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Physical Review A

Measurements on trapped laser-cooled ions using quantum computations

Cassius D'Helon, Gerard J Milburn

Published Dec 1, 1996• 20 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.54.5141

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•Jan 1, 1998•9 citations
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 present a scheme in which an ion trap quantum computer can be used to make arbitrarily accurate measurements of the quadrature phase variables for the collective vibrational motion of the ion. The electronic states of the ion become the `apparatus', and the method is based on regarding the `apparatus' as a quantum computer register which can be prepared in appropriate states by running a Fourier transform algorithm on the data stored within it. The resolution of the measurement rises exponentially with the number of ions used.
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.
The quantum nondemolition measurement is applied to a two-dimensional (2D) trapped-ion model in which two laser beams drive the corresponding vibrational motions and are carrier resonant with the two-level system of the ion. The information about the ionic vibrational energy can be detected by the occupation probability of the internal electronic level. The substantial difference of the 2D model from the one-dimensional one is that two orthogonal beams have a fixed phase shift instead of statistical independence. As a result, the atomic Rabi oscillation is involved in the coherent superposition of two sub-Rabi oscillations induced by the corresponding driving beams. This means that, in the bidimensional case, the phase difference between the two laser beams plays the role of an adjustable external parameter which allows us to optimize the measurement scheme itself, in terms of precision and sensitivity. As in the one-dimensional case, our proposal leads to interesting applications as, for example, the cooling and preparation of arbitrary bimodal Fock states. The model can be considered as a cooling method for the trapped ion from the vibrational thermal state to the vacuum state. Due to the coherent superposition of two sub-Rabi oscillations, the Rabi frequency degeneration and offset may occur in this model. This provides the possibility of generating various entangled superposition of Fock states, the pair coherent state, and entangled pair coherent states.