Demystifying decoherence and the master equation of quantum Brownian motion

Abstract

Quantum decoherence is a proposed mechanism for the emergence of classical physics from the quantum mechanics. It has been developed extensively in recent years, but is sufficiently technically complicated to discourage widespread understanding. In this paper we provide a gentle introduction to quantum decoherence. We introduce state operators and their density matrix representations to describe composite systems, such as an experiment and its environment. We illustrate how the loss of information about a subsystem can cause a quantum system to appear classical. We first analyze a discrete example of phase randomization, then a Bell state, and finally a continuous system. In the final case we provide an accessible derivation of a major early result of decoherence theory, the master equation of quantum Brownian motion. We conclude by applying the master equation to the decoherence of a simple harmonic oscillator, with results reminiscent of our earlier discrete examples.

Effect of trap symmetry and atom-atom interactions on a trapped-atom interferometer with internal state labeling

“…To find the contrast and the phase shift in terms of the components of the one-atom average spin we need an expression for the density operator at a time t after the first π/2 pulse. This expression is given by [50]…”

Effect of trap symmetry and atom-atom interactions on a trapped atom interferometer with internal state labelling

“…To find the contrast and the phase-shift in terms of the components of the one-atom average spin we need an expression for the density operator at a time t after the first π/2 pulse. This expression is given by [49]:…”

Time Dependent Entropy and Decoherence in a Modified Quantum Damped Harmonic Oscillator

“…This condition requires that the system should be in one of relatively permanent states (called by Zurek "preferred states") and the interference between different states should be negligible [27] [28]. The loss of coherence can be achieved by introducing an interaction between the system and environment [23] [29] [30].…”