Unusual dynamical properties of disordered polaritons in microcavities
Georg Engelhardt, Jianshu Cao
Abstract
The collective light-matter interaction in microcavities gives rise to the intriguing phenomena of cavity-mediated transport that can potentially overcome the Anderson localization. Yet, an accurate theoretical treatment is challenging as the matter (e.g., molecules) is subject to large energetic disorder. In this paper, we develop the Green's function solution to the Fano-Anderson model and use the exact analytical solution to quantify the effects of energetic disorder on the spectral and dynamical properties in microcavities. Starting from the microscopic equations of motion, we derive an effective non-Hermitian Hamiltonian and predict a set of scaling laws: (i) The complex eigenenergies of the effective Hamiltonian exhibit an exceptional point, which leads to underdamped coherent dynamics in the weak disorder regime, where the decay rate increases with disorder, and overdamped incoherent dynamics in the strong disorder regime, where the slow decay rate decreases with disorder. (ii) The total density of states of disordered ensembles can be exactly partitioned into the cavity, bright-state, and dark-state local density of states, which are determined by the complex eigensolutions and can be measured via spectroscopy. (iii) The cavity-mediated relaxation and transport dynamics are intimately related such that both the energy-resolved relaxation and transport rates are proportional to the cavity local density of states. The ratio of the disorder-averaged relaxation and transport rates equals the molecule number, which can be interpreted as a result of a quantum random walk. (iv) A turnover in the rates as a function of disorder or molecule density can be explained in terms of the overlap of the disorder distribution function and the cavity local density of states. These findings reveal the significant impact of the dark states on the local density of states and consequently their crucial role in optimizing spectroscopic and transport properties of disordered ensembles in cavities.