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Chinese Journal of Physics

Simplified Scheme for Measuring the Entangled Vibronic States of a Trapped Ion

Shi‐Biao Zheng

Published Jun 1, 2003• 0 citations
OpenAlex

Abstract

We propose a simplified scheme for measuring the entangled state of the motional and electronic degrees of freedom of an ion trapped in a one-dimensional harmonic potential. The scheme is based on the polychromatic excitation of the ion by three lasers tuned to the carrier, the first lower, and the upper vibrational sidebands, respectively. The method directly yields the elements of the Wigner characteristic function matrix in the electronic basis. The scheme can be easily generalized to the two-dimensional case.

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We propose a simplified scheme for measuring the entangled state of the motional and electronic degrees of freedom of an ion trapped in a one-dimensional harmonic potential. The scheme is based on the polychromatic excitation of the ion by three lasers tuned to the carrier, the first lower, and the upper vibrational sidebands, respectively. The method directly yields the elements of the Wigner characteristic function matrix in the electronic basis. The scheme can be easily generalized to the two-dimensional case.
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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.
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 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.