Eur. Phys. J. D 22, 141-156 (2003)
https://doi.org/10.1140/epjd/e2002-00234-8

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

¹ Department of Mathematics and Computer Science, Faculty of Natural Science, Suez Canal University, Ismailia, Egypt
² Department of Optics (Joint Laboratory of Optics of Palacký University and Institute of Physics, Academy of Sciences of the Czech Republic, 17. listopadu 50, 772 07 Olomouc, Czech Republic.) , Palacký University, 17. listopadu 50, 772 07 Olomouc, Czech Republic
³ Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Corresponding author: ^a sebaweh@awalnet.net.sa

Received: 25 September 2001
Revised: 30 May 2002
Published online: 13 December 2002

Abstract

The evolution of the Schrödinger-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).