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arXiv:atom-ph/9601001 · Physical Review A

Motion tomography of a single trapped ion

J. F. Poyatos, R. Walser, J. I. Cirac, P. Zoller, R. Blatt

Published Apr 1, 1996• 116 citations
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Abstract

A method for the experimental reconstruction of the quantum state of motion for a single trapped ion is proposed. It is based on the measurement of the ground-state population of the trap after a sudden change of the trapping potential. In particular, we show how the $Q(\ensuremath{\alpha})$ function and the quadrature distribution $P(x, \ensuremath{\theta})$ can be measured directly. In an example we demonstrate the principle and analyze the sensitivity of the reconstruction process to experimental uncertainties as well as to finite grid limitations. Our method is not restricted to the Lamb-Dicke Limit and works in one or more dimensions.

DOI
10.1103/physreva.53.r1966

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A method for the experimental reconstruction of the quantum state of motion for a single trapped ion is proposed. It is based on the measurement of the ground-state population of the trap after a sudden change of the trapping potential. In particular, we show how the Q(\ensuremathα)Q(\ensuremath{\alpha})Q(\ensuremathα) function and the quadrature distribution P(x,\ensuremathθ)P(x, \ensuremath{\theta})P(x,\ensuremathθ) can be measured directly. In an example we demonstrate the principle and analyze the sensitivity of the reconstruction process to experimental uncertainties as well as to finite grid limitations. Our method is not restricted to the Lamb-Dicke Limit and works in one or more dimensions.
A method for gaining information about the phonon-number moments and the generalized nonlinear and linear quadratures in the motion of trapped ions (in particular, position and momentum) is proposed, valid inside and outside the Lamb-Dicke regime. It is based on the measurement of first time derivatives of electronic populations, evaluated at the motion-probe interaction time t=0. In contrast to other state-reconstruction proposals, based on measuring Rabi oscillations or dispersive interactions, the present scheme can be performed resonantly at infinitesimal short motion-probe interaction times, remaining thus insensitive to decoherence processes.
A method for gaining information about the phonon-number moments and the generalized nonlinear and linear quadratures in the motion of trapped ions (in particular, position and momentum) is proposed, valid inside and outside the Lamb-Dicke regime.It is based on the measurement of first time derivatives of electronic populations, evaluated at the motion-probe interaction time τ = 0.In contrast to other state-reconstruction proposals, based on measuring Rabi oscillations or dispersive interactions, the present scheme can be performed resonantly at infinitesimal short motion-probe interaction times, remaining thus insensitive to decoherence processes.
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.
We describe a method to perform a single quantum measurement of an arbitrary motional observable of a single ion moving in a harmonic potential. We illustrate the measurement procedure with explicit examples, namely the position and phase observables. A necessary tool for this is the ability to synthesize an arbitrary motional state. In addition, we show how to generalize this to higher dimensions, and show explicit examples of how to engineer states in two spatial dimensions, including a proposed experimental configuration.