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Journal of Physics B Atomic Molecular and Optical Physics

Preparation of hybrid entangled states and entangled coherent states for a single trapped ion in a cavity

Jie‐Qiao Liao, Yu Guo, Hao‐Sheng Zeng, Le‐Man Kuang

Published Nov 7, 2006• 14 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/39/22/014

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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.
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 propose a generation method of Bell-type states involving light and the vibrational motion of a single trapped ion. The trap itself is supposed to be placed inside a high-QQQ cavity sustaining a single mode, quantized electromagnetic field. Entangled light-motional states may be readily generated if a conditional measurement of the ion's internal electronic state is made after an appropriate interaction time and a suitable preparation of the initial state. We show that all four Bell states may be generated using different motional sidebands (either blue or red), as well as adequate ionic relative phases.
The mode-mode entanglement between trapped ions and cavity fields is investigated in the dispersive regime. We show how a simple initial preparation of Gaussian coherent states and a postselection may be used to generate motional nonlocal mesoscopic states involving ions in different traps. We also present a study of the entanglement induced by dynamical Stark shifts considering a cluster of NNN trapped ions. In this case, all entanglement is due to the dependence of the Stark shifts on the ions' state of motion manifested as a cross-Kerr interaction between each ion and the field.