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Journal of Physics A Mathematical and General

Generation and some nonclassical properties of a nonlinear finite-dimensional pair coherent state

Eied Mahmoud Khalil

Published Aug 11, 2006• 17 citations
Publisher

Abstract

We propose a scheme for generating a nonlinear finite-dimensional pair coherent state of the vibrational motion of an ion in a two-dimensional trap. It is a type of the correlated two-mode states but in finite dimensions. Based on the resonant ion–cavity interaction, we propose a scheme to generate these states revealing their connection with the converter type of interaction and investigate some of their nonclassical properties.

DOI
10.1088/0305-4470/39/35/007

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We propose a scheme for generating a nonlinear finite-dimensional pair coherent state of the vibrational motion of an ion in a two-dimensional trap. It is a type of the correlated two-mode states but in finite dimensions. Based on the resonant ion–cavity interaction, we propose a scheme to generate these states revealing their connection with the converter type of interaction and investigate some of their nonclassical properties.
In this contribution a nonlinear type of the correlated two-mode states (nonlinear pair-coherent states (NLPCS)) is introduced. Based on the resonant ion–cavity interaction, we propose a scheme to generate these states revealing their connection with the pair-coherent state (PCS) and investigate their nonclassical properties. The practical feasibility of this method is also discussed. The s-parameterized characteristic function (CF) of the NLPCS is considered. The s-parameterized quasi-probability distribution function (QDF) is investigated.
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.
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.