Coherence of the Borromean three-body Förster resonances in Rydberg atoms

Abstract

We have observed recently the Stark-tuned three-body Förster resonances $3\times n{P}_{3/2}(|M|)\to n{S}_{1/2}+(n+1)S_{1/2}+n{P}_{3/2}(|M^{\ast }|)$ 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 $2\times n{P}_{3/2}(|M|)\to n{S}_{1/2}+(n+1)S_{1/2}$ 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.

14 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:1707.01636