The effect of disorder on polaritons in a coupled array of cavities

Abstract

The effect of disorder in the intensity of the driving laser on a coupled array of cavities described by a Bose-Hubbard Hamiltonian for dark-state polaritons is investigated. A canonically-transformed Gutzwiller wave function is used to investigate the phase diagram and dynamics of a one-dimensional system with uniformly distributed disorder in the Rabi frequency. In the phase diagram, we find the emergence of a Bose glass phase that increases in extent as the strength of the disorder increases. We study the dynamics of the system when subject to a ramp in the Rabi frequency which, starting from the superfluid phase, is decreased linearly and then increased to its initial value. We investigate the dependence of the density of excitations, the relaxation of the superfluid order parameter and the excess energy pumped into the system on the inverse ramp rate, $\tau$. We find that, in the absence of disorder, the defect density oscillates with a constant envelope, while the relaxation of the order parameter and excess energy oscillate with $\tau^{-1.5}$ and $\tau^{-2}$ envelopes respectively. In the presence of disorder in the Rabi frequency, the defect density oscillates with a decaying envelope, the relaxation of the order parameter no longer decreases as $\tau$ increases while the residual energy decreases as $\tau$ increases. The rate at which the envelope of the defect density decays increases with increasing disorder strength, while the excess energy falls off more slowly with increasing disorder strength.