Spectral properties of the squeeze operator

Abstract

We show that a single-mode squeeze operator S(z) being an unitary operator with a purely continuous spectrum gives rise to a family of discrete real generalized eigenvalues. These eigenvalues are closely related to the spectral properties of S(z) and the corresponding generalized eigenvectors may be interpreted as resonant states well known in the scattering theory. It turns out that these states entirely characterize the action of S(z). This result is then generalized to N-mode squeezing.