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arXiv:quant-ph/0403003 · Journal of Physics A Mathematical and General

The construction of some important classes of generalized coherent states: the nonlinear coherent states method

R. Roknizadeh, Mohammad Kazem Tavassoly

Published Aug 5, 2004• 92 citations
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Abstract

Considering some important classes of generalized coherent states known in literature, we demonstrated that all of them can be created via conventional fashion, i.e. the "lowering operator eigen-state" and the "displacement operator" techniques using the {\it "nonlinear coherent states"} approach. As a result we obtained a {\it "unified method"} to construct a large class of coherent states which already have been introduced by different prescriptions.

DOI
10.1088/0305-4470/37/33/010

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Considering some important classes of generalized coherent states known in literature, we demonstrated that all of them can be created via conventional fashion, i.e. the "lowering operator eigen-state" and the "displacement operator" techniques using the {\it "nonlinear coherent states"} approach. As a result we obtained a {\it "unified method"} to construct a large class of coherent states which already have been introduced by different prescriptions.
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.
In this work we make use of deformed operators to construct the coherent states of some nonlinear systems by generalization of two definitions: i) As eigenstates of a deformed annihilation operator and ii) by application of a deformed displacement operator to the vacuum state. We also construct the coherent states for the same systems using the ladder operators obtained by traditional methods with the knowledge of the eigenfunctions and eigenvalues of the corresponding Schrödinger equation. We show that both methods yield coherent states with identical algebraic structure.