Quantum Dynamics with Stochastic Non-Hermitian Hamiltonians

TL;DR

This paper investigates how stochastic fluctuations in non-Hermitian Hamiltonians influence quantum dynamics, revealing that noise can stabilize states and enhance control over quantum systems.

Contribution

It introduces an anti-dephasing master equation for stochastic non-Hermitian Hamiltonians and analyzes their effects on quantum state evolution and purification.

Findings

Noise stabilizes lossy quantum states.

Stochastic dynamics enable greater state purification.

Analytical results demonstrate control via noise.

Abstract

We study the quantum dynamics generated by a non-Hermitian Hamiltonian subject to stochastic perturbations in its anti-Hermitian part, describing fluctuating gains and losses. The dynamics averaged over the noise is described by an `anti-dephasing' master equation. We characterize the resulting state evolution and analyze its purity. The properties of such dynamics are illustrated in a stochastic dissipative qubit. Our analytical results show that adding noise allows for a rich control of the dynamics, stabilizing the lossy state and making state purification possible to a greater variety of steady states.