Convergence and adiabatic elimination for a driven dissipative quantum harmonic oscillator

TL;DR

This paper proves that a driven dissipative quantum harmonic oscillator with two-photon processes converges to a protected subspace of coherent states, and characterizes the slow dynamics caused by perturbative single-photon loss using adiabatic elimination.

Contribution

It introduces a novel analysis of convergence to a protected subspace in a driven dissipative quantum harmonic oscillator with two-photon processes and applies adiabatic elimination to understand slow dynamics.

Findings

Convergence to a subspace spanned by two coherent states.

Characterization of slow dynamics via adiabatic elimination.

Insights into the effects of perturbative single-photon loss.

Abstract

We prove that a harmonic oscillator driven by Lindblad dynamics where the typical drive and loss channels are two-photon processes instead of single-photon ones, converges to a protected subspace spanned by two coherent states of opposite amplitude. We then characterize the slow dynamics induced by a perturbative single-photon loss on this protected subspace, by performing adiabatic elimination in the Lindbladian dynamics.