The dissipative quantum Duffing oscillator: a comparison of Floquet-based approaches

TL;DR

This paper compares two Floquet-based methods for analyzing the dissipative quantum Duffing oscillator, providing a comprehensive approach to understanding its dynamics across different driving regimes.

Contribution

It introduces and compares two perturbative Floquet approaches, extending analysis to the entire driving frequency spectrum of the quantum Duffing oscillator.

Findings

Both methods accurately describe oscillator dynamics away from and near resonance.

The combined approach covers the full range of driving frequencies.

Near one-photon resonance, the quasi-degenerate perturbation theory provides detailed insights.

Abstract

We study the dissipative quantum Duffing oscillator in the deep quantum regime with two different approaches: The first is based on the exact Floquet states of the linear oscillator and the nonlinearity is treated perturbatively. It well describes the nonlinear oscillator dynamics away from resonance. The second, in contrast, is applicable at and in the vicinity of a N-photon resonance and it exploits quasi-degenerate perturbation theory for the nonlinear oscillator in Floquet space. It is perturbative both in driving and nonlinearity. A combination of both approaches yields the possibility to cover the whole range of driving frequencies. As an example we discuss the dissipative dynamics of the Duffing oscillator near and at the one-photon resonance.