Symmetry-protected coherent relaxation of open quantum systems

TL;DR

This paper demonstrates that in certain open quantum systems with specific symmetries, the coherent dynamics can be preserved up to a damping factor, which has implications for controlling decoherence in quantum experiments.

Contribution

It reveals how PT symmetry and weak symmetries lead to symmetry-protected coherent relaxation in open quantum systems, extending previous theoretical predictions.

Findings

Weak system-bath coupling preserves unitary dynamics with exponential damping.

Spectrum splits into symmetry sectors with uniform decay rates.

Potential realization in trapped ion experiments.

Abstract

We compute the effect of Markovian bulk dephasing noise on the staggered magnetization of the spin-1/2 XXZ Heisenberg chain, as the system evolves after a N\'eel quench. For sufficiently weak system-bath coupling, the unitary dynamics are found to be preserved up to a single exponential damping factor. This is a consequence of the interplay between $\mathbb{PT}$ symmetry and weak symmetries, which strengthens previous predictions for $\mathbb{PT}$-symmetric Liouvillian dynamics. Requirements are a non-degenerate $\mathbb{PT}$-symmetric generator of time evolution $\hat{\mathcal{L}}$, a weak parity symmetry and an observable that is anti-symmetric under this parity transformation. The spectrum of $\hat{\mathcal{L}}$ then splits up into symmetry sectors, yielding the same decay rate for all modes that contribute to the observable's time evolution. This phenomenon may be realized in trapped ion experiments and has possible implications for the control of decoherence in out-of-equilibrium many-body systems.