Decoherence in the Pure Dephasing Spin-Boson Model with Hermitian or Non-Hermitian Bath

Abstract In this paper, we investigate the decoherence of qubit due to its coupling to a Hermitian or a non-Hermitian environment within the pure dephasing spin-boson model. Using this model, we analytically establish the previously anticipated similarity between the non-equilibrium and the equilibrium correlation functions $P_x(t)$ and $C_x(t)$. We find that integer values of $A$ (coupling strength) or $s$ (bath exponent) has distinctive long time asymptotic behaviors of $P_x(t)$ and $C_x(t)$ from those of the non-integer values, accompanied with a diverging crossover time scale. We also find that the non-Hermitian environment tends to suppress the decoherence of qubit for all values of $A$ and $s$, in contrast to the conclusion of Dey et al . [Phys. Lett. A 383, 125931 (2019)]. Our results show the potential of the non-Hermitian environmental engineering for suppressing the decoherence of qubit.