P-band induced self-organization and dynamics with repulsively driven ultracold atoms in an optical cavity

Abstract: We investigate a Bose-Einstein condensate strongly coupled to an optical cavity via a repulsive optical lattice. We detect a stable self-ordered phase in this regime, and show that the atoms order through an antisymmetric coupling to the P-band of the lattice, limiting the extent of the phase and changing the geometry of the emergent density modulation. Furthermore, we find a non-equilibrium phase with repeated intense bursts of the intra-cavity photon number, indicating non-trivial driven-dissipative dynamics.