Marginal and correlation distribution functions in the squeezed-states representation
Marcelo A. Marchiolli, S. S. Mizrahi, V. V. Dodonov · Journal of Physics A Mathematical and General · 1999
Here we consider the Husimi function (HF) P for the squeezed states and calculate the marginal and correlation distribution functions (MDFs and CDFs) when P is projected onto the photon-number states. According to the value of the squeezing parameter one verifies the occurence of oscillations and beats as already appointed in the literature. We verify that these phenomena are entirely contained in the correlation function. In particular, we show that since the Husimi and its MDFs satisfy partial differential equations where the squeeze parameter plays the role of time, the solutions (the squeezed functions obtained from `initial' unsqueezed functions) can be expressed by means of kernels responsible for the `propagation' of squeezing. From the calculational point of view, this method presents advantages for calculating the MDFs (compared with a direct integration over one of the two phase-space variables of P ) since one can use the symmetry properties of the differential equations.