$\mathcal{PT}$-symmetric slowing down of decoherence

We investigate $\mathcal{P}\mathcal{T}$-symmetric quantum systems ultraweakly 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 a critical slowing down of decoherence. This effect is further exemplified with an experimentally relevant system, a $\mathcal{P}\mathcal{T}$-symmetric qubit easily realizable, e.g., in optical or microcavity experiments.

Figure 1

Critical slowing down of decoherence. The decoherence function $D\left(t\right)$ decays more gradually as $\alpha$ increases. Eventually, it becomes constant at the critical point $\alpha =1$. The red line corresponds to a Hermitian system ($\alpha =0$). The parameters are $\mu =-0.5, \beta =0.5$, and $J_0={\omega }_c=1$. For negative $\alpha$ the situation is symmetric [see, e.g., Eq. (18)].