Non-classicality criteria: Glauber–Sudarshan P function and Mandel parameter
Moorad Alexanian · Journal of Modern Optics · 2017
We calculate exactly the quantum mechanical, temporal Wigner quasiprobability density for a single-mode, degenerate parametric amplifier for a system in the Gaussian state, viz., a displaced-squeezed thermal state. The Wigner function allows us to calculate the fluctuations in photon number and the quadrature variance. We contrast the difference between the non-classicality criteria, which is independent of the displacement parameter α, based on the Glauber–Sudarshan quasiprobability distribution P(β) and the classical/non-classical behaviour of the Mandel QM(τ) parameter, which depends strongly on α. We find a phase transition as a function of α such that at the critical point αc, QM(τ), as a function of τ, goes from strictly classical, for |α||αc|.