In this paper we have constructed the continuum eigenfunctions and eigenvalue spectra for the squeeze operators of both single mode and two modes. Our analyses also show explicitly that proper eigenstates of both single-mode and two-mode squeeze operators do not exist, which implies that the squeeze operators do not have a discrete spectrum.

Physical Review ADec 1, 199014 citations

Eigenfunctions and eigenvalues of the generalized squeeze operator

Chi‐Fai Lo

The author has constructed the eigenfunctions and eigenvalue spectrum for the generalized squeeze operator in the Hilbert space of entire functions. Proper eigenstates exist only for beta > mod alpha mod with a discrete eigenvalue spectrum resembling that of a displaced simple harmonic oscillator, whereas for beta < mod alpha mod the generalized squeeze operator has continuum eigenfunctions only.

Quantum Optics Journal of the European Optical Society Part BDec 1, 19919 citations