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Physical Review A

Motional quantum states of a trapped ion: Measurement and its back action

Sascha Wallentowitz, W. Vogel

Published Oct 1, 1996• 31 citations

Abstract

We develop a method for reconstructing the quantum mechanical state of a trapped ion by bichromatically irradiating it on a weak electronic transition and subsequently probing a strong electronic transition for resonance fluorescence. Based on this recently proposed scheme [S. Wallentowitz and W. Vogel, Phys. Rev. Lett. 75, 2932 (1995)] the density matrix of the vibrational motion can be readily obtained either in a generalized position representation or in the number-state representation. The method allows to uniquely define an ultimate classical noise level by a reference measurement with an ion cooled to its vibrational ground-state. Disturbations of the measurement and their suppression are considered. Moreover, we study the effect of the back action of the measurement principle on the motional quantum state. It consists in the splitting of the state to be measured into two substates, giving rise to quantum interference effects. \textcopyright{} 1996 The American Physical Society.

DOI: 10.1103/physreva.54.3322

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We discuss a simple implementation of a quantum nondemolition measurement of the vibronic state of a trapped ion. This scheme allows the production of Fock states associated to the center-of-mass motion and the determination of the population distribution of the trap levels, and is based on the vibronic level dependence of the frequency of Rabi oscillations between two internal states of the ion, induced by a resonant carrier field. The same scheme can be used to produce a Schr\"odinger-cat-like state after a single interaction between the trapped ion and the carrier pulse, followed by the detection of the ionic internal state. \textcopyright{} 1996 The American Physical Society.

Abstract : We report the creation and full determination of several quantum states of motion of a 9Be ion bound in a RF (Paul) trap. The states are coherently prepared from an ion which has been initially laser cooled to the zero-point of motion. We create states having both classical and non-classical character including thermal, number, coherent, squeezed, and Schrodinger cat states. The motional quantum state is fully reconstructed using two novel schemes that determine the density matrix in the number state basis or the Wigner function. Our techniques allow well controlled experiments decoherence and related phenomena on the quantum-classical borderline.

We show that a series of quantum computations involving an isolated N-quantum-bit ion register can be used to make an approximate quantum nondemolition measurement of the number state distribution of a collective vibrational mode. A unitary transformation is applied to the Fourier transformed state of the ion register to copy the vibrational statistics to the electronic mode, and the number state distribution is then measured in the electronic number state basis using the quantum jumps technique. \textcopyright{} 1996 The American Physical Society.

We report the creation and full determination of several quantum states of motion of a 9Be+ ion bound in a RF (Paul) trap. The states are coherently prepared from an ion which has been initially laser cooled to the zero-point of motion. We create states having both classical and non-classical character including thermal, number, coherent, squeezed, and ‚Schrödinger cat‘ states. The motional quantum state is fully reconstructed using two novel schemes that determine the density matrix in the number state basis or the Wigner function. Our techniques allow well controlled experiments decoherence and related phenomena on the quantum-classical borderline.

We report the creation and full determination of several quantum states of motion of a 9Be+ ion bound in a RF (Paul) trap. The states are coherently prepared from an ion which has been initially laser cooled to the zero-point of motion. We create states having both classical and non-classical character including thermal, number, coherent, squeezed, and ‚Schrödinger cat‘ states. The motional quantum state is fully reconstructed using two novel schemes that determine the density matrix in the number state basis or the Wigner function. Our techniques allow well controlled experiments decoherence and related phenomena on the quantum-classical borderline.