Mechanistic principles of exciton-polariton relaxation

TL;DR

This work provides a microscopic mechanism for exciton-polariton relaxation in optical cavities with finite thickness. Using mixed quantum-classical (multi-trajectory Ehrenfest) dynamics and analytical analysis beyond the long-wavelength limit, the authors show a two-step relaxation: a vertical, momentum-conserving upper-to-lower polariton transition followed by intraband Fröhlich scattering within the lower polariton. In multilayered/finitely thick cavities, phonon-fluctuation synchronization across layers strongly suppresses Fröhlich scattering, yielding long-lived, $k$-localized lower-polariton populations. They derive simple analytical expressions linking thickness (number of layers) to relaxation rate constants, offering a predictive framework for polariton dynamics in realistic filled cavities and guiding design of devices with controlled relaxation behavior.

Abstract

Exciton-polaritons are light-matter hybrid quasi-particles that have emerged as a flexible platform for developing quantum technologies and engineering material properties. However, the fundamental mechanistic principles that govern their dynamics and relaxation remain elusive. In this work, we provide the microscopic mechanistic understanding of the exciton-polariton relaxation process that follows from an excitation in the upper polariton. Using both mixed quantum-classical simulations and analytical analysis, we reveal that phonon-induced upper-to-lower polariton relaxation proceeds via two steps: the first step is a vertical inter-band transition from the upper to the lower polariton, which is followed by a second step that is a phonon-induced Fröhlich scattering within the lower polariton. We find that in materials of finite thickness (which include filled cavities), phonon-induced polaritonic intraband Fröhlich scattering is significantly suppressed. We show that the microscopic origin of this suppression is phonon-fluctuations synchronization (or self-averaging) due to the polaritonic spatial delocalization in the quantization direction. Finally, we show that the same phonon fluctuation-synchronization effect plays a central role across polaritonic relaxation pathways, and we derive simple analytical expressions that relate a material's finite thickness to the corresponding relaxation rate constants.

Figures (6)

• Figure 1: Schematic of polariton dynamics. (a and b) Schematic drawing of a single-layer and multilayered material in an optical cavity. (c and d) Schematic drawing of the single-layer and multilayer band structures with energy on the $y$-axis and wavevector ($k$) along the horizontal axis. $K_{UL}$ ($K_{DL}$, $K_{UD}$) is the relaxation rate from the upper polariton (dark states, upper polariton) to lower polariton (lower polariton, dark states).
• Figure 2: Polariton-band-resolved relaxation dynamics. Polariton-band-resolved population relaxation dynamics in a single-layer material (a-d), and in multi-layered material (5 layers) (e-h), following an excitation to the upper polariton centered at 3.5 eV. The plots from left to right display a snapshot at the initial time, 0.01 ps, 0.10 ps, and 0.30 ps of the population (blue circles), where there is not only a transfer of population from the upper to lower polariton, but also Fröhlich scattering the lower polariton. The degree of this scattering (a-d) is much greater for a single layer of material, than in the multilayered material (e-h), owing to the "phonon-fluctuation synchronization effect" in the multilayered case.
• Figure 3: The vertical nature of the polariton relaxation. (a - c) Upper to lower polariton transfer matrix elements for the first-order (a), second-order (b), and full exponential propagator (c). Note that here we are presenting the absolute values of the matrix elements. Here, we consider a system comprising 40,000 sites and a time step of $\Delta t = 50$ a.u.
• Figure 4: Suppression of Fröhlich scattering in multilayered materials via phonon fluctuation synchronization effect. (a - d) Show the relaxation dynamics in the lower polariton band in single layer vs multilayered material. (e - f) Show the relaxation dynamics in the lower polariton when we constrain phonon sampling. For this simulation we copied the initial position and momentum of the phonons for each layer, eliminating any difference in the phonons layer to layer.
• Figure 5: Population inside and outside the excitation window. (a & b) Population, relative to the lower polariton, inside the coherent relaxation window vs population scattering outside this window in a single layer and in 10 layers. (c) Inside population and fitted exponential function for 1, 5, and 10 layers. (d) Fitted $K_{FS}$ compared to our analytical expression as a function of the number of layers.