Microscopic Theory of Polaron-Polariton Dispersion and Propagation

Abstract

We develop an analytical microscopic theory to describe the polaron-polariton dispersion, formed by hybridizing excitons, photons, and phonons, and their coherent dynamics inside optical cavities. Starting from a microscopic light-matter Hamiltonian, we derive a simple analytical model by pursuing a non-perturbative treatment of the phonon and photon couplings to excitons. Within our theoretical framework, the phonons are treated as classical fields that are then quantized via the Floquet formalism. We show that, to a good approximation, the entire polaron-polariton system can be described using a band picture despite the phonons breaking translational symmetry. Our theory also sheds light on the long-lived coherent ballistic motion of exciton-polaritons with high excitonic character that propagate with group velocities lower than is expected from pure exciton-polariton bands, offering a microscopic explanation for these puzzling experimental observations.

Figures (2)

• Figure 1: (a) Schematic 3-D model of exciton-polariton transport within an optical cavity. (b) Exciton-polariton band structure from simulation and theory with no phonon coupling, (c) with phonon coupling $\gamma_{0}/2$, (d) with phonon coupling $\gamma_{0}$, (e) with phonon coupling $3\gamma_{0}/2$, where $\gamma_{0}$ is the phonon coupling. The parameter $\gamma_{0} = 5.85 \times 10^{-4}$ a.u. Further we use $\Omega = 3900$ cm$^{-1}$, $N = 40001$, $\tau = 0$, $\omega_0 = 2.58$ eV, and $\varepsilon_0 = 3.2$ eV.
• Figure 2: Group velocities extracted from quantum dynamical simulations (filled circles) compared to the predictions of the analytical model (solid lines) introduced in this work, with phonon frequency of (a) $1440 \ \text{cm}^{-1}$ and (b) $360 \ \text{cm}^{-1}$. In (a), the group velocities for different phonon coupling are plotted, with $\gamma_0/2$ represented in red, $\gamma_0$ in green, and $3\gamma_0/2$ in blue. Similarly, in (b), the phonon coupling strengths are depicted as $\gamma_0$ (red), $3\gamma_0/2$ (green), and $2\gamma_0$ (blue).(c),(d) Heatmaps gathered from MFE exciton-polarization propagation over 0.242 ps, corresponding to highlighted points in (Fig 2a). Panels (c) and (d) illustrate the phonon coupling strengths ranging from $\gamma_0/2$ to $3\gamma_0/2$ for a phonon frequency of $1440 \ \text{cm}^{-1}$. (e) Exciton-polariton band structure from simulation and theory with phonon coupling $2\gamma_0$ with similar parameters used in (b). We used $\gamma_{0}= 5.85 \times 10^{-4}$ and $1.46 \times 10^{-4}$ a.u. for figure a and b respectively. Further we use $\Omega = 3900$ cm$^{-1}$, $N = 40001$ for figure a and $N = 30001$ for figure b, $\tau = 0$, $\omega_0 = 2.58$ eV, and $\varepsilon_0 = 3.2$ eV.