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The recent progress towards production of near-ground statequantum-degenerate molecules raises the issue of how such "small" moleculesbehave in an optical lattice. In this Letter we show that the coupling of themolecular orientation to the local electric field direction will provideseveralnew phenomena. In the case where the lasers forming differentcrystallographic directions of the lattice are incoherent, the orientation ofthe molecules is conserved (for L = 1) and a novel form of anisotropicsuperfluidity can be expected. When the lasers are coherent, and the opticallattice is such that the splitting of the rotational levels is large comparedto the centre of mass energies,an adiabaic description of the molecularorientation is appropriate. This leads to geometric vector potentials,pseudo-magnetic monopoles and a frustrated band structure with degenerateminima.

Rotating molecules in optical lattices, alignment and monopole crystals