Reduced Operator Approximation for Modelling Open Quantum Systems

TL;DR

The paper introduces the Reduced Operator Approximation, a new method for modeling open quantum systems that is simple, transparent, and efficient, capturing decoherence and quantum coherence effects over extended times.

Contribution

It presents a novel reduced operator approach using the Heisenberg picture, applicable to various baths, and compares favorably with existing methods like pseudomode and quantum state diffusion.

Findings

Captures decoherence and energy conservation in open quantum systems

Demonstrates long-lasting quantum coherence effects

Applicable to different bath types and interaction strengths

Abstract

We present the Reduced Operator Approximation: a simple, physically transparent and computationally efficient method of modelling open quantum systems. It employs the Heisenberg picture of the quantum dynamics, which allows us to focus on the system degrees of freedom in a natural and easy way. We describe different variants of the method, low- and high-order in the system-bath interaction operators, defining them for either general quantum harmonic oscillator baths or specialising them for independent baths with Lorentzian spectral densities. Its wide applicability is demonstrated on the examples of systems coupled to different baths (with varying system-bath interaction strength and bath memory length), and compared with the exact pseudomode and the popular quantum state diffusion approach. The method captures the decoherence of the system interacting with the bath, while conserving the total energy. Our results suggest that quantum coherence effects persist in open quantum systems for much longer times than previously thought.