Reduced equations of motion for quantum systems driven by diffusive Markov processes

TL;DR

This paper extends a hierarchical equation technique for simulating quantum systems driven by diffusive Markov processes, including non-Gaussian cases, demonstrated through Rydberg atom resonance transfer simulations.

Contribution

It characterizes the class of diffusive Markov processes suitable for this hierarchy, broadening the method's applicability to non-Gaussian stochastic influences.

Findings

Hierarchical equations can be derived for a wider class of diffusive Markov processes.

The technique enables simulation of quantum systems with non-Gaussian, bounded-range stochastic processes.

Application to Rydberg atoms shows the method's effectiveness in realistic scenarios.

Abstract

The expansion of a stochastic Liouville equation for the coupled evolution of a quantum system and an Ornstein-Uhlenbeck process into a hierarchy of coupled differential equations is a useful technique that simplifies the simulation of stochastically-driven quantum systems. We expand the applicability of this technique by completely characterizing the class of diffusive Markov processes for which a useful hierarchy of equations can be derived. The expansion of this technique enables the examination of quantum systems driven by non-Gaussian stochastic processes with bounded range. We present an application of this extended technique by simulating Stark-tuned F\"orster resonance transfer in Rydberg atoms with non-perturbative position fluctuations.