I. I. Beterov

Quasiclassical calculations of blackbody-radiation-induced depopulation rates and effective lifetimes of Rydberg nS, nP, and nD alkali-metal atoms with n ≤ 80

Rates of depopulation by blackbody radiation (BBR) and effective lifetimes of alkali-metal nS, nP, and nD Rydberg states have been calculated in a wide range of principal quantum numbers n ≤ 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.

Applicability of Rydberg atoms to quantum computers

The applicability of Rydberg atoms to quantum computers is examined from an experimental point of view. In many recent theoretical proposals, the excitation of atoms into highly excited Rydberg states was considered as a way to achieve quantum entanglement in cold atomic ensembles via dipole–dipole interactions that could be strong for Rydberg atoms. Appropriate conditions to realize a conditional quantum phase gate have been analysed. We also present the results of modelling experiments on microwave spectroscopy of single- and multi-atom excitations at the one-photon 37S1/2 → 37P1/2 and two-photon 37S1/2 → 38S1/2 transitions in an ensemble of a few sodium Rydberg atoms. The microwave spectra were investigated for various final states of the ensemble initially prepared in its ground state. The results may be applied to the studies on collective laser excitation of ground-state atoms aiming to realize quantum gates.

Quantum gates in mesoscopic atomic ensembles based on adiabatic passage and Rydberg blockade

We present schemes for geometric phase compensation in an 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.

Effect of finite detection efficiency on the observation of the dipole-dipole interaction of a few Rydberg atoms

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.

Two-qubit gates using adiabatic passage of the Stark-tuned Förster resonances in Rydberg atoms

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 Forster 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 Forster 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 90 S +96 S -->90 P +95 P Stark-tuned Forster resonance in Cs Rydberg atoms.

Stark-switching technique for fast quantum gates in Rydberg atoms

An experiment on Ramsey interferometry of the 37S1/2 → 37P1/2 microwave transition in sodium Rydberg atoms has been performed. Interaction of Rydberg atoms with a cw microwave radiation was effectively controlled by a pulse of weak (<1 V cm−1) electric field, that manipulated the transition frequency near 70 050 MHz. The pulse detuned the microwave radiation from exact resonance, and induced additional phases to the wavefunctions of Rydberg states due to the quadratic Stark shifts. As a result, the Ramsey fringes were observable both on scanning the frequency of the microwave field and on scanning the strength of the electric field pulse. The experiment confirmed that this Stark-switching technique provides a fast and effective control of the atom–light interactions, and preserves the atomic coherence. Possible applications of this technique to experiments on quantum computers are discussed.

Stark-tuned Förster resonance and dipole blockade for two to five cold Rydberg atoms: Monte Carlo simulations for various spatial configurations

Results of numerical Monte Carlo simulations for the Stark-tuned Förster 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 Förster 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 Förster resonance and finite laser line width. The results are discussed in the context of quantuminformation processing with Rydberg atoms.

Ionization of sodium and rubidiumnS,nP, andnDRydberg atoms by blackbody radiation

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 =8–6 5 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 dependences 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 =8–2 0 at 300 K. Agood agreement for all states except nS with n 15 is observed. We also present the useful analytical formulas for the quick estimation of BBR ionization rates of Rydberg atoms.

Simulated quantum process tomography of quantum gates with Rydberg superatoms

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.

Publisher's Note: Line shapes and time dynamics of the Förster resonances between two Rydberg atoms in a time-varying electric field [Phys. Rev. A 94 , 043417 (2016)]

E. A. Yakshina, D. B. Tretyakov, I. I. Beterov, V. M. Entin, C. Andreeva, A. Cinins, A. Markovski, Z. Iftikhar, A. Ekers, and I. I. Ryabtsev Rzhanov Institute of Semiconductor Physics SB RAS, 630090 Novosibirsk, Russia Novosibirsk State University, 630090 Novosibirsk, Russia Institute of Electronics, Bulgarian Academy of Sciences, 1784 Sofia, Bulgaria University of Latvia, LV-1002 Riga, Latvia Technical University of Sofia, 1000 Sofia, Bulgaria Institut d’Optique, 91127 Palaiseau, France and King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia (Dated: 24 October 2016)