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arXiv:quant-ph/0612222 · Physical Review A

Entanglement in the dispersive interaction of trapped ions with a quantized field

F. L. Semião, K. Furuya

Published Apr 16, 2007• 11 citations
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Abstract

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 $N$ 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.

DOI
10.1103/physreva.75.042315

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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.
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 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.
We study the generation of an entangled motional coherent state of two distant ions trapped in two cascaded cavities, in which the motional mode of the each ion is coupled to the respective cavity field via a linear-mixing interaction. The master equation is solved analytically by using the characteristic function method. It is found that the generated entangled coherent state resulted from the initial preparation of an even coherent state is more robust than that from an odd coherent state under the dissipation of the cavity.
A proposal for realizing one- and two-mode degenerate Raman coupled models, of the type proposed by Knight [Phys. Scr. T 12, 51 (1986)] in the context of quantum optics, for the motion of a trapped two-level ion, is presented. The interaction has a dispersive effect on the vibrational motion of the ion. For the one-mode case, an initial vibrational coherent state evolves into superpositions of coherent states (Schr\"odinger-cat states) correlated with the internal states of the ion. In the two-mode case, with initial coherent states in each mode, entanglements of coherent states between the modes correlated with the internal ionic states are obtained. Detection of such states is briefly discussed.
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.