Mean-field Mixed Quantum-Classical Approach for Many-Body Quantum Dynamics of Exciton-Polaritons

TL;DR

This work addresses the challenge of simulating many-body quantum dynamics of exciton–polaritons in the presence of phonon-induced disorder beyond the single-excitation subspace. It introduces a mean-field, mixed quantum–classical framework that combines a multitrajectory Ehrenfest treatment of phonons with a Gross–Pitaevskii–like ansatz for the exciton–photon sector, preserving the total excitation number $ ext{N}_ ext{ex}$. The study reveals a nonmonotonic dependence of transport and decoherence on the excitation number $ ext{N}_ ext{ex}$ and on-site interaction strength $U$, with an intermediate $U$ and specific $ ext{N}_ ext{ex}$ regime yielding enhanced coherence and ballistic-like polariton transport despite phonon-induced disorder. These findings provide a scalable foundation for more accurate beyond-mean-field quantum-dynamical methods and inform design principles for polaritonic devices where coherence is essential.

Abstract

In this work, we use a mixed quantum-classical (mean-field) many-body approach for simulating the quantum dynamics of excitons and exciton-polaritons beyond the single-excitation subspace. We combine the multitrajectory Ehrenfest approach, which propagates slow degrees of freedom classically, with the Gross-Pitaevskii method, which propagates fast degrees of freedom in a mean-field fashion. We use this mean-field many-body Ehrenfest approach to analyze how the phonon-induced dynamic disorder and the many-body interaction affect the incoherent and coherent dynamics of excitons and exciton-polaritons. We examine how the number of excitations and the strength of repulsive exciton-exciton interaction nonlinearly influence the transport, Fröhlich scattering and decoherence.

Figures (5)

• Figure 1: Quantum dynamics of a bare excitonic material. (a) Initial excitonic density (at $t=0$) (black solid line), excitonic density at $t=4.84$ ps for non-interacting excitons(blue solid line), and for interacting excitons(red solid line). (b) Time-dependent mean-square displacement (MSD) ($\mathrm{\AA}^{2}\mathrm{ps^{-1}}$) for single exciton (black solid line), 10 non-interacting excitons (blue solid line), and 10 interacting ($U=0.1$ a.u.) excitons (red solid line). (c) Excitonic density evolution for 10 non-interacting excitons. (d) Excitonic density evolution for 10 interacting excitons. (e) Time-dependent MSD for different variations of on-site interaction strength $U$ with a fixed number of excitations ($N_\text{ex}=10$). (f) Time-dependent MSD, for different numbers of excitations at constant on-site interaction strength $U=0.001$ a.u. (g) Diffusion constant ($\mathrm{\AA}^{2}\mathrm{ps^{-1}}$), over different variations of interaction strength $U$ at constant number of excitations, (${N_\text{ex}=10}$). (h) Diffusion constant over different variations of number of excitations (${N_\text{ex}}$) at fixed interaction strength ($U=0.001$ a.u.). All simulations have been performed with hopping parameter $\tau = 300$ cm$^{-1}$ and phonon-coupling strength $\gamma=3500$ cm$^{-1}\mathrm{\AA}^{-1}$, at temperatures $150$ K.
• Figure 2: Dynamics of non-interacting exciton-polaritons in the strong coupling regime. (a) Schematic illustration of polariton production by optimal excitation of material through laser in the lower polariton band. (b) Upper and lower polariton bands in the exciton-polariton dispersion plot, energies recorded in electron volts (eV), curved arrows denote Fröhlich scattering. (c) Polaritonic population at $t \approx 0.25$ ps under single excitation (blue lines) and multiple-excitations ($N_\text{ex}=1000$ ) (red lines). (d) Fröhlich scattering in reciprocal space as a function of time for gradually increasing number of excitations. (e) Group velocity obtained for both single (solid lines) and multiple excitations (triangles), with phonon-coupling parameter $\gamma=\gamma_{0}$ (red) $\gamma= 1.5\gamma_{0}$ (blue) and $\gamma= 2\gamma_{0}$ (green). (f) Polariton density evolution for $N_text{ex}=1000$. (g) Polariton density evolution for single excitation. The temperature is set to 300K.
• Figure 3: Dynamics of interacting excitons-polaritons. (a) Time-dependent mean-square displacement (MSD) for $N_\text{ex}=1$ (black dashed line), $N_\text{ex}=1000$, non-interacting excitons (red solid line), $N_\text{ex}=1000$ interacting excitons (green solid line), with strength $U=0.06$ .a.u. (b) Time-dependent MSD for fixed number of excitations ($N_\text{ex}=1000$) and different on-site interactions. (c) Polariton density at $t\approx 0.25$ ps with on-site interaction (red solid line) and without on-site interaction (blue solid line). (d) Polariton density evolution with no on-site interactions. (e) Polariton density evolution with moderate on-site interaction strength $U=0.02$ a.u. (f) Polariton density evolution with high on-site interaction strength $U=0.3$ a.u. The temperature is set to 300K.
• Figure 4: Scattered population of exciton-polaritons. (a) Time-dependent scattered population at a fixed excitation number ($N_\mathrm{ex} = 1000$) and different on-site interactions. (b) Scattered population at $t=181$ fs at various $U$, for $N_\mathrm{ex} = 100$ (green solid line), $N_\mathrm{ex} = 500$ (red solid line) and $N_\mathrm{ex} = 1000$ (black solid line). (c) Time-dependent scattered population at a constant $U=0.001$ a.u. with varying number of excitations $N_\mathrm{ex}$. (d) Scattered population over various numbers of excitations at $t=242$ fs, and different on-site interactions.
• Figure 5: Time-dependent purity of exciton-polaritons. (a) Purity versus time for a single excitation (grey solid line), at $N_\mathrm{ex} = 500$ (red solid line) and at $N_\mathrm{ex} = 1000$ (blue solid line), $U$ is set to 0. (b) Purity versus time at $N_\mathrm{ex} = 1000$ and different on-site interactions.