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Journal of Modern Optics

Preparation of multicomponent cat states of the motion of a trapped ion by a single conditional measurement

Shi‐Biao Zheng

Published Mar 1, 1999• 1 citation
Publisher

Abstract

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.

DOI
10.1080/09500349908231290

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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.
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.
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.