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Generalized coherent states associated with the C_λ-extended oscillator

C. Quesne
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Abstract

Two new types of coherent states associated with the C_λ-extended oscillator, where C_λ is the cyclic group of order λ, are introduced. The first ones include as special cases both the Barut-Girardello and the Perelomov su(1,1) coherent states for λ=2, as well as the annihilation-operator coherent states of the C_λ-extended oscillator spectrum generating algebra for higher λvalues. The second ones, which are eigenstates of the C_λ-extended oscillator annihilation operator, extend to higher λvalues the paraboson coherent states, to which they reduce for λ=2. All these states satisfy a unity resolution relation in the C_λ-extended oscillator Fock space (or in some subspace thereof). They give rise to Bargmann representations of the latter, wherein the generators of the C_λ-extended oscillator algebra are realized as differential-operator-valued matrices (or differential operators). The statistical and squeezing properties of the new coherent states are investigated over a wide range of parameters and some interesting nonclassical features are exhibited.

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C. Quesne. 2001-08-29. Generalized coherent states associated with the C_λ-extended oscillator. https://doi.org/10.1006/aphy.2001.6184

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