Fate of symmetry protected coherence in open quantum system

TL;DR

This paper studies how anti-unitary symmetries affect coherence in open quantum systems, revealing that such symmetries may not protect coherence as unitary symmetries do, with implications for topological states.

Contribution

It provides a detailed analysis of the differing effects of anti-unitary versus unitary symmetries on coherence protection in open quantum systems, including a classification table and model confirmations.

Findings

Anti-unitary symmetry does not protect coherence in open systems.

Unitary symmetry can preserve initial coherence.

Classification table of symmetry effects on coherence.

Abstract

We investigate the fate of coherence in the dynamical evolution of a symmetry protected quantum system. Under the formalism of system-plus-bath for open quantum system, the anti-unitary symmetry exhibits significant difference from the unitary one in protecting initial coherence. Specifically, taking advantage of Lindblad master equation, we find that a pure state in the symmetry protected degenerate subspace will decohere even though both the system Hamiltonian and system-environment interaction respect the same anti-unitary symmetry. In contrast, the coherence will persist when the protecting symmetry is unitary. We provide an elaborate classification table to illustrate what kinds of symmetry combinations are able to preserve the coherence of initial state, which is confirmed by several concrete models in spin-$3/2$ system. Our results could help to explore the possible experimental realization of stable time-reversal symmetric topological states.