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Journal of Optics B Quantum and Semiclassical Optics

Preparation of motional cat states for trapped ions using a standing wave in strong excitation

Li-Xiang Li, Guang‐Can Guo

Published Jan 1, 1999• 4 citations
Publisher

Abstract

We propose a scheme to generate cat states for trapped ions using a standing wave in both the strong excitation regime and the Lamb-Dicke limit. A single strong standing-wave laser, exciting the ion for a short time, will leave the ion in an entangled state. After a measurement of the internal state, the external state will collapse to an odd or even coherent state.

DOI
10.1088/1464-4266/1/3/307

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Journal of Modern Optics•Mar 1, 1999•1 citation
We propose a scheme to generate cat states for trapped ions using a standing wave in both the strong excitation regime and the Lamb-Dicke limit. A single strong standing-wave laser, exciting the ion for a short time, will leave the ion in an entangled state. After a measurement of the internal state, the external state will collapse to an odd or even coherent state.
A scheme is presented for the generation of macroscopic quantum-interference states for the motion of a trapped ion. In the scheme the ion is driven by a standing-wave laser beam whose carrier frequency is tuned to the ion transition. The distinct feature of the scheme is that the time required to generate the desired state is limited only by the available laser intensity, not by inherent mechanisms such as off-resonant excitations. Therefore, our scheme may allow the generation of the desired state at a high speed, which is important in view of decoherence. In the two-dimension case, entangled coherent states can be obtained. The scheme can also be used to generate entangled states for multiple modes of NNN trapped ions with a single strong standing-wave laser pulse.
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.
A scheme is proposed for preparing superpositions of many equidistant coherent states on a circle for the motion of an ion in an anisotropic two-dimensional trap, in which the ion is tightly bound in the y direction. In the scheme the ion is excited by one laser field in the x direction and then by two laser fields propagating along the x and y directions alternately many times. Then a state-selective measurement on the ion is made, which collapses the vibrational motion to a coherent state superposition.