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arXiv:0909.3239 · Physical Review Letters

Observation of the Stark-Tuned Förster Resonance between Two Rydberg Atoms

I. I. Ryabtsev, Denis B. Tretyakov, Ilya I. Beterov, Vasily M. Entin

Published Feb 18, 2010• 113 citations
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Abstract

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 Förster resonance using the Stark effect. The observed resonance line shapes are in good agreement with numerical Monte Carlo simulations.

DOI
10.1103/physrevlett.104.073003

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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 Förster resonance using the Stark effect. The observed resonance line shapes are in good agreement with numerical Monte Carlo simulations.
Long-range interactions between cold Rydberg atoms are being investigated for neutral-atom quantum computing, quantum simulations, phase transitions in cold Rydberg gases and other applications. Fine tuning of the interaction strength can be implemented using Förster resonances between Rydberg atoms controlled by an electric field. The observation of the Stark-tuned Förster 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 Förster resonance. The application of the radio-frequency field causes additional Förster resonances 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 Förster resonance. We present a detailed experimental and theoretical analysis of the line shape and time dynamics of the Stark-tuned Förster resonances Rb( nP 3/2 ) + Rb( nP 3/2 ) → Rb( nS 1/2 ) + Rb([ n + 1] S 1/2 ) for two Rb Rydberg atoms interacting in a time-varying electric field.
Results of numerical Monte Carlo simulations for the Stark-tuned $\mathrm{F}\stackrel{\mathrm{\ifmmode\cdot\else\textperiodcentered\fi{}\ifmmode\cdot\else\textperiodcentered\fi{}}}{\mathrm{o}}$rster 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 $\mathrm{F}\stackrel{\mathrm{\ifmmode\cdot\else\textperiodcentered\fi{}\ifmmode\cdot\else\textperiodcentered\fi{}}}{\mathrm{o}}$rster 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 $\mathrm{F}\stackrel{\mathrm{\ifmmode\cdot\else\textperiodcentered\fi{}\ifmmode\cdot\else\textperiodcentered\fi{}}}{\mathrm{o}}$rster resonance and finite laser linewidth. The results are discussed in the context of quantum-information processing with Rydberg atoms.
Ultracold Rydberg atoms in a static electric field can exchange energy via the dipole-dipole interaction. The Stark effect shifts the energy levels of the atoms which tunes the energy exchange into resonance at specific values of the electric field (F\"orster resonances). We excite rubidium atoms to Rydberg states by focusing either a 480 nm beam from a tunable dye laser or a pair of diode lasers into a magneto-optical trap. The trap lies at the center of a configuration of electrodes. We scan the electric field by controlling the voltage on the electrodes while measuring the fraction of atoms that interact. Dipole-dipole interaction spectra are presented for initially excited rubidium ndndnd states for n=31n=31n=31 to 46 and for four different pairs of initially excited rubidium nsnsns states. We also present the dipole-dipole interaction spectra for individual rubidium 32ddd (j,mj)(j,\phantom{\rule{0.16em}{0ex}}{m}_{j})(j,mj​) fine structure levels that have been selectively excited. The data are compared to calculated spectra.
Cold Rydberg atoms subject to long-range dipole-dipole interactions represent a particularly interesting system for exploring few-body interactions and probing the transition from 2-body physics to the many-body regime. In this work we report the direct observation of a resonant 4-body Rydberg interaction. We exploit the occurrence of an accidental quasicoincidence of a 2-body and a 4-body resonant Stark-tuned Förster process in cesium to observe a resonant energy transfer requiring the simultaneous interaction of at least four neighboring atoms. These results are relevant for the implementation of quantum gates with Rydberg atoms and for further studies of many-body physics.
Abstract We present a scheme for implementation of controlled-Z and controlled-NOT gates via rapid adiabatic passage and Stark-tuned Förster resonance. By sweeping the Förster resonance once without passing through it and adiabatically tuning the angle-dependent Rydberg–Rydberg interaction of the dipolar nature, the system can be effectively described by a two-level system with the adiabatic theorem. The single adiabatic passage leads to a gate fidelity as high as 0.999 and a greatly reduced gate operation time. We investigate the scheme by considering an actual atomic level configuration with rubidium atoms, where the fidelity of the controlled-Z gate is still higher than 0.99 under the influence of the Zeeman effect.
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.