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

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.