Eur. Phys. J. D (2017) 71: 171
https://doi.org/10.1140/epjd/e2017-70701-2

Regular Article

Decoherence in quantum lossy systems: superoperator and matrix techniques

¹ Atomic and Molecular Group, Faculty of Physics, Yazd University, 89195-741 Yazd, Iran
² The Laboratory of Quantum Information Processing, Yazd University, 89195-741 Yazd, Iran
³ Instituto Nacional de Astrofísica, Óptica Electrónica, Calle Luis Enrique Erro No. 1, Sta. Ma. Tonantzintla, Pue. CP 72840, Mexico

^a e-mail: mktavassoly@yazd.ac.ir

Received: 8 November 2016
Received in final form: 2 April 2017
Published online: 22 June 2017

Abstract

Due to the unavoidably dissipative interaction between quantum systems with their environments, the decoherence flows inevitably into the systems. Therefore, to achieve a better understanding on how decoherence affects on the damped systems, a fundamental investigation of master equation seems to be required. In this regard, finding out the missed information which has been lost due to irreversibly of the dissipative systems, is also of practical importance in quantum information science. Motivating by these facts, in this work we want to use superoperator and matrix techniques, by which we are able to illustrate two methods to obtain the explicit form of density operators corresponding to damped systems at arbitrary temperature T ≥ 0. To establish the potential abilities of the suggested methods, we apply them to deduce the density operator of some practical well-known quantum systems. Using the superoperator techniques, at first we obtain the density operator of a damped system which includes a qubit interacting with a single-mode quantized field within an optical cavity. As the second system, we study the decoherence of a quantized field within an optical damped cavity. We also use our proposed matrix method to study the decoherence of a system which includes two qubits in the interaction with each other via dipole-dipole interaction and at the same time with a quantized field in a lossy cavity. The influences of dissipation on the decoherence of dynamical properties of these systems are also numerically investigated. At last, the advantages of the proposed superoperator techniques in comparison with matrix method are explained.