Phase space interference and the WKB approximation for squeezed number states

Abstract

Squeezed number states for a single mode Hamiltonian are investigated from two complementary points of view. Firstly the more relevant features of their photon distribution are discussed using the WKB wave functions. In particular the oscillations of the distribution and the parity behavior are derived and compared with the exact results. The accuracy of the approximation is verified and it is shown that for high photon number it fails to reproduce the true distribution. This is contrasted with the fact that for moderate squeezing the WKB approximation gives the analytical justification to the interpretation of the oscillations as the result of the interference of areas with definite phases in phase space. It is shown with a computation at high squeezing using a modified prescription for the phase space representation which is based on Wigner–Cohen distributions that the failure of the WKB approximation does not invalidate the area overlap picture.