On the coherent states associated with deformed Bogoliubov (p, q)-transformations without first finite Fock states

Abstract

We construct a family of deformed boson coherent states associated with deformed Bogoliubov (p, q)-transformations in an infinite dimensional subspace of the harmonic oscillator Hilbert space without first finite Fock states. We investigate their over-completeness and show that they allow the resolution of unity in the form of an ordinary integral (for Q = pq < 1) or a generalized Q-deformed one (for Q = pq > 1). We study in detail analytically and numerically some of the geometrical and physical properties of these deformed coherent states in the context of deformed quantum optics. In particular, we show that for Q > 1 they exhibit sub-Poissonian statistics and no quadrature squeezing occurs while for Q < 1 their photon number statistics is super-Poissonian and there is a simultaneous squeezing in both field quadratures (double squeezing). Additionally, by a natural extension, we construct the corresponding multi-photon deformed coherent states and investigate their properties.