Adiabatic elimination for multi-partite open quantum systems with non-trivial zero-order dynamics

TL;DR

This paper develops high-order adiabatic elimination formulas for multi-partite open quantum systems, preserving quantum structure and enabling efficient modeling of complex systems with fast dissipative environments.

Contribution

It introduces a method to reduce quantum system models by decomposing environments and extending to systems with fast Hamiltonian dynamics, improving accuracy and efficiency.

Findings

Reduced models preserve Lindblad form.

Application to superconducting resonator matches experimental data.

Efficient treatment of multi-component environments avoids quantum curse of dimension.

Abstract

We provide model reduction formulas for open quantum systems consisting of a target component which weakly interacts with a strongly dissipative environment. The time-scale separation between the uncoupled dynamics and the interaction allows to employ tools from center manifold theory and geometric singular perturbation theory to eliminate the variables associated to the environment (adiabatic elimination) with high-order accuracy. An important specificity is to preserve the quantum structure: reduced dynamics in (positive) Lindblad form and coordinate mappings in Kraus form. We provide formulas of the reduced dynamics. The main contributions of this paper are (i) to show how the decomposition of the environment into $K$ components enables its efficient treatment, avoiding the quantum curse of dimension; and (ii) to extend the results to the case where the target component is subject to Hamiltonian evolution at the fast time-scale. We apply our theory to a microwave superconducting quantum resonator subject to material losses, and we show that our reduced-order model can explain the transmission spectrum observed in a recent pump probe experiment.