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

In this paper, we investigate the decoherence of qubit due to its coupling to a Hermitian or a non-Hermitian bath within the pure dephasing spin-boson model. First, using this model, we analytically establish the previously anticipated similarity between the non-equilibrium and the equilibrium correlation functions $P_x(t)$ and $C_x(t)$. Then, in the short/long time asymptotic behaviors of $P_x(t)$, we find singular dependence on $A$ (coupling strength) and $s$ (bath exponent) at their integer values. Finally, we find that the non-Hermitian bath tends to suppress the decoherence of qubit for all values of $A$ and $s$, in contrast to the conclusion of Dey et al. . Our results show the potential of non-Hermitian environment engineering in suppressing the decoherence of qubit.