Generalized coherent states associated with the Cλ-extended oscillator

Two new types of coherent states associated with the C-lambda-extended oscillator, where C-lambda is the cyclic group of order;, are introduced. The first ones include as special cases both the Barut-Giradello and the Perelomov su(1, 1) coherent states for. lambda = 2, as well as the annihilation-operator coherent states of the C-lambda-extendcd oscillator spectrum-gencrating algebra for higher 2, values. The second ones, which are eigenstates of the C-lambda-extended oscillator .annihilation operator, extend to higher lambda values the paraboson coherent states, to which they reduce for lambda = 2. All these states satisfy a unity resolution relation in the C-lambda-extended oscillator Fock space (or in some subspace thereof). They give rise to Bargmann representations of the latter, wherein the generators of the C-lambda-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. (C) 2001 Academic Press.