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arXiv:1911.09664 · Physical Review Letters

Time Dependence of Few-Body Förster Interactions among Ultracold Rydberg Atoms

Zhimin Cheryl Liu, Nina P. Inman, Thomas J. Carroll, Michael W. Noel

Published Mar 31, 2020• 7 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.124.133402

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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.
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.
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.
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.
Three-body F\"orster resonances controlled by a dc electric field are of interest for the implementation of three-qubit quantum gates with single atoms in optical traps using their laser excitation into strongly interacting Rydberg states. In our recent theoretical paper [Zh. Eksp. Teor. Fiz. 168, 14 (2025)], it was found that the proposed earlier three-body F\"orster resonance $3\ifmmode\times\else\texttimes\fi{}n{P}_{3/2}\ensuremath{\rightarrow}n{S}_{1/2}+(n+1){S}_{1/2}+n{P}_{1/2}$ in Rb Rydberg atoms presents a splitting, with one of the split components having weaker dependence of the resonant electric field (and the corresponding dynamic shift) on the distance RRR between the atoms. Here we study this effect in more detail, since this resonance appears as the most suitable for performing experiments on observing coherent oscillations of populations of collective three-body states and implementing three-qubit quantum gates based on them. For a linear spatial configuration of three interacting Rydberg atoms, the physical mechanism of this phenomenon is revealed and analytical formulas are obtained that describe the behavior of split structure of the F\"orster resonance depending on RRR. It is found that the splitting is a measure of the energy of the resonant dipole-dipole exchange interaction with an excitation hopping between neighboring Rydberg states SSS and PPP.
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.