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arXiv:quant-ph/0103077

K-quantum nonlinear coherent states: formulation, realization and nonclassical effects

Nguyen Ba An

Published Mar 14, 2001• 8 citations
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Abstract

We introduce a generalized class of states called K-quantum nonlinear coherent states. Each K-state has K j-components corresponding to one and the same eigenvalue. Each Kj-component can be composed of K K=1-states in a correlated manner. The introduced states are shown to be realized in the long-term behavior of the vibrational motion of an ion properly trapped and laser-driven. Nonclassical properties of the states are studied in detail.

DOI
10.48550/arxiv.quant-ph/0103077

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We introduce a generalized class of states called K-quantum nonlinear coherent states. Each K-state has K j-components corresponding to one and the same eigenvalue. Each Kj-component can be composed of K K=1-states in a correlated manner. The introduced states are shown to be realized in the long-term behavior of the vibrational motion of an ion properly trapped and laser-driven. Nonclassical properties of the states are studied in detail.
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.
Nonclassical states of light are of fundamental importance in quantum optics. The properties of these states are due to the quantal nature of the electromagnetic field. In recent years there have been many experimental demonstrations of the realizability of nonclassical states in various physical schemes such as resonance fluorescence, four-wave mixing, centre-of-mass motion of a trapped ion and manipulation of field in a cavity. It is of interest to introduce new classes of nonclassical states and investigate their properties. In this context, generalization of the concept of coherent states (CSs) has played a major role. New concepts such as the nonlinear coherent states (NCSs) and interference in phase space have emerged from such studies. In this tutorial review we are concerned with the construction of new classes of nonclassical states by generalizing the notion of CSs. Our investigations on the photon-added coherent states (PACSs) indicate that these states can be interpreted as NCSs. Also, we introduce a new class of nonclassical states related to the PACSs. Having introduced a realizable example of NCSs, we extend the notion of even and odd CSs to the case of NCSs by introducing even and odd NCSs. With this new definition we interrelate some of the well known states of light. We suggest a scheme to generate a class of even and odd NCSs in the centre-of-mass motion of a trapped, laser-cooled, two-level ion.
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.
In this paper, after a brief review on the entangled coherent state, a general form of the entangled nonlinear coherent state has been introduced based on the nonlinear coherent states approach. By choosing particular f-deformation functions, theoretical schemes for generation of two distinct classes of such states associated with SU(1,1) and SU(2) groups are presented. The entanglement characteristic of the corresponding entangled coherent states has been studied by evaluating the concurrence. In the continuation, other nonclassical behaviors of the produced states have been analyzed by investigating sub-Poissonian photon statistics, the oscillatory photon number distribution, one- and two-mode quadrature squeezing, and sum and difference squeezing. Accordingly, in addition to their entanglement property, other nonclassicality features of the introduced states are well established in detail.