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arXiv:quant-ph/9911005 · Physical Review A

Filtering number states of the vibrational motion of an ion

H. M. Moya-Cessa, P. Tombesi

Published Jan 4, 2000• 36 citations
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Abstract

We propose a scheme to generate number states, and specific superpositions of them, of the vibrational motion of a trapped ion via laser excitation of two vibronic transitions. Without detrimental effects on the internal state preparation, the ion can be initially in thermal motion and undergo spontaneous emission. In particular, qubits that are robust against noise $(\ensuremath{\alpha}|0〉+\ensuremath{\beta}|1〉$ states) can be generated with arbitrary amplitudes.

DOI
10.1103/physreva.61.025401

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We propose a scheme to generate number states, and specific superpositions of them, of the vibrational motion of a trapped ion via laser excitation of two vibronic transitions. Without detrimental effects on the internal state preparation, the ion can be initially in thermal motion and undergo spontaneous emission. In particular, qubits that are robust against noise (\ensuremathα∣0〉+\ensuremathβ∣1〉(\ensuremath{\alpha}|0〉+\ensuremath{\beta}|1〉(\ensuremathα∣0〉+\ensuremathβ∣1〉 states) can be generated with arbitrary amplitudes.
A scheme is proposed to generate an arbitrary entangled state of the two-dimensional vibrational motion of a trapped ion. In the scheme the ion is excited by a sequence of laser pulses tuned to the appropriate vibrational sidebands. In order to generate a pure state with upper phonon numbers M and N in the X and Y directions, respectively, we require no more than (M+2)(N+1)(M+2)(N+1)(M+2)(N+1) operations.
We present a scheme to generate an arbitrary two-dimensional quantum state of motion of a trapped ion. This proposal is based on a sequence of laser pulses, which are tuned appropriately to control transitions on the sidebands of two modes of vibration. Not more than (M+1)(N+1)(M+1)(N+1)(M+1)(N+1) laser pulses are needed to generate a pure state with a phonon number limit M and N.
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.