Abstract
We investigate the quantum statistics of three harmonic oscillators mutually interacting with each other determining quadratures squeezing, second-order correlation function and phase space distributions. We assume that the modes are initially prepared in coherent states. We show that the initial coherent states can evolve into squeezed states which are not minimum uncertainty states governed by the interaction parameters. Moreover, we demonstrate 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 specific modes and under certain conditions the oscillatory behaviour in the photon-number distribution and the bifurcation phenomenon in the phase distribution for squeezed light.