Trajectory-based Non-adiabatic Simulations of the Polariton Relaxation Dynamics

We benchmark the accuracy of various trajectory-based non-adiabatic methods in simulating the polariton relaxation dynamics under the collective coupling regime. The Holstein-Tavis-Cummings (HTC) Hamiltonian is used to describe the hybrid light-matter system of N molecules coupled to a single cavity mode. We apply various recently developed trajectory-based methods to simulate the population relaxation dynamics by initially exciting the upper polariton state, and benchmark the results against populations computed from exact quantum dynamical propagation using the hierarchical equations of motion (HEOM) approach. In these benchmarks, we have systematically varied the number of molecules N , light-matter detunings, and the light-matter coupling strengths. Our results demonstrate that the symmetrical quasi-classical method with γ correction (γ-SQC) and spin-mapping linearized semi-classical (spin-LSC) approaches yield more accurate polariton population dynamics than traditional mixed quantum-classical (MQC) methods such as the Ehrenfest and surface hopping techniques.