Variational approach to time-dependent fluorescence of a driven qubit

TL;DR

This paper introduces a variational method using the Dirac-Frenkel principle and Davydov ansatz to analyze the time-dependent fluorescence spectra of a driven qubit across different coupling regimes, capturing complex dynamics beyond traditional approaches.

Contribution

It develops a flexible variational approach that accurately computes time-dependent spectra of a driven qubit, especially in strong coupling regimes where perturbative methods fail.

Findings

Method agrees with master-equation in weak coupling

Counter-rotating terms significantly affect spectra under strong driving

Spectral profiles can deviate from Mollow triplet due to dissipation and multiphoton effects

Abstract

We employ the Dirac-Frenkel variational principle and multiple Davydov ansatz to study time-dependent fluorescence spectra of a driven qubit in the weak- to strong qubit-reservoir coupling regimes, where both the Rabi frequency and spontaneous decay rate are comparable to the transition frequency of the qubit. Our method agrees well with the time-local master-equation approach in the weak-coupling regime, and offers a flexible way to compute the spectra from the bosonic dynamics instead of two-time correlation functions. While the perturbative master equation breaks down in the strong-coupling regime, our method actually becomes more accurate due to the use of bosonic coherent states under certain conditions. We show that the counter-rotating coupling between the qubit and the reservoir has considerable contributions to the photon number dynamics and the spectra under strong driving conditions even though the coupling is moderately weak. The time-dependent spectra are found to be generally asymmetric, a feature that is derived from photon number dynamics. In addition, it is shown that the spectral profiles can be dramatically different from the Mollow triplet due to strong dissipation and/or multiphoton processes associated with the strong driving. Our formalism provides a unique perspective to interpret time-dependent spectra.