  For over a decade, cold atoms in lattice potentials have been an attractive
platform to simulate phenomena known from solid state theory, as the
Mott-insulator transition. In contrast, the field of photonics usually deals
with non-equilibrium physics. Recent advances towards photonic simulators of
solid state equilibrium effects include polariton double-site and lattice
experiments, as well as the demonstration of a photon condensate in a
dye-filled microcavity. Here we demonstrate a technique to create variable
micropotentials for light using thermo-optic imprinting within an
ultrahigh-reflectivity mirror microcavity filled with a dye-polymer solution
that is compatible with photon gas thermalization. By repeated
absorption-emission cycles photons thermalize to the temperature of the dye
solution, and in a single microsite we observe a photon Bose-Einstein
microcondensate. Effective interactions between the otherwise nearly
non-interacting photons are observed due to thermo-optic effects, and in a
double-well system tunnel coupling between sites is demonstrated, as well as
the hybridization of eigenstates. Prospects of the new experimental platform
include photonic structures in which photons thermalize into entangled manybody
states.
