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Journal of Modern Optics

Some non-classical properties of a class of new nonlinear coherent states

A.‐S. F. Obada, Mahmoud Darwish, H. H. Salah

Published Jun 15, 2005• 5 citations
Publisher

Abstract

Some of the properties of a nonlinear coherent state associated with the centre of mass motion of trapped atoms are considered. Especially the autocorrelation function, motional quanta number distribution, the phase properties, the Husimi–Kano Q function and the Wigner–Moyal W function of this nonlinear coherent state are discussed. Jumps in the motional quanta distribution function are reported depending on the dependence on the Lamb–Dicke parameters.

DOI
10.1080/09500340512331330846

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Some of the properties of a nonlinear coherent state associated with the centre of mass motion of trapped atoms are considered. Especially the autocorrelation function, motional quanta number distribution, the phase properties, the Husimi–Kano Q function and the Wigner–Moyal W function of this nonlinear coherent state are discussed. Jumps in the motional quanta distribution function are reported depending on the dependence on the Lamb–Dicke parameters.
We consider a class of nonlinear coherent states, which are right-hand eigenstates of the product of the boson annihilation operator and a nonlinear function of the number operator. Such states may appear as stationary states of the center-of-mass motion of a trapped and bichromatically laser-driven ion far from the Lamb-Dicke regime. Besides coherence properties, they exhibit nonclassical features such as amplitude squeezing and self-splitting, which is accompanied by pronounced quantum interference effects. \textcopyright{} 1996 The American Physical Society.
Some of the properties of nonlinear squeezed vacuum states associated with trapped ions are considered, especially the photon number distribution, the phase properties, the Husimi–Kano Q function and the Wigner–Moyal W function of these nonlinear squeezed vacuum states. The structure of these functions is shown to depend on the nonlinearity parameter, its functional dependence and the squeezing parameter. It is shown that increasing the nonlinearity parameter results in the photon number distribution being squeezed independent.
Using the nonlinear coherent states approach, a general formalism for the construction of various classes of nonlinear trio coherent states in the context of multi-mode quantum states has been proposed. In particular, taking into account the most popular nonlinearity function associated with f -deformed coherent states, i.e. the nonlinearity function of the centre-of-mass motion of a trapped ion, it is illustrated that the corresponding trio coherent state possesses some interesting nonclassical properties. To establish this observation, sub-Poissonian statistics, three-mode squeezing, the behaviour of Vogel's characteristic function and the existence of entanglement are investigated. Due to the intrinsic non-classicality nature of the considered three-mode states, their physical production may be of high interest in the quantum optics field. Thus, we have finally demonstrated how nonlinear motional trio coherent states can be generated in three-dimensional anisotropic traps, appropriately.