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Communications in Theoretical Physics

Robust Entanglement for Multiple Trapped Ions in Thermal Motion

Zheng Shi-Biao

Published Feb 1, 2005• 1 citation
Publisher

Abstract

A robust scheme is proposed for producing maximally entangled states for many trapped ions in thermal motion. In the scheme the ions are simultaneously illuminated by two standing-wave laser fields. During the operation the phases of the lasers are inverted, which not only cancels the vibration-dependent parts in the evolution operator, but also suppresses direct off-resonant coupling of the internal states. Thus, our scheme allows the production of entanglement for hot trapped ions with laser fields of high intensity, which makes the entanglement speed extremely high.

DOI
10.1088/0253-6102/43/2/023

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A robust scheme is proposed for producing maximally entangled states for many trapped ions in thermal motion. In the scheme the ions are simultaneously illuminated by two standing-wave laser fields. During the operation the phases of the lasers are inverted, which not only cancels the vibration-dependent parts in the evolution operator, but also suppresses direct off-resonant coupling of the internal states. Thus, our scheme allows the production of entanglement for hot trapped ions with laser fields of high intensity, which makes the entanglement speed extremely high.
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.
An alternative scheme is proposed for one-step generation of multiparticle cluster state with trapped ions in thermal motion. In this scheme, the ions are simultaneously illuminated by a standing-wave laser tuned to the carrier. During the operations, the vibrational mode is virtually excited, thus the quantum operations are insensitive to the heating. It is shown that the high fidelity multiparticle entanglement could be generated in just one step even including the small fluctuations of parameters. In addition, the ion does not need to be exactly positioned at the node of the standing wave, which is also important from the viewpoint of experiment.
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.