the noise of both the vector and the matrix., Comment: 14 pages, in Russian, 10 figures

The three-body F\"orster 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 F\"orster 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., Comment: 9 pages, 4 figures

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 F\"{o}rster resonances in Rydberg atoms., Comment: 13 pages, 15 figures. This is a tutorial, submitted to Journal of Physics B. arXiv admin note: text overlap with arXiv:1606.08198, arXiv:1310.3921