Formula omitted]symmetric tight-binding 1D chains: Coupling to the continuum and superradiance transition

Abstract

By the use of the transfer matrix (TM) approach and effective non-Hermitian Hamiltonian (EnHH) approach we study transport and scattering properties of PT−symmetric tight-binding one-dimensional (1D) chains. In the TM approach we derive an exact expression for the transmission T through 1D chains that incorporates all the scattering-system parameters: incident-wave energy E, chain length L, gain/loss amplitude γ, and coupling strength to perfect leads χ. We show that the behavior of T vs. L strongly depends on the value of γ with respect to the critical value γcr, defined through γcr2=4−E2. For γ<γcr, the transmission T is a periodic function of L, however, for γ>γcr, T decreases exponentially with L. We also predict the unforeseen dependence T∝L−2 at γ=γcr. By the use of the EnHH approach to the same model which is now connected to continuum through left and write ends, we focus on the onset of the superradiance transition as a function of E, L, γ, and χ. The main interest here is in the competition between the balanced gain/loss terms in the bulk of the chain and the coupling to continuum through the ends of the chain. Our results demonstrate that the presence of the gain/loss in the bulk strongly modifies the width of non-superradiant states, however, did not change the width of the superradiant ones. The analytical predictions are supported by detailed numerical simulations.