  A Bose-Einstein condensate (BEC) is a quantum phase of matter achieved at low
temperatures. Photons, one of the most prominent species of bosons, do not
typically condense due to the lack of a particle number-conservation. We
recently described a photon thermalization mechanism which gives rise to a
grand canonical ensemble of light with effective photon number conservation
between a subsystem and a particle reservoir. This mechanism occurs during
Doppler laser cooling of atoms where the atoms serve as a temperature reservoir
while the cooling laser photons serve as a particle reservoir. Here we address
the question of the possibility of a BEC of photons in this laser cooling
photon thermalization scenario and theoretically demonstrate that a Bose
condensation of photons can be realized by cooling an ensemble of two-level
atoms (realizable with alkaline earth atoms) inside a Fabry-Perot cavity.
