The quantum-jump approach to dissipative dynamics in quantum optics

TLDR

Dissipation of a microsystem results from coupling to a large reservoir, leading to irreversible decay when the reservoir degrees of freedom are traced out, and earlier ensemble-based treatments have been extended to single-system descriptions conditioned on measurement records. This review surveys quantum‑jump, Monte Carlo wave‑function, and quantum‑trajectory methods for modeling dissipative dynamics in quantum optics. The authors derive these methods, apply them to contemporary quantum‑optics problems, and compare them with traditional ensemble approaches.

Abstract

Dissipation, the irreversible loss of energy and coherence, from a microsystem is the result of coupling to a much larger macrosystem (or reservoir) that 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, which results in an irreversible decay as excitation leaks out of the initially excited microsystems into the outer reservoir environment. Earlier treatments of this dissipation used density matrices to describe an ensemble of microsystems, either in the Schr\"odinger picture with master equations, or in the 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. These methods, variously described as quantum-jump, Monte Carlo wave function, 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.