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Australian Journal of Physics

Preparation of superpositions of SU(2) coherent states of the motion of a trapped ion.

Shi‐Biao Zheng

Published Jun 22, 2000• 2 citations
Publisher

Abstract

A scheme is presented for the generation of superpositions of two two-mode SU(2) coherent states of the motion for a trapped ion. In the scheme an ion is trapped in a two-dimensional isotropic harmonic potential and driven by two resonant laser beams. Under certain conditions, the motional two-mode SU(2) cat state can be generated after a conditional measurement on the internal state following the ion-laser interaction.

DOI
10.1071/ph99064

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A scheme is presented for the generation of superpositions of two two-mode SU(2) coherent states of the motion for a trapped ion. In the scheme an ion is trapped in a two-dimensional isotropic harmonic potential and driven by two resonant laser beams. Under certain conditions, the motional two-mode SU(2) cat state can be generated after a conditional measurement on the internal state following the ion-laser interaction.
We propose a scheme for generating superpositions of coherent states for both the centre-of-mass and relative vibrational modes of two trapped ions. In the proposed scheme two trapped ions are driven by two laser beams dispersively tuned to the first lower- and upper-vibrational sideband transitions, respectively. Under certain conditions, the measurement of the internal states leaves one vibrational mode in a superposition of two coherent states. Entangled coherent states for these two vibrational modes can also be generated. The scheme can be used to measure the Wigner function of one vibrational mode given that the other mode is initially in the vacuum state.
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.