  Laser cooling of atomic motion enables a wide variety of technological and
scientific explorations using cold atoms. Here we focus on the effect of laser
cooling on the photons instead of on the atoms. Specifically, we show that
non-interacting photons can thermalize with the atoms to a grand canonical
ensemble with a non-zero chemical potential. This thermalization is
accomplished via scattering of light between different optical modes, mediated
by the laser cooling process. While optically thin modes lead to traditional
laser cooling of the atoms, the dynamics of multiple scattering in optically
thick modes has been more challenging to describe. We find that in an
appropriate set of limits, multiple scattering leads to thermalization of the
light with the atomic motion in a manner that approximately conserves total
photon number between the laser beams and optically thick modes. In this
regime, the subsystem corresponding to the thermalized modes is describable by
a grand canonical ensemble with a chemical potential set by the energy of a
single laser photon. We consider realization of this regime using two-level
atoms in Doppler cooling, and find physically realistic conditions for rare
earth atoms. With the addition of photon-photon interactions, this system could
provide a new platform for exploring many-body physics.
