Statistical properties of three quantized interacting oscillators

We investigate the quantum statistics of three harmonic oscillators mutuall y interacting with each other determining quadratures squeezing, second-ord er correlation function and phase space distributions. We assume that the m odes are initially prepared in coherent states. We show that the initial co herent states can evolve into squeezed states which are not minimum uncerta inty states governed by the interaction parameters. Moreover, we demonstrat e that the interaction is able to produce squeezing of different types, i.e . single-mode, two-mode and three-mode squeezing. Further, we show for spec ific modes and under certain conditions the oscillatory behaviour in the ph oton-number distribution and the bifurcation phenomenon in the phase distri bution for squeezed light.