Semiclassical equations of motion for interacting bosons in a one-dimensional optical lattice inside a recoil-resolved cavity
We formulate the equations of motion describing a Bose-Einstein condensate in an optical lattice placed inside a high-finesse optical cavity. A transverse pump field drives the system allowing for the atoms to couple with the cavity mode. The recoil-resolved cavity generates a dynamical long-range interaction between the atoms, which competes with the inherent short-range interaction captured within the Bose-Hubbard model. By using realistic parameters, our work constitutes a crucial step in understanding nonequilibrium phases in an experimentally relevant light-matter system.