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arXiv:1404.0438 · Physical Review A

Controlling the interactions of a few cold Rb Rydberg atoms by radio-frequency-assisted Förster resonances

Denis B. Tretyakov, Vasily M. Entin, Elena A. Yakshina, Ilya I. Beterov, C. Andreeva, I. I. Ryabtsev

Published Oct 31, 2014• 52 citations
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Abstract

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.

DOI
10.1103/physreva.90.041403

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arXiv:1510.05350•Physical Review A•Feb 12, 2016•12 citations
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.
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.
Enhancing interactions between Rydberg atoms is a key challenge in contemporary quantum technologies. Stronger interactions enable faster Rydberg gates in digital processors and larger entangled states in analog simulation. Achieving the same interaction strength at lower principal quantum number addresses current constraints in available Rabi frequency and field sensitivity in large scale tweezer or cavity QED experiments. Here, we demonstrate a new technique using AC Stark shifts from a microwave drive to tune into a Förster resonance, thereby modifying the interaction scaling with distance from 1/R61/R^61/R6 to 1/R31/R^31/R3. We validate enhanced Rydberg interactions (in strength and range) by probing cavity Rydberg polariton blockade at n=44n=44n=44 in 87^{87}87Rb, improving from g(2)(0)=1.0(1)g^{(2)}(0) = 1.0 (1)g(2)(0)=1.0(1) in the Van-der-Waals regime to g(2)(0)=0.38(1)g^{(2)}(0) = 0.38 (1)g(2)(0)=0.38(1) in the dipolar regime on the Förster resonance. Importantly, our technique allows minimal shifts of the original Rydberg state, suppressing detuning errors in gate protocols while maintaining quadratic insensitivity to DC electric fields.
The observation of the Stark-tuned F\"orster 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 F\"orster resonance. In our experiments with a few cold Rb Rydberg atoms, we have found that the transients at the edges of the electric pulses strongly affect the line shapes of the F\"orster resonances, since the population transfer at the resonances occurs on a time scale of $\ensuremath{\sim}100$ ns, which is comparable with the duration of the transients. For example, a short-term ringing at a certain frequency causes additional radio-frequency-assisted F\"orster resonances, while nonsharp edges lead to asymmetry. The intentional application of the radio-frequency field induces transitions 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 F\"orster resonance. We present a detailed experimental and theoretical analysis of the line shape and time dynamics of the Stark-tuned F\"orster resonances $\mathrm{Rb}(n{P}_{3/2})+\mathrm{Rb}(n{P}_{3/2})\ensuremath{\rightarrow}\mathrm{Rb}(n{S}_{1/2})+\mathrm{Rb}([n+1]{S}_{1/2})$ for two Rb Rydberg atoms interacting in a time-varying electric field.
We demonstrated a tuned dipole interaction between Rydberg atoms by employing a controllable electric field in a cold cesium ensemble. The | n P 3/2 ⟩ ( n = 38–40) Rydberg pairs are prepared with a three-photon scheme and detected via the state-selective field ionization technique. A weak DC electric field is used to tune the Rydberg pair interaction from the van der Waals interaction regime to the dipole–dipole interaction regime. The Förster resonant interaction and an adiabatic resonance energy transfer between the n P and n S Rydberg states are attained by precisely tuning the electric field. Rydberg excitation blockade with and without the electric field is investigated by changing the excitation pulse duration, which demonstrates that the dipole interaction–induced blockade effect is stronger than the van der Waals interaction–induced blockade effect. The precise control of the Rydberg interaction is of great significance to the coherent interaction in many-body systems and non-radiative collision processes.
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.
Cold Rydberg atoms are known to display dipole-dipole interaction-allowed resonances, also called F\"orster resonances, which lead to an efficient energy transfer when the proper electric field is used. This electric field also enables resonances, which do not respect the dipole-dipole selection rules under zero field. A few of these quasiforbidden resonances have been observed but they are often overlooked. Here we show that in cold 133Cs^{133}\mathrm{Cs}133Cs atoms there is a large number of these resonances that display a significant transfer efficiency due to their strong interactions, even at low electric field. We also develop a graphical method enabling us to find all possible resonances simultaneously. The resulting dramatic increase in the total number of addressable resonant energy transfers at different electric fields could have implications in the search for few-body interactions or macromolecules built from Rydberg atoms.