Decoherence in a $\mathcal{PT}$-symmetric qubit

TL;DR

This paper studies how a $ ext{PT}$-symmetric qubit interacts with its environment, revealing that decoherence is suppressed near the transition from real to complex eigenvalues, with implications for quantum coherence control.

Contribution

It introduces a mapping of a $ ext{PT}$-symmetric qubit to a spin boson model and demonstrates decoherence suppression near the spectral transition point.

Findings

Decoherence is suppressed at the transition from real to complex eigen spectrum.

Strong suppression of decoherence due to vacuum and thermal bath fluctuations.

Initial correlations influence decoherence suppression near the transition.

Abstract

We investigate the decoherence in a $\mathcal{PT}$-symmetric qubit coupled with a bosonic bath. Using cannonical transformations, we map the non-Hermitian Hamiltonian representing the$\mathcal{PT}$-symmetric qubit to a spin boson model. Identifying the parameter {\alpha} that demarcates the hermiticity and non-hermiticity in the model, we show that the qubit does not decohere at the transition from real eigen spectrum to complex eigen spectrum. Using a general class of spectral densities, the strong suppression of decoherence is observed due to both vaccum and thermal fluctuations of the bath, and initial correlations as we approach the transition point.