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arXiv:1110.4804 · Physical Review A

Sympathetic Wigner-function tomography of a dark trapped ion

Safoura Sadat Mirkhalaf, Klaus Mølmer

Published Apr 12, 2012• 7 citations
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Abstract

A protocol is provided to reconstruct the Wigner function for the motional state of a trapped ion via fluorescence detection on another ion in the same trap. This ``sympathetic tomography'' of a dark ion without optical transitions suitable for state measurements is based on the mapping of its motional state onto one of the collective modes of the ion pair. The quantum state of this vibrational eigenmode is subsequently measured through sideband excitation of the bright ion. Physical processes to implement the desired state transfer are derived and the accomplishment of the scheme is evaluated for different mass ratios.

DOI
10.1103/physreva.85.042109

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A protocol is provided to reconstruct the Wigner function for the motional state of a trapped ion via fluorescence detection on another ion in the same trap. This ``sympathetic tomography'' of a dark ion without optical transitions suitable for state measurements is based on the mapping of its motional state onto one of the collective modes of the ion pair. The quantum state of this vibrational eigenmode is subsequently measured through sideband excitation of the bright ion. Physical processes to implement the desired state transfer are derived and the accomplishment of the scheme is evaluated for different mass ratios.
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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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