  Bose-Einstein condensation, the macroscopic ground state accumulation of
particles with integer spin (bosons) at low temperature and high density, has
been observed in several physical systems, including cold atomic gases and
solid state physics quasiparticles. However, the most omnipresent Bose gas,
blackbody radiation (radiation in thermal equilibrium with the cavity walls)
does not show this phase transition, because the chemical potential of photons
vanishes and, when the temperature is reduced, photons disappear in the cavity
walls. Theoretical works have considered photon number conserving
thermalization processes, a prerequisite for Bose-Einstein condensation, using
Compton scattering with a gas of thermal electrons, or using photon-photon
scattering in a nonlinear resonator configuration. In a recent experiment, we
have observed number conserving thermalization of a two-dimensional photon gas
in a dye-filled optical microcavity, acting as a 'white-wall' box for photons.
Here we report on the observation of a Bose-Einstein condensation of photons in
a dye-filled optical microcavity. The cavity mirrors provide both a confining
potential and a non-vanishing effective photon mass, making the system formally
equivalent to a two-dimensional gas of trapped, massive bosons. By multiple
scattering off the dye molecules, the photons thermalize to the temperature of
the dye solution (room temperature). Upon increasing the photon density we
observe the following signatures for a BEC of photons: Bose-Einstein
distributed photon energies with a massively populated ground state mode on top
of a broad thermal wing, the phase transition occurring both at the expected
value and exhibiting the predicted cavity geometry dependence, and the ground
state mode emerging even for a spatially displaced pump spot.
