Lindbladian Evolution with Selfadjoint Lindblad Operators as Averaged Random Unitary Evolution

TL;DR

This paper demonstrates that Lindbladian evolutions with selfadjoint Lindblad operators can be viewed as averaged random unitary processes, providing new methods for solving master equations and connecting to experimental quantum systems.

Contribution

It introduces a novel interpretation of Lindbladian evolution as an average over random unitaries and proposes a simplified solution method applicable to various models.

Findings

A fast method to solve Lindbladian master equations is proposed.

The approach accurately describes phase damping in Jaynes-Cummings models.

Predictions align with experimental results in cavity QED and ion traps.

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.