Dephasing by a Continuous-Time Random Walk Process

TL;DR

This paper provides an exact method to evaluate dephasing functions for continuous-time random walk processes, enabling analysis of non-Gaussian and Gaussian stochastic dynamics in quantum systems.

Contribution

It introduces an exact evaluation technique for dephasing functions involving continuous-time random walks, bridging non-Gaussian and Gaussian stochastic models.

Findings

Derived explicit formulas for dephasing functions of continuous-time random walks.

Applied the method to extract qubit-lattice interaction parameters from experimental data.

Calculated the 2D spectrum of a harmonic oscillator with random frequency modulations.

Abstract

Stochastic treatments of magnetic resonance spectroscopy and optical spectroscopy require evaluations of functions like <exp(i int_0^t Q(s)ds)>, where t is time, Q(s) is the value of a stochastic process at time s, and the angular brackets denote ensemble averaging. This paper gives an exact evaluation of these functions for the case where Q is a continuous-time random walk process. The continuous time random walk describes an environment that undergoes slow, step-like changes in time. It also has a well-defined Gaussian limit, and so allows for non-Gaussian and Gaussian stochastic dynamics to be studied within a single framework. We apply the results to extract qubit-lattice interaction parameters from dephasing data of P-doped Si semiconductors (data collected elsewhere), and to calculate the two-dimensional spectrum of a three level harmonic oscillator undergoing random frequency modulations.