Dynamically generated quadrature and photon-number variances for Gaussian states

Abstract

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 nonclassicality criteria, which is independent of the displacement parameter $\alpha$, based on the Glauber-Sudarshan quasiprobability distribution $P(\beta )$ and the classical/nonclassical behavior of the Mandel $Q_M(\tau )$ parameter, which depends strongly on $\alpha$. We find a phase transition as a function of $\alpha$ such that at the critical point ${\alpha }_c$, $Q_M(\tau )$, as a function of $\tau$, goes from strictly classical, for $|\alpha |<|{\alpha }_c|$, to a mixed classical/nonclassical behavior, for $|\alpha |>|{\alpha }_c|$.

arXiv admin note: substantial text overlap with arXiv:1610.08821

References in corpus (4)

• Negative Full Counting Statistics Arise From Interference Effects
• Homodyne Detection and Quantum State Reconstruction
• Temporal second-order coherence function for displaced-squeezed thermal states
• Nonclassicality criteria: Quasiprobability distributions and correlation functions

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• Quadrature coherence scale driven fast decoherence of bosonic quantum field states
• Decoherence and nonclassicality of photon-added/subtracted multi-mode Gaussian states
• Convex roofs witnessing Kirkwood-Dirac nonpositivity
• Interferometric measurement of the quadrature coherence scale using two replicas of a quantum optical state
• Quadrature Coherence Scale of Linear Combinations of Gaussian Functions in Phase Space