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      Lindbladian Evolution with Selfadjoint Lindblad Operators as Averaged Random Unitary Evolution

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          Abstract

          It is shown how any Lindbladian evolution with selfadjoint Lindblad operators, either Markovian or nonMarkovian, can be understood as an averaged random unitary evolution. Both mathematical and physical consequences are analyzed. First a simple and fast method to solve this kind of master equations is suggested and particularly illustrated with the phase-damped master equation for the multiphoton resonant Jaynes-Cummings model in the rotating-wave approximation. A generalization to some intrinsic decoherence models present in the literature is included. Under the same philosophy a proposal to generalize the Jaynes-Cummings model is suggested whose predictions are in accordance with experimental results in cavity QED and in ion traps. A comparison with stochastic dynamical collapse models is also included.

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          The Quantum Jump Approach to Dissipative Dynamics in Quantum Optics

          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.
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            Intrinsic decoherence in quantum mechanics

            G. Milburn (1991)
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              Generation of Nonclassical Motional States of a Trapped Atom

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                Author and article information

                Journal
                28 August 2002
                Article
                quant-ph/0208175
                f93d6ae0-c52e-4b59-850f-db2d1296f3f3
                History
                Custom metadata
                16 pages, 4 ps figures
                quant-ph

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