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arXiv:quant-ph/0001027 · Journal of Optics B Quantum and Semiclassical Optics

New nonlinear coherent states and some of their nonclassical properties

B Roy, P Roy

Published Feb 1, 2000• 111 citations
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Abstract

We construct a displacement-operator-type nonlinear coherent state and examine some of its properties. In particular, it is shown that this nonlinear coherent state exhibits nonclassical properties such as squeezing and sub-Poissonian behaviour.
DOI
10.1088/1464-4266/2/1/311

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Abstract Since radiation field states are very important in the interaction with the various atomic structures, in this article we introduce a new type of quantum states, which we call ‘Mth nonlinear coherent states’. We define these states based on acting of the number operator M times n ˆ M on a nonlinear coherent state. By analyzing the photon distribution function and its overlap with the nonlinear coherent states, it becomes clear that these states are very similar to the corresponding nonlinear coherent states. We also investigate the nonclassical features of such states for different values of M, and it is determined that the occurrence of sub-Poissonian photon statistics, normal squeezing, and amplitude squared squeezing are considerable nonclassical properties of the Mth nonlinear coherent states. Also, examining the Husimi function shows a local behavior for the introduced states. Furthermore, by calculating the Wigner function, we find out that in some points of the phase space, the value of this function is negative which could be considered as a nonclassical feature for these states.
Using the nonlinear coherent states method , a formalism for the construction of the coherent states associated with ‘ inverse bosonic operators ’ and their dual family has been proposed. Generalizing the approach, the ‘inverse of f -deformed ladder operators’ corresponding to the nonlinear coherent states in the context of quantum optics and the associated coherent states have been introduced. Finally, after applying the proposal to a few known physical systems, particular nonclassical features as sub-Poissonian statistics and the squeezing of the quadratures of the radiation field corresponding to the introduced states have been investigated.