  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.
