Generalized master equation for driven quantum oscillators: microscopic origin of nonlinear dissipation and asymmetric resonances

TL;DR

This paper derives a generalized master equation for driven nonlinear quantum oscillators, revealing how nonlinearities and driving influence dissipation and resonance behaviors in quantum systems.

Contribution

It introduces a microscopic framework that incorporates nonlinearities and driving into the dissipative dynamics of quantum oscillators, extending traditional models.

Findings

Suppresses large-amplitude excitations and phase-space fluctuations.

Reduces bistability and causes asymmetric resonance responses.

Shows drive-dependent nonlinear damping effects.

Abstract

Driven nonlinear quantum oscillators are a central platform for quantum technologies, yet their dissipative dynamics are typically described using Lindblad or Caldeira-Leggett master equations derived under assumptions that exclude nonlinearities and driving. Here, we derive a generalized Caldeira-Leggett master equation for driven nonlinear oscillators by retaining the full nonlinear and time-dependent system dynamics in the construction of the dissipator. For position- and momentum-dependent system-bath coupling, the dissipator itself becomes dynamically dressed, generating nonlinear and drive-dependent dissipative channels beyond conventional fixed-dissipator approaches. This produces nonlinear damping together with dissipation-induced corrections to the effective drive. The resulting dissipative dynamics suppress large-amplitude excitations and reduce phase-space fluctuations. For a driven Kerr oscillator, this leads to the suppression of bistability, asymmetric resonance responses, and strongly modified fluctuation distributions. More broadly, our results establish a microscopic framework in which nonlinear dynamics and driving directly reshape the dissipative sector of driven open quantum systems.