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We show that density-dependent synthetic gauge fields may be engineered by combining periodically modulated interactions and Raman-assisted hopping in spin-dependent optical lattices. These fields lead to a density-dependent shift of the momentum distribution, may induce superfluid-to-Mott insulator transitions, and strongly modify correlations in the superfluid regime. We show that the interplay between the created gauge field and the broken sublattice symmetry results, as well, in an intriguing behavior at vanishing interactions, characterized by the appearance of a fractional Mott insulator.
Greschner et al. (Fri,) studied this question.