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

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.