Abstract:Optics has proved a fertile ground for the experimental simulation of quantum mechanics. Most recently, optical realizations of P T -symmetric quantum mechanics have been shown, both theoretically and experimentally, opening the door to international efforts aiming at the design of practical optical devices exploiting this symmetry. Here, we focus on the optical P T -symmetric dimer, a two-waveguide coupler where the materials show symmetric effective gain and loss, and provide a review of the linear and nonlinear optical realizations from a symmetry-based point of view. We go beyond a simple review of the literature and show that the dimer is just the smallest of a class of planar N-waveguide couplers that are the optical realization of the Lorentz group in 2 + 1 dimensions. Furthermore, we provide a formulation to describe light propagation through waveguide couplers described by non-Hermitian mode coupling matrices based on a non-Hermitian generalization of the Ehrenfest theorem.

Abstract:We provide an analytic propagator for non-Hermitian dimers showing linear gain or losses in the quantum regime. In particular, we focus on experimentally feasible realizations of the P T -symmetric dimer and provide their mean photon number and second order two-point correlation. We study the propagation of vacuum, single photon spatially-separable, and two-photon spatially-entangled states. We show that each configuration produces a particular signature that might signal their possible uses as photon switches, semi-classical intensity-tunable sources, or spatially entangled sources to mention a few possible applications.