Unusual Dynamical Properties of Disordered Polaritons in Micocavities
- URL: http://arxiv.org/abs/2112.04060v2
- Date: Tue, 22 Mar 2022 04:36:05 GMT
- Title: Unusual Dynamical Properties of Disordered Polaritons in Micocavities
- Authors: Georg Engelhardt and Jianshu Cao
- Abstract summary: We develop the Green's function solution to the Fano-Anderson model.
We quantify the effects of energetic disorder on the spectral and transport properties in microcavities.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The strong light-matter interaction in microcavities gives rise to intriguing
phenomena, such as cavity-mediated transport that can potentially overcome the
Anderson localization. Yet, an accurate theoretical treatment is challenging as
the matter (e.g.,molecules) are subject to large energetic disorder. In this
article, 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 transport properties in microcavities. Starting
from microscopic equation of motions, we derive an effective non-Hermitian
Hamiltonian and predict a set of scaling laws: (i) The complex eigen-energies
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 eigen solutions and can be measured via spectroscopy.
(iii) The cavity-mediated relaxation and transport dynamics are intimately
related such that 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 transport properties of disordered ensembles in cavities.
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