Emission spectral non-Markovianity in qubit–cavity systems in the ultrastrong coupling regime

Abstract

We study the emission spectra of the dissipative Rabi and Jaynes–Cummings models in the non-Markovian and ultrastrong coupling regimes. We have derived a polaron-transformed Nakajima–Zwanzig master equation (PTNZE) to calculate the emission spectra, which eliminates the well-known limitations of the Markovian approximation and the standard second-order perturbation. Using the time-dependent variational approach with the multiple Davydov ansatz as a benchmark, the PTNZE is found to yield accurate emission spectra in certain ultrastrong coupling regimes where the standard second-order Nakajima–Zwanzig master equation breaks down. It is shown that the emission spectra of the dissipative Rabi and Jaynes–Cummings models are, in general, asymmetric under various initial conditions. Direct comparisons of spectra for the two models illustrate the essential role of the qubit–cavity counter-rotating term and the spectral features under different qubit–cavity coupling strengths and system initial conditions.