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Physical Review A

Dynamics of open systems governed by the Milburn equation

Vladimír Bužek, Martin Konôpka

Published Sep 1, 1998• 33 citations
Publisher

Abstract

Within the framework of the Milburn model of intrinsic decoherence [G. J. Milburn, Phys. Rev. A 44, 5401 (1991)], which is based on an assumption of an existence of the fundamental time step, we study the dynamics of open systems. We show that evolution of an open system governed by the Milburn equation can be significantly modified compared to the standard Schr\"odinger quantum mechanics. This modification is most pronounced when an open system is strongly coupled to its environment.

DOI
10.1103/physreva.58.1735

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Within the framework of the Milburn model of intrinsic decoherence [G. J. Milburn, Phys. Rev. A 44, 5401 (1991)], which is based on an assumption of an existence of the fundamental time step, we study the dynamics of open systems. We show that evolution of an open system governed by the Milburn equation can be significantly modified compared to the standard Schr"odinger quantum mechanics. This modification is most pronounced when an open system is strongly coupled to its environment.
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.
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.
With a choice of boundary conditions for solutions of the Schrödinger equation, state vectors and density operators even for closed systems evolve asymmetrically in time. For open systems, standard quantum mechanics consequently predicts irreversibility and signatures of the extrinsic arrow of time. The result is a new framework for the treatment of decoherence, not based on a reduced dynamics or a master equation. As an application, using a general model we quantitatively match previously puzzling experimental results and can conclude that they are the measurable consequence of the indistinguishability of separate, uncontrolled interactions between systems and their environment.
A model for intrinsic decoherence in quantum mechanics is proposed, based on a simple modification of unitary Schr\"odinger evolution. On sufficiently small time scales the system evolves by a random sequence of unitary phase changes generated by the Hamiltonian. The Schr\"odinger equation is obtained to zeroth order in the expansion parameter. Higher-order corrections lead to a loss of coherence in the energy basis. The rate of coherence loss becomes very large as the energy scale of the system is increased. The expansion parameter determines an uncertainty in the time step on very short times scales. A number of testable consequences are derived including anomalous dispersion of a free particle, decay of oscillatory systems, destruction of interference-fringe visibility, and a phase shift of interference fringes.