Superfluid--Mott insulator transition of spin-1 bosons in optical resonators

We consider an antiferromagnetic spin-1 Bose-Einstein condensate confined in a Fabry-P\'erot optical resonator, in which the intracavity light field form an optical lattice potential for the atoms. Special emphasis is paid to the cavity-mediated superfluid--Mott insulator transition. We found that exotic phase diagrams can appear due to the competition between cavity-induced nonlinear interaction and the atomic spin-dependent collision interactions.