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Physical Review A

Milburn theory of decoherence using a random kicked dynamics

Juan Cesar Flores

Published Apr 1, 1995• 6 citations
Publisher

Abstract

A connection between random kicked systems and the Milburn theory for quantum decoherence is presented. The dynamics of the kicked system suggests a possible generalization of the Milburn model for decoherence including external fields. Irreversibility is explored using a suitable Lyapunov function and the stationary solution is examined.

DOI
10.1103/physreva.51.2774

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A connection between random kicked systems and the Milburn theory for quantum decoherence is presented. The dynamics of the kicked system suggests a possible generalization of the Milburn model for decoherence including external fields. Irreversibility is explored using a suitable Lyapunov function and the stationary solution is examined.
By building a system-environment separated representation and proving an identity, we derive out a general and obvious solution of decoherence dynamics in the Milburn's model for an open system with the so-called near environment. Moreover, our solution is suitable to consider the environment-introduced decoherence and Milburn's decoherence jointly or respectively. As a general formulation and tool, it is convenient for calculating the decoherence and disentanglement in quantum information processing and communication, and is helpful for seeking the methods of decoherence control and understanding the nature of decoherence.
The irreversible time evolution of a quantum system interacting with a large environmental system can be described by a quantum master equation. When an external field is applied to a quantum system, a non-Markovian mater equation is derived in a rigorous way, where the relaxation terms in the quantum master equation include the effects of the external field. It is shown that, when the external field is a sequence of phase-modulation pulses, the decoherence of the quantum system can be suppressed under certain conditions. To see the effects of phase-modulation pulses, the irreversible time evolutions of qubit and photon systems are investigated in detail.
Milburn has recently proposed [Phys. Rev. A 44, 5401 (1991)] a variation of the Schr\"odinger equation which models decoherence as the system evolves through intrinsic mechanisms beyond conventional quantum mechanics rather than dissipative interaction with an environment. In this paper we give an exact solution of this equation and apply it to the Jaynes-Cummings model of atom-field interaction with nontrivial dynamics. We show that the intrinsic decoherence is responsible for deterioration of quantum coherence effects in this model, such as revivals of the atomic inversion. We discuss the applicability of the Milburn equation.