Theory and Quantum Dynamics Simulations of Exciton-Polariton Motional Narrowing

The motional narrowing effect has been extensively studied for cavity exciton-polariton systems in recent decades both experimentally and theoretically, which is featured by (1) the subaverage behavior, and (2) the asymmetric linewidths for the upper polariton (UP) and the lower polariton (LP). However, a minimal theoretical model that is clear and adequate to address all these effects, as well as the linewidth scaling relations remains missing. In this work, based on the single mode 1D Holstein-Tavis-Cummings (HTC) model, we studied the motional narrowing effect of the polariton linear absorption (LA) spectra via both semi-analytic derivations and numerically exact quantum dynamics simulations using the hierarchical equations of motion (HEOM) approach. The results reveal that under collective light-matter coupling between a cavity mode and $N$ molecules, the polariton linewidth scales as $1/\sqrt{N}$ under the slow limit, while scales as $1/N$ under the fast limit, due to the polaron decoupling effect. Further, by varying the detunings, the polariton linewidths exhibit significant motional narrowing, covering both characters mentioned above. Our analytic linewidth expressions agree well with the numerical exact simulations in all the parameter regimes we explored. These results indicate that the physics of motional narrowing is adequately accounted for by the single-mode 1D HTC model. We envision that both the numerical results and the analytic polariton linewidths expression presented in this work will offer great theoretical value for providing a better understanding of the exciton-polariton motional narrowing based on the HTC model.