Stochastic unraveling of Redfield master equations and its application
  to electron transfer problems

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Abstract

A method for stochastic unraveling of general time-local quantum master equations (QMEs) is proposed. The present kind of jump algorithm allows a numerically efficient treatment of QMEs which are not in Lindblad form, i.e. are not positive semidefinite by definition. The unraveling can be achieved by allowing for trajectories with negative weights. Such a property is necessary, e.g. to unravel the Redfield QME and to treat various related problems with high numerical efficiency. The method is successfully tested on the damped harmonic oscillator and on electron transfer models including one and two reaction coordinates. The obtained results are compared to those from a direct propagation of the reduced density matrix (RDM) as well as from the standard quantum jump method. Comparison of the numerical efficiency is performed considering both the population dynamics and the RDM in the Wigner phase space representation.

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Monte Carlo wave-function method in quantum optics

Klaus Mølmer, Yvan Castin, Jean Dalibard (1993)

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The Quantum Jump Approach to Dissipative Dynamics in Quantum Optics

M Plenio, P. Knight (1997)

Dissipation, the irreversible loss of energy and coherence, from a microsystem, is the result of coupling to a much larger macrosystem (or reservoir) which is so large that one has no chance of keeping track of all of its degrees of freedom. The microsystem evolution is then described by tracing over the reservoir states, resulting in an irreversible decay as excitation leaks out of the initially excited microsystems into the outer reservoir environment. Earlier treatments of this dissipation described an ensemble of microsystems using density matrices, either in Schroedinger picture with Master equations, or in Heisenberg picture with Langevin equations. The development of experimental techniques to study single quantum systems (for example single trapped ions, or cavity radiation field modes) has stimulated the construction of theoretical methods to describe individual realizations conditioned on a particular observation record of the decay channel, in the environment. These methods, variously described as Quantum Jump, Monte Carlo Wavefunction and Quantum Trajectory methods are the subject of this review article. We discuss their derivation, apply them to a number of current problems in quantum optics and relate them to ensemble descriptions.