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.

💡 Research Summary

In this work the authors study decoherence of a single qubit coupled to either a Hermitian or a non‑Hermitian bosonic environment within the pure‑dephasing spin‑boson model. The total Hamiltonian is written as
(H = H_S + H_{SB} + H_{NB}) with (H_S = \frac{\epsilon}{2}\sigma_z), a longitudinal coupling (H_{SB}= \sigma_z\sum_k \lambda_k (a_k^\dagger + a_k)), and a bath Hamiltonian that may be Hermitian ((\tau=0)) or non‑Hermitian ((\tau>0)):
(H_{NB}= \sum_k\big