Non-Markovian perturbation theories for phonon effects in strong-coupling cavity quantum electrodynamics

Phonon interactions are inevitable in cavity quantum electrodynamical systems based on solid-state emitters or fluorescent molecules, where vibrations of the lattice or chemical bonds couple to the electronic degrees of freedom. Due to the non-Markovian response of the vibrational environment, it remains a significant theoretical challenge to describe such effects in a computationally efficient manner. This is particularly pronounced when the emitter-cavity coupling is comparable to or larger than the typical phonon energy range, and polariton formation coincides with vibrational dressing of the optical transitions. In this Article, we consider four non-Markovian perturbative master equation approaches to describe such dynamics over a broad range of light-matter coupling strengths and compare them to numerically exact reference calculations using a tensor network. The master equations are derived using different basis transformations and a perturbative expansion in the new basis is subsequently introduced and analyzed. We find that two approaches are particularly successful and robust. The first of these is suggested and developed in this Article and is based on a vibrational dressing of the exciton-cavity polaritons. This enables the description of distinct phonon-polariton sidebands that appear when the polariton splitting exceeds the typical phonon frequency scale in the environment. The second approach is based on a variationally optimized polaronic vibrational dressing of the electronic state. Both of these approaches demonstrate good qualitative and quantitative agreement with reference calculations of the emission spectrum and are numerically robust, even at elevated temperatures, where the thermal phonon population is significant.Comment: 17 pages, 10 figure

A stochastic approach to the quantum noise of a single-emitter nanolaser

It is shown that the intensity quantum noise of a single-emitter nanolaser can be accurately computed by adopting a stochastic interpretation of the standard rate equation model under the only assumption that the emitter excitation and photon number are stochastic variables with integer values. This extends the validity of rate equations beyond the mean-field limit and avoids using the standard Langevin approach, which is shown to fail for few emitters. The model is validated by comparison to full quantum simulations of the relative intensity noise and second-order intensity correlation function, g(2)({\tau} ). Surprisingly, even when the full quantum model displays vacuum Rabi oscillations, which are not accounted for by rate equations, the intensity quantum noise is correctly predicted by the stochastic approach. Adopting a simple discretization of the emitter and photon populations, thus, goes a long way in describing quantum noise in lasers. Besides providing a versatile and easy-to-use tool for modeling a new generation of nanolasers with many possible applications, these results provide insight into the fundamental nature of quantum noise in lasers.Comment: Revised and resubmitted for revie

Modal properties of dielectric bowtie cavities with deep sub-wavelength confinement

We present a design for an optical dielectric bowtie cavity which features deep sub-wavelength confinement of light. The cavity is derived via simplification of a complex geometry identified through inverse design by topology optimization, and it successfully retains the extreme properties of the original structure, including an effective mode volume of $V_\text{eff}= 0.083 \pm 0.001 \; (\lambda_\text{c}/2n_\text{Si})^3$ at its center. Based on this design, we present a modal analysis to show that the Purcell factor can be well described by a single quasinormal mode in a wide bandwidth of interest. Owing to the small mode volume, moreover, the cavity exhibits a remarkable sensitivity to local shape deformations, which we show to be well described by perturbation theory. The intuitive simplification approach to inverse design geometries coupled with the quasinormal mode analysis demonstrated in this work provides a powerful modeling framework for the emerging field of dielectric cavities with deep sub-wavelength confinement.Comment: 24 pages, 13 figures, research articl

Unidirectional Quantum Transport in Optically Driven VV-type Quantum Dot Chains

We predict a mechanism for achieving complete population inversion in a continuously driven InAs/GaAs semiconductor quantum dot featuring $V$-type transitions. This highly nonequilibrium steady state is enabled by the interplay between $V$-type interband transitions and a non-Markovian decoherence mechanism, introduced by acoustic phonons. The population trapping mechanism is generalized to a chain of coupled emitters. Exploiting the population inversion, we predict unidirectional excitation transport from one end of the chain to the other without external bias, independent of the unitary interdot coupling mechanism