EVEN AND ODD COHERENT STATES OF A HARMONIC-OSCILLATOR IN A FINITE-DIMENSIONAL HILBERT-SPACE AND THEIR SQUEEZING PROPERTIES

The even and odd coherent states (CSs) of a finite-dimensional Hilbert space harmonic oscillator (FDHSHO) are constructed and some propertie s of these states are studied. Their quadrature squeezing and amplitud e-squared squeezing are investigated in detail. It is shown that, whil e the squeezing behaviour of the even and odd CSs of the FDHSHO approa ches that of the even and odd CSs of the usual harmonic oscillator as the dimension of the Hilbert space tends to infinity, this behaviour i s nontrivally different if the dimension of the Hilbert space is finit e. In the latter case, it is found that the even and odd CSs exhibit b oth amplitude-squared squeezing and quadrature squeezing.