A weakly interacting gas of bosonic atoms moving in the periodic
potential of an optical lattice goes through a phase transition at a
sufficiently low temperature. This phase transition is characterized
by the macroscopic occupation of the single particle ground state and
called as Bose-Einstein condensation. This Bose-Einstein condensate
is, however, sensitive to particle interactions. When the interaction
between particles becomes strong, the Bose-Einstein condensate can
freeze into a Mott insulator.
When the Bose gas is placed inside an optical resonator, atom-light
interaction may create an infinite range interaction between the atoms
and may cause, in certain geometries, another interesting phase
transition: the formation of a charge-density wave. The charge-density
wave combined with Bose-Einstein condensation is called as super solid.
During the talk, we discuss the Bose gas inside an optical resonator,
paying special attention to another very important feature: the
driven-dissipative nature of the cavity. The photons eventually escape
the cavity resulting in a quantum noise for the atomic dynamics.