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Lecture notes in physics

Quantum Nondemolition Measurement and Quantum State Manipulation in Two Dimensional Trapped Ion

W. Kaige, Sabrina Maniscalco, Anna Napoli, ANTONINO MESSINA

Published Jan 1, 2001• 0 citations
Publisher
DOI
10.1007/3-540-45409-8_3

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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.
A quantum-nondemolition (QND) measurement of the vibrational energy of a trapped ion may be made by placing it at a node of a cavity optical standing wave. In certain parameter regimes there is a backaction evading coupling between the ion's vibrational energy eigenstates and the coherent states of the cavity field. This facilitates a QND measurement of the ion trap state via a homodyne measurement on the cavity output field. This scheme has the advantage that the required measurements minimally disturb the ion.