Controllable high-speed polariton waves in a PT-symmetric lattice

Parity-time (PT) symmetry gives rise to unusual phenomena in many physical systems, presently attracting a lot of attention. One essential and non-trivial task is the fabrication and design of the PT-symmetric lattices in different systems. Here we introduce a method to realize such a lattice in an exciton-polariton condensate in a planar semiconductor microcavity. We theoretically demonstrate that in the regime, where lattice profile is nearly PT-symmetric, a polariton wave can propagate at very high velocity resulting from the beating of a ground state condensate created in the lowest energy band at very small momentum and a condensate simultaneously created in higher energy states with large momentum. The spontaneous excitation of these two states in the nonlinear regime due to competition between multiple eigenmodes becomes possible since the spectrum of nearly PT-symmetric structure reveals practically identical amplification for Bloch waves from the entire Brillouin zone. There exists a wide velocity range for the resulting polariton wave. This velocity can be controlled by an additional coherent pulse carrying a specific momentum. We also discuss the breakup of the PT-symmetry when the polariton lifetime exceeds a certain threshold value.