Quantum decoherence dynamics in stochastically fluctuating environments

TL;DR

This paper investigates how stochastic environmental noise, with linear or quadratic dependence, affects quantum decoherence and energy level renormalization in a two-level system, revealing the role of noise stationarity.

Contribution

It provides analytical expressions for decoherence functions under nonstationary Ornstein-Uhlenbeck and telegraph noise, highlighting the impact of noise statistics on decoherence.

Findings

Quadratic noise dependence causes energy level renormalization even with stationary noise.

Nonstationary noise can either enhance or suppress decoherence depending on the noise type and dependence.

Quadratic influence of RTN results in frequency renormalization without decoherence.

Abstract

We theoretically study the decoherence of a two-level quantum system coupled to noisy environments exhibiting linear and quadratic fluctuations within the framework of a stochastic Liouville equation. It is shown that the intrinsic energy levels of the quantum system renormalize under either the linear or quadratic influence of the environmental noise. In the case of quadratic dependence, the renormalization of the energy levels of the system emerges even if the environmental noise exhibits stationary statistical properties. This is in contrast to the case under linear influence, where the intrinsic energy levels of the system renormalize only if the environmental noise displays nonstationary statistics. We derive the analytical expressions of the decoherence function in the cases where the fluctuation of the frequency difference depends linearly and quadratically on the nonstationary Ornstein-Uhlenbeck noise (OUN) and random telegraph noise (RTN) processes, respectively. In the case of the linear dependence of the OUN, the environmental nonstationary statistical property can enhance the dynamical decoherence. However, the nonstationary statistics of the environmental noise can suppress the quantum decoherence in this case under the quadratic influence of the OUN. In the presence of the RTN, the quadratic influence of the environmental noise does not give rise to decoherence but only causes a determinate frequency renormalization in dynamical evolution. The environmental nonstationary statistical property can suppress the quantum decoherence of the case under the linear influence of the RTN.