Controlled long-range interactions between Rydberg atoms and ions

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Controlled long-range interactions between Rydberg atoms and ions

T. Secker, R. Gerritsma, A. W. Glaetzle, and A. Negretti

Phys. Rev. A 94, 013420 – Published 22 July 2016

Abstract

We theoretically investigate trapped ions interacting with atoms that are coupled to Rydberg states. The strong polarizabilities of the Rydberg levels increase the interaction strength between atoms and ions by many orders of magnitude, as compared to the case of ground-state atoms, and may be mediated over micrometers. We calculate that such interactions can be used to generate entanglement between an atom and the motion or internal state of an ion. Furthermore, the ion could be used as a bus for mediating spin-spin interactions between atomic spins in analogy to much employed techniques in ion-trap quantum simulation. The proposed scheme comes with attractive features as it maps the benefits of the trapped-ion quantum system onto the atomic one without obviously impeding its intrinsic scalability. No ground-state cooling of the ion or atom is required and the setup allows for full dynamical control. Moreover, the scheme is to a large extent immune to the micromotion of the ion. Our findings are of interest for developing hybrid quantum information platforms and for implementing quantum simulations of solid-state physics.

Received 15 February 2016

DOI:https://doi.org/10.1103/PhysRevA.94.013420

Physics Subject Headings (PhySH)

Long-range interactions

Rydberg atoms & molecules

Atomic, Molecular & Optical

Authors & Affiliations

T. Secker^1,2, R. Gerritsma^1,2,*, A. W. Glaetzle^3,4, and A. Negretti⁵

¹Institute of Physics, University of Amsterdam, 1098 XH Amsterdam, The Netherlands
²QUANTUM, Institut für Physik, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany
³Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
⁴Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
⁵Zentrum für Optische Quantentechnologien and The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, D-22761 Hamburg, Germany

^*r.gerritsma@uva.nl

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Vol. 94, Iss. 1 — July 2016

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Images

Figure 1
(a) We consider an ion (red ball) trapped in a Paul trap (gray electrodes) experiencing a harmonic confinement with trapping frequency $ω_{i}$ and lowering (raising) operators $a (a^{†})$ . A distance $d$ away, an atom (blue ball) is optically trapped with Rabi frequency $Ω_{d}$ and coupled to a Rydberg state with a time-dependent laser (blue arrow) of Rabi frequency $Ω (t)$ . (b) Internal atomic (right) and ionic (left) level scheme. The Rydberg state experiences a position-dependent Stark shift $Δ (R)$ , with $R$ the distance between the atom and the ion, due to the electric field of the ion. The resulting force may be used to entangle the atom and the ion when coupling to the Rydberg state depending on the internal state of the atom as described in the text.
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Figure 2
Eigenenergies $ε_{k}$ of ${\hat{H}}_{BO}$ for ${}^{6}{Li}$ interacting with an ion as a function of the ion-core distance $R$ that emanate from the $n = 30$ and the $n = 29$ manifolds based on our simulation without trapping fields. The $30 S$ and $30 P$ energies lie separated at $- 3754.4$ and $- 3666.7$ GHz. The dashed red line shows a $- C_{4}^{∣ 30 S_{1 / 2} 〉} / R^{4}$ potential shifted down by the $30 S$ energy that is based on second-order perturbation theory within the dipole approximation. Here, $C_{4}^{∣ 30 S_{1 / 2} 〉}$ was taken from Refs. [46, 47]. We see that the $30 S$ state remains well separated from the others down to distances of $\sim 500$ nm, whereas second-order perturbation theory works well for distances $\geq 1 μ m$ .
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Figure 3
Adiabatic potentials for a ground-state atom and an ion (solid black), for a dressed atom with $Ω = 2 π$ 10 MHz and $Δ = 2 π$ 1 GHz (red dashed-dotted line) and $2 π$ 0.4 GHz (blue dashed line) assuming coupling to the $∣ 30 S_{1 / 2} 〉$ state of lithium.
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Figure 4
Dynamics of the populations $P_{↑ ↑}, ...$ during the gate for the input state $| ψ_{i} {〉 = (| ↑ 〉}_{a} + {| ↓ 〉}_{a} {) (| ↑ 〉}_{i} + {| ↓ 〉}_{i}) / 2$ and after performing an additional $π / 2$ pulse (see text). The dashed line indicates the time at which the gate is finished.
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Figure 5
Expectation values $〈 {\hat{x}}_{i} 〉$ and $〈 {\hat{x}}_{a} 〉$ during the gate for each of the four possible spin input states. The insets also show zoom ins of the ion and atom motion, clearly showing the micromotion. Some residual atomic motion occurs for the states ${| ↑ 〉}_{a}$ , where the atom gets pulled closer to the ion.
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Figure 6
Comparison of the effective potential emanating from the $30 S$ of ${}^{6}{Li}$ state with (dots) and without (gray line) trapping field in the radial direction. The three points correspond to the trapping field at maximal positive and negative and zero amplitude. In this calculation, we used the following parameters, $Ω_{rf} = 2 π 2.5$ MHz, $q = 0.28$ , assuming an ${Yb}^{+}$ ion trapped at the origin.
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