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Communications in Theoretical Physics

Storage of Entangled States with Multiple Trapped Ions in Thermal Motion

Gong Xiao-Long, Wen‐Xing Yang

Published Apr 1, 2006• 1 citation
Publisher

Abstract

This paper presents an alternative scheme to realize the storage of entangled states for multiple trapped ions including W state, Bell states, and GHZ states even with ions which exchange vibrational energy with a heating surrounding. Our scheme requires that the ions be simultaneously excited by two laser beams with different frequencies. In this scheme the vibrational degrees of freedom are only regarded as intermediate states and the ions exchange energy via the mediation of the vibration of the vibrational mode in coupling processes. The scheme is insensitive to both the initial vibrational state and heating if the system remains in the Lamb–Dicke regime. Since the effective Rabi frequency has a small dependence on the vibrational quantum number the heating will have no direct effect on the internal state evolution.

DOI
10.1088/0253-6102/45/4/007

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This paper presents an alternative scheme to realize the storage of entangled states for multiple trapped ions including W state, Bell states, and GHZ states even with ions which exchange vibrational energy with a heating surrounding. Our scheme requires that the ions be simultaneously excited by two laser beams with different frequencies. In this scheme the vibrational degrees of freedom are only regarded as intermediate states and the ions exchange energy via the mediation of the vibration of the vibrational mode in coupling processes. The scheme is insensitive to both the initial vibrational state and heating if the system remains in the Lamb–Dicke regime. Since the effective Rabi frequency has a small dependence on the vibrational quantum number the heating will have no direct effect on the internal state evolution.
We present an alternative scheme to prepare entangled states of multiple trapped ions in thermal motion. In this scheme the vibrational degrees of freedom are only regarded as intermediate states and the ions exchange energy via the mediation of the vibration of the vibrational mode in coupling processes. The scheme is insensitive to both the initial vibrational state and heating if the system remains in the Lamb–Dicke regime. Since the effective Rabi frequency has a small dependence on the vibrational quantum number, the heating will have no direct effect on the internal state evolution. The scheme can also be used for the storage of entangled states.
A scheme is presented for generating entangled states of the W\mathrm{W}W type for trapped ions in thermal motion. In the scheme the ions are simultaneously excited by a laser. Our scheme is insensitive to both the initial motional state and heating as long as the system remains in the Lamb-Dicke regime.
We propose a simple and fast scheme for producing maximally entangled states for many trapped ions. The scheme only requires a single laser beam tuned to the ionic carrier frequency. Our scheme works in the regime, where the Rabi frequency is of the order of the vibrational frequency. Our scheme operates in a fast way and is insensitive to heating of vibrational motion, which is important in view of decoherence. Thus, our scheme opens promising prospects for entanglement engineering in a scalable way.
Following the recent proposal by Briegel et al. [Phys. Rev. Lett. 86 (2001) 910], a procedure is proposed for one-step realizing quantum control phase gates with two trapped ions in thermal motion. It is shown that the scheme can also be used to create a new special type of entangled states, i.e., cluster states of many trapped ions. In the scheme the two-trapped ions are simultaneously excited by a single laser beam and the frequency of the laser beam is slightly off resonance with the first lower vibration sideband of the trapped ions. The distinct advantage of the scheme is that it does not use the vibrational mode as the data bus. Furthermore, our scheme is insensitive to both the initial motional state and heating (or decay) as long as the system remains in the Lamb–Dicke regime.
We propose a scheme for preparation of entangled coherent states for the motion of an ion in a two-dimensional anisotropic trap. In the scheme, the ion is driven by four laser beams along different directions in the ion trap plane, resulting in carrier excitation and couplings between the internal and external degrees of freedom. When the total quantum number of the vibrational modes initially has a definite parity, the competition between the unitary dynamics and spontaneous emission will force the system to evolve to a steady state, where the vibrational modes are in a two-mode cat state. We show that the method can be extended to realization of entangled coherent states for three vibrational modes of an ion in a three-dimensional anisotropic trap.