Decoherence factor as a convolution: an interplay between a Gaussian and an exponential coherence loss

TL;DR

This paper models the decoherence factor as a convolution of Gaussian and exponential functions, revealing how the transition between different decoherence regimes depends on system-environment interaction strength.

Contribution

It introduces a novel convolution-based framework to describe the transition between Gaussian and exponential decoherence, supported by two key models.

Findings

Decoherence factor is described by a convolution of Gaussian and exponential functions.

Strong coupling leads to Gaussian decoherence, weak coupling to exponential decoherence.

The framework is demonstrated with spin-bath and quantum Brownian motion models.

Abstract

This paper identifies and investigates nature of the transition between Gaussian and exponential forms of decoherence. We show that the decoherence factor (that controls the time dependence of the suppression of the off-diagonal terms when the density matrix is expressed in the pointer basis representation) can be described by the convolution of Gaussian and exponential functions, their contributions modulated by the strength of the system-environment interaction. In the strong and weak coupling limits, decoherence reduces to the familiar Gaussian and exponential forms, respectively. The mechanism is demonstrated with two paradigmatic examples of decoherence -- a spin-bath model and the quantum Brownian motion.