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Latin America Optics and Photonics Conference

Entanglement Between a Moving Mirror and a Trapped Ion

Clóvis Corrêa, A. Vidiella-Barranco

Published Jan 1, 2012• 0 citations
Publisher

Abstract

It is presented a scheme for generating entanglement between a moving mirror and the vibrational degree of freedom of a single trapped ion. The system consists of an interferometer with an optomechanical cavity at one arm and a cavity with a single trapped ion at another arm. Because of the radiation pressure, it is possible to entangle the cavity field with the moving mirror at the optomechanical arm and by tuning the cavity field with the internal levels of the ion, it is possible to generate an entangled state comprising the cavity and the ion arm. The cavity fields may be coupled via a beam splitter, making possible to generate entanglement between the moving mirror and the vibrational state of motion of a single trapped ion.

DOI
10.1364/laop.2012.ls2b.4

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It is presented a scheme for generating entanglement between a moving mirror and the vibrational degree of freedom of a single trapped ion. The system consists of an interferometer with an optomechanical cavity at one arm and a cavity with a single trapped ion at another arm. Because of the radiation pressure, it is possible to entangle the cavity field with the moving mirror at the optomechanical arm and by tuning the cavity field with the internal levels of the ion, it is possible to generate an entangled state comprising the cavity and the ion arm. The cavity fields may be coupled via a beam splitter, making possible to generate entanglement between the moving mirror and the vibrational state of motion of a single trapped ion.
We propose a scheme to generate a particular kind of tripartite entangled states using a single two-level trapped ion coupled to a quantized monomode electromagnetic field within an optical cavity. The resulting state involves motional Schr\\"odinger-cat states of the trapped ion, its internal electronic states, and Fock states of the cavity field. By means of a measurement of the internal state of the ion, it is also possible to generate either entangled bipartite states involving light and motion or single motional Schr\\"odinger-cat states. Our proposal is based on a previously introduced intensity dependent Hamiltonian [Phys. Rev. A 66, 063403 (2002)] for a trapped ion in a cavity.
We show how the motional fluctuations of two systems of very different sizes---a trapped ion and a mirror---can be coupled coherently, via their common interaction with an optical cavity. Specifically, we show that the fluctuations can be transferred from one system to the other by using pulsed excitation of the cavity mode, and vibrational fluctuations can exhibit entanglement in steady state. We numerically display a sudden death of this entanglement at certain pulse parameters and ambient equilibrium temperature. More interestingly, the state of the driving pulse can also be coherently mapped, in a selective way, into the vibrational mode of the trapped ion or the mirror, which acts as a quantum memory for the optical pulse. We further present a detailed analysis to show that it is also possible to map the state of the pulse into a binomial entangled state of its vibrational fluctuations. We finally investigate how to sympathetically cool the mirror by cooling the ionic vibration, thanks to an effective coupling between the two modes.
We consider the motion of the end mirror of a cavity inside which a two-level atom trapped. The fast vibrating mirror induces nonlinear couplings between the cavity field and the atom. We analyze this optical effect by showing the population of the atom in its internal degrees of freedom as a function of time. On the other side, fast atom-field variables result in an additional potential for the atomic center-of-mass motion and the mirror vibration, leading to entanglement in the motion and the vibration. The entanglement has been numerically simulated and discussed.
In this paper, we study generation of entangled states in a system which consists of a single trapped ion in a cavity. We obtain a cross-Kerr-like interaction between the cavity field (photons) and the centre-of-mass motion (phonons) of the trapped ion in the Lamb–Dicke and large detuning regime. Based on this cross-Kerr-like interaction, we create hybrid entangled states between the phonon mode and the ionic internal states, and between the cavity field and ionic internal states, respectively. We also show that it is possible to prepare entangled coherent states between the cavity field and the phonon mode. We explicitly obtain an entangled state between two pairs of Schrödinger-cat states.