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Journal of Physics A Mathematical and General

A master equation for quantum systems driven by Poisson white noise

J. Łuczka, Mariusz Niemiec

Published Sep 7, 1991• 21 citations
Publisher

Abstract

An evolution equation for a reduced statistical operator of quantum systems driven by Poisson white noise is derived. It is applied to a simple system and compared with a counterpart driven by Gaussian white noise.
DOI
10.1088/0305-4470/24/17/010

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We present a detailed derivation of the master equation describing a general time-dependent quantum system with classical Poisson white noise and outline its various properties. We discuss the limiting cases of Poisson white noise and provide approximations for the different noise strength regimes. We show that using the eigenstates of the noise superoperator as a basis can be a useful way of expressing the master equation. Using this, we simulate various settings to illustrate different effects of Poisson noise. In particular, we show a dip in the fidelity as a function of noise strength where high fidelity can occur in the strong-noise regime for some cases. We also investigate recent claims [J. Jing et al., Phys. Rev. A 89, 032110 (2014)] that this type of noise may improve rather than destroy adiabaticity.
Quantum systems are unavoidably open to their surrounding degrees of freedom. The theory of open quantum systems is thus crucial to understanding the fluctuations, dissipation, and decoherence of a quantum system of interest. Typically, the bath is modeled as an ensemble of harmonic oscillators, which yields Gaussian statistics of the bath influence on the quantum systems. However, there are also phenomena in which the bath consists of two-state systems, spins, or anharmonic oscillators; therefore, the non-Gaussian properties of the bath become important. Nevertheless, a theoretical framework to describe quantum systems under the influence of such non-Gaussian baths is not well established. Here, we develop a theory to describe quantum dissipative systems affected by Poisson noise properties of the bath, because the Lévi-Itô decomposition theorem asserts that Poisson noise is fundamental in describing arbitrary white noise beyond Gaussian properties. We introduce a quantum bath model that allows for the consistent description of dissipative quantum systems. The obtained master equation reveals non-Gaussian bath effects in the white noise regime, and provides an essential step toward describing open quantum dynamics under the influence of generic baths.
A model of a system driven by quantum white noise with singular quadratic self- interaction is considered and an exact solution for the evolution operator is found.It is shown that the renormalized square of the squeezed classical white noise is equivalent to the quantum Poisson.process.A convenient regularization of singular quantum differential equations for the evolution operator is suggested.We describe how equations driven by nonlinear functionals of white noise can be derived in nonlinear quantum optics by using the stochastic limit.