$\mathcal{P}\mathcal{T}$-symmetric slowing-down of decoherence

TL;DR

This paper demonstrates that $ ext{PT}$-symmetric interactions in open quantum systems can significantly slow down decoherence, with explicit models and experimental relevance discussed.

Contribution

It provides a detailed analysis of $ ext{PT}$-symmetric dephasing dynamics and explains the mechanism behind the critical slowing down of decoherence in such systems.

Findings

$ ext{PT}$-symmetric systems exhibit purely dephasing, unital dynamics.

Explicit quantum canonical transformation for the dynamical map.

Experimental realization with $ ext{PT}$-symmetric qubits in optical setups.

Abstract

We investigate $\mathcal{P}\mathcal{T}$-symmetric quantum systems ultra-weakly coupled to an environment. We find that such open systems evolve under $\mathcal{P}\mathcal{T}$-symmetric, purely dephasing and unital dynamics. The dynamical map describing the evolution is then determined explicitly using a quantum canonical transformation. Furthermore, we provide an explanation of why $\mathcal{P}\mathcal{T}$-symmetric dephasing type interactions lead to \emph{critical slowing down of decoherence}. This effect is further exemplified with an experimentally relevant system -- a $\mathcal{P}\mathcal{T}$-symmetric qubit easily realizable, \emph{e.g.}, in optical or microcavity experiments.