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Journal of Physics A Mathematical and General

Unified approach to the analogues of single-photon and multiphoton coherent states for generalized bosonic oscillators

P. Shanta, S. Chaturvedi, Venkatraman Srinivasan, R. Jagannathan

Published Oct 7, 1994• 50 citations
Publisher

Abstract

A large class of bosonic coherent states known in the literature have been constructed in a unified way by Shanta et. al. (1994). It is shown that this method can be easily extended to generalized bosonic-oscillator systems.
DOI
10.1088/0305-4470/27/19/016

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We obtain a large class of multiphoton annihilation operator (F) eigenstates by constructing an operator ${\mathit{G}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$ such that [F,${\mathit{G}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$]=1. We show that almost all known coherent states, including the squeezed states and other nonclassical states such as the cat and the kitten states follow from our approach. Further, we show that all of them can be expressed as an exponential operator acting on the vacuum of the operator F. The technique can be easily generalized to deformed bosons.
We show that the photon-added squeezed vacuum a m S ( z )|0 and the photon-added squeezed one-photon state a m S ( z )|1 , where m is a non-negative integer, may be regarded as even and odd nonlinear coherent states, respectively. To achieve this, we derive an operator-valued function f ( N , m ) of the number operator N = a a such that a m S ( z )| i ( i = 0,1) are eigenstates of f ( N , m ) a 2 . Based on this, and using the unified method developed by Shanta et al , we find that a m S ( z )| i can be equivalently expressed in exponential forms. The eigenstates of f ( N ,- m ) a 2 are also constructed and their nonclassical features are studied in detail.