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Physical Review A

Scheme for direct measurement of the Wigner function of a trapped ion in the intermediate-excitation regime

Shi‐Biao Zheng

Published Apr 25, 2005• 2 citations
Publisher

Abstract

We propose a scheme to directly measure the Wigner function for the motion of a trapped ion. Unlike the previous scheme [Phys. Rev. Lett. 78, 2547 (1997)], the present scheme works in the intermediate-excitation regime, which may be of experimental importance in view of decoherence. The scheme can also be used to perform a quantum nondemolition measurement of the vibrational energy and prepare motional Schr\"odinger cat states.

DOI
10.1103/physreva.71.043820

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We propose a scheme to directly measure the Wigner function for the motion of a trapped ion. Unlike the previous scheme [Phys. Rev. Lett. 78, 2547 (1997)], the present scheme works in the intermediate-excitation regime, which may be of experimental importance in view of decoherence. The scheme can also be used to perform a quantum nondemolition measurement of the vibrational energy and prepare motional Schr"odinger cat states.
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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.
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In this letter, a procedure is proposed for reconstructing the motional quantum state of N trapped ions. Unlike other previous schemes, the present scheme works in the dispersive regime in the presence of dissipation. In our scheme, we show that it is possible to directly measure the quasiprobability distribution function corresponding to the motional coherent state in a trapped-ion system subjected to dissipation. We also provide an example of a motional Schrödinger cat state reconstruction to exemplify our procedure.