Microscopic physics of quantum self-organization of optical lattices in cavities

We study quantum particles at zero temperature in an optical lattice coupled to a resonant cavity mode. The cavity field substantially modifies the particle dynamics in the lattice, and for strong particle-field coupling leads to self-organization of the particles, a configuration with only every second site occupied. We study the growth of this order out of a homogeneous initial distribution for few particles. Simulations reveal that the growth dynamics crucially depends on the initial quantum many-body state of the particles and can be monitored via the cavity fluorescence. Studying the relaxation time of the ordering reveals inhibited tunnelling due to the interaction with the cavity field. However, the relaxation becomes very quick for strong coupling.