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arXiv:1707.01636 · Physical Review Letters

Observation of the Borromean Three-Body Förster Resonances for Three Interacting Rb Rydberg Atoms

Denis B. Tretyakov, Ilya I. Beterov, Elena A. Yakshina, Vasily M. Entin, I. I. Ryabtsev, Patrick Cheinet, P. Pillet

Published Oct 27, 2017• 31 citations
arXivHTMLPDF

Abstract

Three-body Förster resonances at long-range interactions of Rydberg atoms were first predicted and observed in Cs Rydberg atoms by Faoro et al. [Nat. Commun. 6, 8173 (2015)NCAOBW2041-172310.1038/ncomms9173]. In these resonances, one of the atoms carries away an energy excess preventing the two-body resonance, leading thus to a Borromean type of Förster energy transfer. But they were in fact observed as the average signal for the large number of atoms N≫1. In this Letter, we report on the first experimental observation of the three-body Förster resonances 3×nP_{3/2}(|M|)→nS_{1/2}+(n+1)S_{1/2}+nP_{3/2}(|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 Förster 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.

DOI
10.1103/physrevlett.119.173402

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Three-body Förster resonances at long-range interactions of Rydberg atoms were first predicted and observed in Cs Rydberg atoms by Faoro et al. [Nat. Commun. 6, 8173 (2015)NCAOBW2041-172310.1038/ncomms9173]. In these resonances, one of the atoms carries away an energy excess preventing the two-body resonance, leading thus to a Borromean type of Förster energy transfer. But they were in fact observed as the average signal for the large number of atoms N≫1. In this Letter, we report on the first experimental observation of the three-body Förster resonances 3×nP_{3/2}(|M|)→nS_{1/2}+(n+1)S_{1/2}+nP_{3/2}(|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 Förster 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.
We have observed recently the Stark-tuned three-body F\"orster resonances $3\ifmmode\times\else\texttimes\fi{}n{P}_{3/2}(|M|)\ensuremath{\rightarrow}n{S}_{1/2}+(n+1){S}_{1/2}+n{P}_{3/2}(|{M}^{*}|)$ 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 $2\ifmmode\times\else\texttimes\fi{}n{P}_{3/2}(|M|)\ensuremath{\rightarrow}n{S}_{1/2}+(n+1){S}_{1/2}$ and corresponds to a transition when the three interacting atoms change their states simultaneously (two atoms go to the SSS states, and the third atom remains in the PPP 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.
Rubidium Rydberg atoms in either |m_{j}| sublevel of the 36p_{3/2} state can exchange energy via Stark-tuned Förster resonances, including two-, three-, and four-body dipole-dipole interactions. Three-body interactions of this type were first reported and categorized by Faoro et al. [Nat. Commun. 6, 8173 (2015)NCAOBW2041-172310.1038/ncomms9173] and their Borromean nature was confirmed by Tretyakov et al. [Phys. Rev. Lett. 119, 173402 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.173402]. We report the time dependence of the N-body Förster resonance N×36p_{3/2,|m_{j}|=1/2}→36s_{1/2}+37s_{1/2}+(N-2)×36p_{3/2,|m_{j}|=3/2}, for N=2, 3, and 4, by measuring the fraction of initially excited atoms that end up in the 37s_{1/2} state as a function of time. The essential features of these interactions are captured in an analytical model that includes only the many-body matrix elements and neighboring atom distribution. A more sophisticated simulation reveals the importance of beyond-nearest-neighbor interactions and of always-resonant interactions.
Controlling the interactions between ultracold atoms is crucial for quantum simulation and computation purposes. Highly excited Rydberg atoms are considered in this prospect for their strong and controllable interactions known in the dipole-dipole case to induce non-radiative energy transfers between atom pairs, similarly to fluorescence resonance energy transfer (FRET) in biological systems. Here we predict few-body FRET processes in Rydberg atoms and observe the first three-body resonance energy transfer in cold Rydberg atoms using cold caesium atoms. In these resonances, additional relay atoms carry away an energy excess preventing the two-body resonance, leading thus to a Borromean type of energy transfer. These few-body processes present strong similarities with multistep FRET between chromophores sometimes called donor-bridge-acceptor or superexchange. Most importantly, they generalize to any Rydberg atom and could lead to new implementations of few-body quantum gates or entanglement.
Three-body Förster resonances controlled by a dc electric field are of interest for the implementation of three-qubit quantum gates with single atoms captured in optical traps and laser-excited into strongly interacting Rydberg states. In Ref. [P. Cheinet et al., Quantum Electronics 50(3), 213 (2020)], we proposed and analyzed a new type of three-body Förster resonance 3×nP3/2→nS1/2+(n+1)S1/2+nP1/2{\rm 3}\times nP_{3/2} \to nS_{1/2} +(n+1)S_{1/2} +nP_{1/2}3×nP3/2​→nS1/2​+(n+1)S1/2​+nP1/2​ that can be realized with Rb Rydberg atoms for an arbitrary principal quantum number nnn. Its peculiarity is that the third atom goes into a state with a total angular moment J=1/2J=1/2J=1/2, which has no Stark structure, so two-body Förster resonances are completely absent. In the present work, an extended theoretical study of this three-body Förster resonance is performed for various spatial configurations of three interacting Rb Rydberg atoms and conditions for their experimental implementation are determined. It was found that one of the resonances has a weak dependence of the resonant electric field on the distance between atoms and is therefore most suitable for performing experiments to observe coherent oscillations of populations of collective three-body states and implement three-qubit quantum gates based on them.
Abstract The three-body Förster resonances 3 × nP3/2(|M|) →nS1/2 + (n + 1)S1/2 + nP3/2(|M*|), controlled by a constant electric field, were realised 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 × nP3/2 → nS1/2 + (n + 1)S1/2, as well as the possibility of their implementation only for states with values of the principal quantum numbers n ⩽38. A three-body resonance of a new type, 3 × nP3/2 → nS1/2 + (n + 1)S1/2 + nP1/2, which can be realised for arbitrary n, is proposed and analysed. Its specific feature is also that the third atom transits into a state with a different total angular momentum 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 oscillations of the populations of collective states, which is of interest for developing new schemes of three-qubit quantum gates controlled by an electric field.
Application of few-body Förster resonances for implementation of multiqubit quantum gate circuits has been investigated. New types of three-atom Borromean transitions based on the relay atom have been proposed and numerically studied. In particular, a Stark-controlled non-isolated three-atom Förster resonance between high-lying n = 80, 81, 82 S − P states of Rb atoms isolated in individual optical traps has been modeled. Isolated three-atom Förster resonance has also been demonstrated for n = 70, 71 states of Rb atoms. The resonances were investigated in a fixed spatial configuration, allowing us to demonstrate the coherent population and phase dynamics of the collective states involved. Three-qubit Toffoli gates schemes have been developed and numerically modeled based on the demonstrated resonances. Also, a generalized doubly controlled phase CCPHASE gate scheme has been developed based on the radiofrequency-induced three-body Förster resonance. Additionally, a similar quantum gate scheme has been proposed based on two-atom RF-induced Förster resonance with controlled displacement. The fast performance and high fidelity of the proposed schemes, as well as their potential robustness to errors, allow us to expect a successful experimental implementation in the near future.