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

TL;DR

This work analyzes decoherence in a pure dephasing spin-boson setup with both Hermitian and PT-symmetric non-Hermitian baths. By deriving analytic forms for the decoherence function γ(t) and the correlation functions P_x(t) and C_x(t), it reveals a formal similarity between equilibrium and non-equilibrium dynamics at zero bias, and provides detailed short- and long-time asymptotics across Ohmic, sub-Ohmic, and super-Ohmic baths. A central result is that a finite non-Hermitian bath (τ>0) can suppress decoherence for all coupling strengths and bath exponents by mapping the problem to an effective Hermitian SBM with renormalized spectral parameters. This undermines previous claims and suggests non-Hermitian environment engineering as a versatile tool for protecting qubits in open quantum systems.

Abstract

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.

Figures (4)

• Figure 1: (color online) $P_{x}(t)$ (solid line) and $|C_{x}(t)|$ (dashed line) as functions of time $t$ for $s=1$ and various $A$ values. (a) Short time regime; (b)-(d) long time regime. Parameters are $\epsilon=0$, $T=0$, and $B=1$.
• Figure 2: (color online) (a) $P_x(t)$ and $|C_x(t)|$ for various $s$ values in the short time regime; (b)-(d): $|\ln[P_x(t)/P_0]|$ and $|\ln|C_x(t)/P_0||$ for various $s$ values in the long time regime. Parameters are $\epsilon=0$, $T=0$, $A=1$, and $B=1$.
• Figure 3: (color online) $P_x(t)$ for various $s$ and $\tau$ values. (a) $s=1.0$, (b) $s=0.5$, and (c) $s=2.5$. In each panel, from bottom to top, $\tau=0.0$, $0.2$, $0.4$, $0.6$, $1.0$, and $2.0$. Parameters are $\epsilon=0$, $T=0$, $A=1$, and $B=1$.
• Figure 4: (color online) $P_x(t)$ at fixed $t$ as functions of $\tau$. (a) $s=1.0$, (b) $s=0.5$, and (c) $s=2.5$. In each panel, from top to bottom, $t=0.1$, $0.3$, $1.0$, $3.0$, $10.0$, $30.0$, and $100.0$. Parameters are $\epsilon=0$, $T=0$, $A=1$, and $B=1$.