Diagonalization of the generalized squeeze operators and the generalized squeezed number states

Abstract

The generalized single-mode and two-mode squeeze operators are diagonalized by employing Bogolyubov and Bogolyubov-Valatin transformations, and the unitary operators performing these transformations are derived. The authors find that the eigenvalues are complex exponential functions with the exponential factors of harmonic-oscillator spectra and the eigenstates are a new kind of squeezed number state different from the ordinary squeezed number states.