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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

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

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

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

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 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

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

We demonstrate a hybrid method based on field ionization and state-selective de-excitation capable of measuring the lifetimes of high-lying Rydberg states. For nS Rydberg states of Rb atoms with principal quantum number $60\leq n\leq88$, we measure both the individual target state lifetimes and those of the ensemble of Rydberg states populated via black-body radiation-induced transitions. We find good overall agreement with numerical calculations of the expected lifetimes in both cases. However, for the target state lifetimes, we find a local deviation towards shorter lifetimes for states around $n=72$, which we interpret as a signature of a modified black-body spectrum in the finite volume in which our experiments take place., Comment: 7 pages, 3 figures

We propose a scheme of fast three-qubit Toffoli quantum gate for ultracold neutral-atom qubits. The scheme is based on the Stark-tuned three-body F\"{o}rster resonances, which we have observed in our recent experiment [D.B.Tretyakov et al., Phys.Rev.Lett. 119, 173402 (2017)]. The three-body resonance corresponds to a transition when the three interacting atoms change their states simultaneously, and it occurs at a different dc electric field with respect to the two-body F\"{o}rster resonance. A combined effect of three-body and two-body F\"{o}rster interactions in external electric and magnetic fields near the three-body resonance results in complex coherent behavior of the populations and phases of collective states of a three-atom system. We have found that it is possible to obtain experimental conditions suitable to implement three-qubit Toffoli gate with 96.8\% fidelity and less than 3~$\mu$s duration., Comment: 7 pages, 5 figures, Version 2 revised according to referee's comments. Typo in Eq.(2) corrected in Version 3

We have observed recently the Stark-tuned three-body F\"orster resonances ${\rm 3}\times nP_{3/2} (|M|)\to nS_{1/2} +(n+1)S_{1/2} +nP_{3/2} (|M^{*} |)$ at long-range interactions of a few cold Rb Rydberg atoms [D.B.Tretyakov et al., Phys. Rev. Lett. 119, 173402 (2017)]. The three-body resonance appears at a different dc electric field with respect to the ordinary two-body resonance ${\rm 2}\times nP_{3/2} (|M|)\to nS_{1/2} +(n+1)S_{1/2} $ and corresponds to a transition when the three interacting atoms change their states simultaneously (two atoms go to the $S$ states, and the third atom remains in the $P$ state but changes its moment projection), with the negligible contribution of the two-body resonance to the population transfer. It thus has a Borromean character and represents an effective three-body operator, which can be used to directly control the three-body interactions in quantum simulations and quantum gates implemented with Rydberg atoms. In this paper we theoretically investigate the coherence of such three-body resonances and we show that high-contrast Rabi-like population oscillations are possible for the localized Rydberg atoms in a certain spatial configuration. This paves the way to implementing three-qubit quantum gates and quantum simulations based on three-body Rydberg interactions., Comment: 14 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:1707.01636

High-fidelity entangled Bell states are of great interest in quantum physics. Entanglement of ultracold neutral atoms in two spatially separated optical dipole traps is promising for implementation of quantum computing and quantum simulation and for investigation of Bell states of material objects. We propose a new method to entangle two atoms via long-range Rydberg-Rydberg interaction. Alternatively to previous approaches, based on Rydberg blockade, we consider radiofrequency-assisted Stark-tuned F\"{o}rster resonances in Rb Rydberg atoms. To reduce the sensitivity of the fidelity of Bell states to the fluctuations of interatomic distance, we propose to use the double adiabatic passage across the radiofrequency-assisted Stark-tuned F\"{o}rster resonances, which results in a deterministic phase shift of the two-atom state., Comment: 8 pages, 7 figures

Three-body F\"orster resonances at long-range interactions of Rydberg atoms were first predicted and observed in Cs Rydberg atoms by R.Faoro et al., Nature Comm. 6, 8173 (2015). In these resonances, one of the atoms carries away an energy excess preventing the two-body resonance, leading thus to a Borromean type of F\"orster energy transfer. But they were in fact observed as the average signal for the large number of atoms $N\gg1$. In this Letter we report on the first experimental observation of the three-body F\"orster resonances ${\rm 3}\times nP_{3/2} (|{\rm M}|)\to nS_{1/2} +(n+1)S_{1/2} +nP_{3/2} (|{\rm M}^{*} |)$ in a few Rb Rydberg atoms with $n=36, 37$. We have found here clear evidence that there is no signature of the three-body F\"orster resonance for exactly two interacting Rydberg atoms, while it is present for $N=3-5$ atoms. This demonstrates the assumption that three-body resonances can generalize to any Rydberg atom. As such resonance represents an effective three-body operator, it can be used to directly control the three-body interactions in quantum simulations and quantum information processing with Rydberg atoms., Comment: 8 pages, 5 figures

We propose schemes of controlled-Z and controlled-NOT gates with ultracold neutral atoms based on deterministic phase accumulation during double adiabatic passage of the Stark-tuned F\"{o}rster resonance of Rydberg states. The effect of deterministic phase accumulation during double adiabatic passage in a two-level quantum system has been analyzed in detail. Adiabatic rapid passage using nonlinearly chirped pulses with rectangle intensity profile has been discussed. Nonlinear time dependence of the energy detuning from the F\"{o}rster resonance is used to achieve a high fidelity of population transfer between Rydberg states. Fidelity of two-qubit gates has been studied with an example of the $90S+96S\to 90P+95P$ Stark-tuned F\"{o}rster resonance in Cs Rydberg atoms., Comment: 10 pages, 7 figures. Version 2 revised according to the referees' comments. Fig.1 replaced in Version 3. Accepted to PRA

The observation of the Stark-tuned F\"orster resonances between Rydberg atoms excited by narrowband cw laser radiation requires usage of a Stark-switching technique in order to excite the atoms first in a fixed electric field and then to induce the interactions in a varied electric field, which is scanned across the F\"orster resonance. In our experiments with a few cold Rb Rydberg atoms we have found that the transients at the edges of the electric pulses strongly affect the line shapes of the F\"orster resonances, since the population transfer at the resonances occurs on a time scale of $\sim$100 ns, which is comparable with the duration of the transients. For example, a short-term ringing at a certain frequency causes additional radio-frequency-assisted F\"orster resonances, while non-sharp edges lead to asymmetry. The intentional application of the radio-frequency field induces transitions between collective states, whose line shape depends on the interaction strengths and time. Spatial averaging over the atom positions in a single interaction volume yields a cusped line shape of the F\"orster resonance. We present a detailed experimental and theoretical analysis of the line shape and time dynamics of the Stark-tuned F\"orster resonances ${\rm Rb}(nP_{3/2} )+{\rm Rb}(nP_{3/2} )\to {\rm Rb}(nS_{1/2} )+{\rm Rb}([n+1]S_{1/2} )$ for two Rb Rydberg atoms interacting in a time-varying electric field., Comment: 16 pages, 8 figures

Atoms in highly excited (Rydberg) states have a number of unique properties which make them attractive for applications in quantum information. These are large dipole moments, lifetimes and polarizabilities, as well as strong long-range interactions between Rydberg atoms. Experimental methods of laser cooling and precision spectroscopy enable the trapping and manipulation of single Rydberg atoms and applying them for practical implementation of quantum gates over qubits of a quantum computer based on single neutral atoms in optical traps. In this paper, we give a review of the experimental and theoretical work performed by the authors at the Rzhanov Institute of Semiconductor Physics SB RAS and Novosibirsk State University on laser and microwave spectroscopy of cold Rb Rydberg atoms in a magneto-optical trap and on their possible applications in quantum information. We also give a brief review of studies done by other groups in this area., Comment: 20 pages, 12 figures

We have numerically simulated quantum tomography of single-qubit and two-qubit quantum gates with qubits represented by mesoscopic ensembles containing random numbers of atoms. Such ensembles of strongly interacting atoms in the regime of Rydberg blockade are known as Rydberg superatoms. The Stimulated Raman Adiabatic Passage (STIRAP) in the regime of Rydberg blockade is used for deterministic Rydberg excitation in the ensemble, required for storage of quantum information in the collective state of the atomic ensemble and implementation of two-qubit gates. The optimized shapes of the STIRAP pulses are used to achieve high fidelity of the population transfer. Our simulations confirm validity and high fidelity of single-qubit and two-qubit gates with Rydberg superatoms., Comment: 12 pages, 7 figures, to appear in Special issue on Rydberg atomic physics of Journal of Physics B. Typos in Table 2 corrected in version 3

We have implemented a simple and cost-effective digital system for long-term frequency stabilisation and locking to an arbitrary wavelength of the single-frequency ring CW Ti:Sapphire laser. This system is built around two confocal Fabry-Perot cavities, one of which is used to narrow short-term line width of the laser and the other to improve long-term stability of the laser frequency. The second interferometer is also in the path of the radiation from an external-cavity diode laser stabilized to an atomic transition. Our system is an extension of a commercial Tekhnoscan laser lock. This system has been successfully used in experiments on high-resolution laser spectroscopy of ultracold Rydberg atoms., Comment: 15 pages, 4 figures, to appear in Optical Engineering

We show that Jaynes-Cummings dynamics can be observed in mesoscopic atomic ensembles interacting with a classical electromagnetic field in the regime of Rydberg blockade, where the time dynamics of the average number of Rydberg excitations in mesoscopic ensembles displays collapses and revivals typical of this model. As the frequency of Rabi oscillations between collective states of Rydberg blockaded ensembles depends on the number of interacting atoms, for randomly loaded optical dipole traps we predict collapses and revivals of Rabi oscillations. We have studied the effects of finite interaction strengths and finite laser line width on the visibility of the revivals. We have shown that observation of collapses and revivals of Rabi oscillations can be used as a signature of Rydberg blockade without the need to measure the exact number of Rydberg atoms., Comment: 8 pages, 5 figures. Typos in Eq.10 and reference list corrected in v3. Versions 4 and 5 are revised according to referee's suggestions

Long-range interactions between cold Rydberg atoms, which are used in many important applications, can be enhanced using F\"orster resonances between collective many-body states controlled by an external electric field. Here we report on the first experimental observation of highly-resolved radio-frequency-assisted F\"orster resonances in a few cold Rb Rydberg atoms. We also observed radio-frequency-induced F\"orster resonances which cannot be tuned by a dc electric field. They imply an efficient transition from van der Waals to resonant dipole-dipole interaction due to Floquet sidebands of Rydberg levels appearing in the rf-field. This method can be applied to enhance the interactions of almost arbitrary Rydberg atoms with large principal quantum numbers., Comment: 5 pages, 4 figures

We discuss methods for coherently controlling mesoscopic atomic ensembles where the number of atoms varies randomly from one experimental run to the next. The proposed schemes are based on adiabatic passage and Rydberg blockade and can be used for implementation of a scalable quantum register formed by an array of randomly loaded optical dipole traps., Comment: 14 pages, 7 figures, to be published in Proceedings of the 6th International Symposium on Modern Problems of Laser Physics (MPLP-2013)

We present schemes for geometric phase compensation in adiabatic passage which can be used for the implementation of quantum logic gates with atomic ensembles consisting of an arbitrary number of strongly interacting atoms. Protocols using double sequences of stimulated Raman adiabatic passage (STIRAP) or adiabatic rapid passage (ARP) pulses are analyzed. Switching the sign of the detuning between two STIRAP sequences, or inverting the phase between two ARP pulses, provides state transfer with well defined amplitude and phase independent of atom number in the Rydberg blockade regime. Using these pulse sequences we present protocols for universal single-qubit and two-qubit operations in atomic ensembles containing an unknown number of atoms., Comment: 4 figures, supplemental information now included

The structure of the Cooper minima in the transition probabilities and photoionization cross-sections for low-excited and Rydberg nS, nP, nD and nF states of alkali-metal atoms has been studied using a Coulomb approximation and a quasiclassical model. The range of applicability of the quasiclassical model has been defined from comparison with available experimental and theoretical data on dipole moments, oscillator strengths, and photoionization cross-sections. A new Cooper minimum for transitions between rubidium Rydberg states has been found., Comment: 12 pages, 13 figures

Experiments on the spectroscopy of the F\"orster resonance Rb(37P)+Rb(37P) -> Rb(37S)+Rb(38S) and microwave transitions nP -> n'S, n'D between Rydberg states of cold Rb atoms in a magneto-optical trap have been performed. Under ordinary conditions, all spectra exhibited a 2-3 MHz line width independently of the interaction time of atoms with each other or with microwave radiation, although the ultimate resonance width should be defined by the inverse interaction time. Analysis of the experimental conditions has shown that the main source of the line broadening was the inhomogeneous electric field of cold photoions appeared at the excitation of initial Rydberg nP states by broadband pulsed laser radiation. Using an additional pulse of the electric field, which rapidly removed the photoions after the laser pulse, lead to a substantial narrowing of the microwave and F\"orster resonances. An analysis of various sources of the line broadening in cold Rydberg atoms has been conducted., Comment: 10 pages, 6 figures

Three-photon laser excitation of Rydberg states by three different laser beams can be arranged in a star-like geometry that simultaneously eliminates the recoil effect and Doppler broadening. Our analytical and numerical calculations for a particular laser excitation scheme 5S_{1/2}->5P_{3/2}->6S_{1/2}->nP in Rb atoms have shown that compared to the one- and two-photon laser excitation this approach provides much narrower line width and longer coherence time for both cold atom samples and hot vapors, if the intermediate one-photon resonances of the three-photon transition are detuned by more than respective single-photon Doppler widths. This method can be used to improve fidelity of Rydberg quantum gates and precision of spectroscopic measurements in Rydberg atoms., Comment: 7 pages, 4 figures

We propose to use adiabatic rapid passage with a chirped laser pulse in the strong dipole blockade regime to deterministically excite only one Rydberg atom from randomly loaded optical dipole traps or optical lattices. The chirped laser excitation is shown to be insensitive to the random number \textit{N} of the atoms in the traps. Our method overcomes the problem of the $\sqrt {N} $ dependence of the collective Rabi frequency, which was the main obstacle for deterministic single-atom excitation in the ensembles with unknown \textit{N}, and can be applied for single-atom loading of dipole traps and optical lattices., Comment: 6 pages, 5 figures. Version 5 is expanded and submitted to PRA. Typo in Fig.4 corrected in Version 2. Version 3 and 4 are duplicates of V2

Results of numerical Monte Carlo simulations for the Stark-tuned F\"orster resonance and dipole blockade between two to five cold rubidium Rydberg atoms in various spatial configurations are presented. The effects of the atoms' spatial uncertainties on the resonance amplitude and spectra are investigated. The feasibility of observing coherent Rabi-like population oscillations at a F\"orster resonance between two cold Rydberg atoms is analyzed. Spectra and the fidelity of the Rydberg dipole blockade are calculated for various experimental conditions, including nonzero detuning from the F\"orster resonance and finite laser linewidth. The results are discussed in the context of quantum-information processing with Rydberg atoms., Comment: 11 pages, 7 figures

Two-photon ionization of Rubidium atoms in a magneto-optical trap and a Bose-Einstein condensate (BEC) is experimentally investigated. Using 100 ns laser pulses, we detect single ions photoionized from the condenstate with a 35(10)% efficiency. The measurements are performed using a quartz cell with external electrodes, allowing large optical access for BECs and optical lattices., Comment: 14 pages, 7 figures

Cold atoms in highly excited Rydberg states are promising candidates to implement quantum logic gates of a quantum computer via long-range dipole-dipole interaction. Two-qubit gates require a controlled interaction of only two close Rydberg atoms. We report on the first spectroscopic observation of the resonant dipole-dipole interaction between two cold rubidium Rydberg atoms confined in a small laser excitation volume. The interaction strength was controlled by fine-tuning of the Rydberg levels into a Forster resonance using the Stark effect. The observed resonance line shapes are in good agreement with numerical Monte Carlo simulations., Comment: 4 pages, 3 figures, shorter version and references updated in v2

We present our results on the experiments with cold Rb Rydberg atoms in a magneto-optical trap (MOT). Characteristic features of our experiment were the excitation of Rydberg atoms in a small volume within the cold atom cloud and sorting of the measured signals and spectra over the number of registered Rydberg atoms. We have measured the effective lifetime of the Rydberg state 37P, as well as its polarizability in a weak electric field. The results are in good agreement with the theoretical calculations. We have shown that localization of the small excitation volume around the zero-magnetic-field point makes possible to increase the spectral resolution and to obtain narrow microwave resonances in Rydberg atoms without switching off the MOT quadrupole magnetic field. We have measured the dependence of the amplitude of the dipole-dipole interaction resonances on the number of Rydberg atoms, which has a linear character and agrees with the theory for weak dipole-dipole interaction., Comment: 9 pages, 6 figures. To appear in JETP, 2009. Typo in eq.(7) corrected in v2

Rates of depopulation by blackbody radiation (BBR) and effective lifetimes of alkali-metal \textit{nS}, \textit{n}P and \textit{nD} Rydberg states have been calculated in a wide range of principal quantum numbers $n \le 80$ at the ambient temperatures of 77, 300 and 600 K. Quasiclassical formulas were used to calculate the radial matrix elements of the dipole transitions from Rydberg states. Good agreement of our numerical results with the available theoretical and experimental data has been found. We have also obtained simple analytical formulas for estimates of effective lifetimes and BBR-induced depopulation rates, which well agree with the numerical data., Comment: 12 pages, 6 figures, 8 tables. Typo in Eq.16 corrected in V2. Typos in Eq.5 and Eq.9 corrected in V3. Error in calculation of Rb nP_{3/2} effective lifetimes corrected in V4: see new data in Table II and Table VII, Erratum to be published in PRA

We have studied an ionization of alkali-metal Rydberg atoms by blackbody radiation (BBR). The results of the theoretical calculations of ionization rates of Li, Na, K, Rb and Cs Rydberg atoms are presented. Calculations have been performed for nS, nP and nD states which are commonly used in a variety of experiments, at principal quantum numbers n=8-65 and at the three ambient temperatures of 77, 300 and 600 K. A peculiarity of our calculations is that we take into account the contributions of BBR-induced redistribution of population between Rydberg states prior to photoionization and field ionization by extraction electric field pulses. The obtained results show that these phenomena affect both the magnitude of measured ionization rates and shapes of their dependences on n. A Cooper minimum for BBR-induced transitions between bound Rydberg states of Li has been found. The calculated ionization rates are compared with our earlier measurements of BBR-induced ionization rates of Na nS and nD Rydberg states with n=8-20 at 300 K. A good agreement for all states except nS with n>15 is observed. Useful analytical formulas for quick estimation of BBR ionization rates of Rydberg atoms are presented. Application of BBR-induced ionization signal to measurements of collisional ionization rates is demonstrated., Comment: 36 pages, 16 figures. Paper is revised following NJP referees' comments and suggestions

Results of theoretical calculations of ionization rates of Rb and Na Rydberg atoms by blackbody radiation (BBR) are presented. Calculations have been performed for nS, nP and nD states of Na and Rb, which are commonly used in a variety of experiments, at principal quantum numbers n=8-65 and at three ambient temperatures of 77, 300 and 600 K. A peculiarity of our calculations is that we take into account the contributions of BBR-induced redistribution of population between Rydberg states prior to photoionization and field ionization by extraction electric field pulses. The obtained results show that these phenomena affect both the magnitude of measured ionization rates and shapes of their dependencies on n. The calculated ionization rates are compared with the results of our earlier measurements of BBR-induced ionization rates of Na nS and nD Rydberg states with n=8-20 at 300 K. A good agreement for all states except nS with n>15 is observed. We also present the useful analytical formulae for quick estimation of BBR ionization rates of Rydberg atoms., Comment: 14 pages, 6 figures, 6 tables in Appendix

We have developed a simple analytical model describing multi-atom signals that are measured in experiments on dipole-dipole interaction at resonant collisions of a few Rydberg atoms. It has been shown that finite efficiency of the selective field-ionization detector leads to the mixing up of the spectra of resonant collisions registered for various numbers of Rydberg atoms. The formulas which help to estimate an appropriate mean Rydberg atom number for a given detection efficiency are presented. We have found that a measurement of the relation between the amplitudes of collisional resonances observed in the one- and two-atom signals provides a straightforward determination of the absolute detection efficiency and mean Rydberg atom number. We also performed a testing experiment on resonant collisions in a small excitation volume of a sodium atomic beam. The resonances observed for 1 to 4 detected Rydberg atoms have been analyzed and compared with theory., Comment: 10 pages, 4 figures; equations 8,9,18,19,23,26-31, figures 3 and 4(d), and measurements revised in version 3

Collisional and thermal ionization of sodium nS and nD Rydberg atoms with n=8-20 has been studied. The experiments were performed using a two-step pulsed laser excitation in an effusive atomic beam at atom density of about 2 10^{10} cm^{-3}. Molecular and atomic ions from associative, Penning, and thermal ionization processes were detected. It has been found that the atomic ions were created mainly due to photoionization of Rydberg atoms by photons of blackbody radiation at the ambient temperature of 300K. Blackbody ionization rates and effective lifetimes of Rydberg states of interest were determined. The molecular ions were found to be from associative ionization in Na(nL)+Na(3S) collisions. Rate constants of associative ionization have been measured using an original method based on relative measurements of Na_{2}^{+} and Na^{+} ion signals., Comment: 23 pages, 10 figures

The effect of microwave radiation on the resonance fluorescence of a cloud of cold $^{85}Rb$ atoms in a magnetooptical trap is studied. The radiation frequency was tuned near the hyperfine splitting frequency of rubidium atoms in the 5S ground state. The microwave field induced magnetic dipole transitions between the magnetic sublevels of the 5S(F=2) and 5S(F=3) states, resulting in a change in the fluorescence signal. The resonance fluorescence spectra were recorded by tuning the microwave radiation frequency. The observed spectra were found to be substantially dependent on the transition under study and the frequency of a repump laser used in the cooling scheme., Comment: 6 pages, 4 figures

A nondegenerate four-level N-type scheme was experimentally implemented to observe electromagnetically induced transparency (EIT) at the $^{87}$Rb D$_{2}$ line. Radiations of two independent external-cavity semiconductor lasers were used in the experiment, the current of one of them being modulated at a frequency equal to the hyperfine-splitting frequency of the excited 5P$_{3/2}$ level. In this case, apart from the main EIT dip corresponding to the two-photon Raman resonance in a three-level $\Lambda$-scheme, additional dips detuned from the main dip by a frequency equal to the frequency of the HF generator were observed in the absorption spectrum. These dips were due to an increase in the medium transparency at frequencies corresponding to the three-photon Raman resonances in four-level N-type schemes. The resonance shapes are analyzed as functions of generator frequency and magnetic field., Comment: 3 pages, 2 figures