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