Even and odd coherent states of a harmonic oscillator in a finite-dimensional Hilbert space and their squeezing properties

Abstract

The even and odd coherent states (CSs) of a finite-dimensional Hilbert space harmonic oscillator (FDHSHO) are constructed and some properties of these states are studied. Their quadrature squeezing and amplitude-squared squeezing are investigated in detail. It is shown that, while the squeezing behavior of the even and odd CSs of the FDHSHO approaches that of the even and odd CSs of the usual harmonic oscillator as the dimension of the Hilbert space tends to infinity, this behavior is nontrivally different if the dimension of the Hilbert space is finite. In the latter case, it is found that the even and odd CSs exhibit both amplitude-squared squeezing and quadrature squeezing.