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

Abstract

The three-body Förster resonances $3\times n{P}_{3/2}\to n{S}_{1/2}+(n+1)S_{1/2}+n{P}_{3/2}^{\ast }$ 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 $2\times n{P}_{3/2}\to n{S}_{1/2}+(n+1)S_{1/2},$ 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 $3\times n{P}_{3/2}\to n{S}_{1/2}+(n+1)S_{1/2}+n{P}_{1/2},$ 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.

9 pages, 4 figures