Quantum statistics of the degenerate parametric amplifier

Abstract

From the quantum mechanics and the quantum optics point of view the problem of the time-dependent Hamiltonian which describes the degenerate parametric amplifier is presented. Under a certain integrability condition the solution of the Heisenberg equations of motion is given. The wave function for both the Schrödinger picture and quasi-coherent states, as well as the Green's function is obtained. The Glauber second order correlation function, and the squeezing and higher order squeezing is examined. The quasi-probability distribution function is also considered.