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Chinese Physics

Preparation of nonclassical states and measurement of the Wigner function for the collective motion of N trapped ions

Zheng Shi-Biao

Published Oct 26, 2004• 10 citations
Publisher

Abstract

We propose a scheme for generating nonclassical states for the centre-of-mass vibrational mode of N trapped ions, including superpositions of several coherent states on a circle and Fock states. In the scheme N trapped ions are driven by a laser beam tuned to the carrier. The scheme also provides a new prospect for laser cooling. The scheme can be used to measure the Wigner function of the collective vibrational mode.

DOI
10.1088/1009-1963/13/11/017

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We propose a scheme for generating nonclassical states for the centre-of-mass vibrational mode of N trapped ions, including superpositions of several coherent states on a circle and Fock states. In the scheme N trapped ions are driven by a laser beam tuned to the carrier. The scheme also provides a new prospect for laser cooling. The scheme can be used to measure the Wigner function of the collective vibrational mode.
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 proposed a scheme for the reconstruction of the quantum states for the center-of-mass vibrational mode of two trapped ions. In the scheme the ions are multichromatically excited by three lasers. Then measurement of the difference between probabilities of the ions being both in electronic ground and excited states directly yields the Wigner characteristic function for the center-of-mass vibrational state. The scheme can also be used to prepare entangled coherent states for the center-of-mass and relative vibrational modes.
We proposed a scheme for the reconstruction of the quantum states for the center-of-mass vibrational mode of two trapped ions. In the scheme the ions are multichromatically excited by three lasers. Then measurement of the difference between probabilities of the ions being both in electronic ground and excited states directly yields the Wigner characteristic function for the center-of-mass vibrational state. The scheme can also be used to prepare entangled coherent states for the center-of-mass and relative vibrational modes.
In this paper, a procedure is proposed for measuring Wigner characteristic function for motion of a single trapped ion. In the scheme, the trapped ion is driven by two laser beams with different frequencies tuned to the first lower and upper vibrational sidebands, respectively. Unlike other previous scheme, our scheme does not require the displacement of the external state before the ion-laser interaction and thus our scheme might be more simple and feasible. The scheme can also be used to prepare the motional Schrodinger cat states and entangled coherent states.