Evolution of cat states in a dissipative parametric amplifier: decoherence and entanglement

TL;DR

This paper investigates how Schrödinger-cat states evolve in a dissipative parametric amplifier, analyzing decoherence, entanglement, and quantum properties like squeezing and photon statistics, highlighting environmental and internal decoherence sources.

Contribution

It provides a detailed analysis of decoherence mechanisms affecting cat states in a dissipative amplifier, including effects of pump decay and phase relations, with new insights into underdamped and overdamped regimes.

Findings

Decoherence arises from environment, pump decay, and phase relations.

Two damping regimes: underdamped with collapse to mixture, overdamped with thermal field.

Quantum properties like squeezing and photon distribution are affected by dissipation.

Abstract

The evolution of the Schr\"{o}dinger-cat states in a dissipative parametric amplifier is examined. The main tool in the analysis is the normally ordered characteristic function. Squeezing, photon-number distribution and reduced factorial moments are discussed for the single- and compound-mode cases. Also the single-mode Wigner function is demonstrated. In addition to the decoherence resulting from the interaction with the environment (damped case) there are two sources which can cause such decoherence in the system even if it is completely isolated: these are the decay of the pump and the relative phases of the initial cat states. Furthermore, for the damped case there are two regimes, which are underdamped and overdamped. In the first (second) regime the signal mode or the idler mode "collapses" to a statistical mixture (thermal field).