Quantum Dynamics with Stochastic Non-Hermitian Hamiltonians

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.

v2: Accepted in Phys. Rev. Lett. 4+10 pages. New appendices: B, D.1, G

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