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Chinese Physics Letters

Generation of Pair Coherent States in Two-dimensional Trapped Ion

Kaige Wang, Sabrina Maniscalco, Anna Napoli, A Messina

Published Feb 8, 2001• 4 citations
Publisher

Abstract

We consider 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 of the ion. Due to the coherent superposition of two sub-Rabi oscillations involved in the bimodal vibrations, the Rabi frequency degeneration and offset may occur in this model. This provides the possibility of generating the pair coherent state in the 2D trapped ion.

DOI
10.1088/0256-307x/18/3/319

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We consider 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 of the ion. Due to the coherent superposition of two sub-Rabi oscillations involved in the bimodal vibrations, the Rabi frequency degeneration and offset may occur in this model. This provides the possibility of generating the pair coherent state in the 2D trapped ion.
We propose a scheme for generating vibrational pair coherent states of the motion of an ion in a two-dimensional trap. In our scheme, the trapped ion is excited bichromatically by three laser beams along different directions in the $X\ensuremath{-}Y$ plane of the ion trap. We show that if the initial vibrational state is given by a two-mode Fock state, the final steady state, indicated by the extinction of the fluorescence emitted by the ion, is a pure state. The motional state of the ion in the equilibrium realizes that of the highly correlated pair coherent state.
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.
We propose a scheme for generating mesoscopic superpositions of two distinguishable pair coherent states of motion in a two-dimensional ion trap. In our scheme, the trapped ion is excited bichromatically by five laser beams along different directions in the X-Y plane of the ion trap. Four of these have the same frequency and can be derived from the same source, reducing the demands on the experimentalist. We show that if the initial vibrational state is given by a two-mode Fock state, as demonstrated in recent experiments, these highly correlated two-mode ``Schr\"odinger cat'' states are realized when the system reaches its steady state, which is indicated by the extinction of the fluorescence emitted by the ion. \textcopyright{} 1996 The American Physical Society.