  We propose and analyze a mechanism for Bose-Einstein condensation of
stationary dark-state polaritons. Dark-state polaritons (DSPs) are formed in
the interaction of light with laser-driven 3-level Lambda-type atoms and are
the basis of phenomena such as electromagnetically induced transparency (EIT),
ultra-slow and stored light. They have long intrinsic lifetimes and in a
stationary set-up with two counterpropagating control fields of equal intensity
have a 3D quadratic dispersion profile with variable effective mass. Since DSPs
are bosons they can undergo a Bose-Einstein condensation at a critical
temperature which can be many orders of magnitude larger than that of atoms. We
show that thermalization of polaritons can occur via elastic collisions
mediated by a resonantly enhanced optical Kerr nonlinearity on a time scale
short compared to the decay time. Finally condensation can be observed by
turning stationary into propagating polaritons and monitoring the emitted
light.
