Saptarshi Mandal, Kush Saha, K. Sengupta
Motivated by recent experiments [Y.J. Lin {\it et al.}, Nature {\bf 471}, 83 (2011)], we study Mott phases and superfluid-insulator (SI) transitions of two-species ultracold bosonic atoms in a two-dimensional square optical lattice with nearest neighbor hopping amplitude $t$ in the presence of a spin-orbit coupling characterized by a tunable strength $\gamma$. Using a strong-coupling expansion, we chart out the phase diagrams of the bosons in the presence of such spin-orbit interaction and compute their momentum distribution in the Mott phase near the SI transition point. We show that the momentum distribution of the bosons displays precursor peaks whose position in the Brillouin zone can be varied by tuning $\gamma$. We also study the superfluid phases of the bosons near the SI transition and compute the collective modes of the bosons in these phases. Our study reveals the presence of reentrant SI transitions as a function of $\gamma$ for non-zero $t$. We also point out the presence of unconventional quantum critical points at $t/\gamma=0$ which are accompanied by emergence of an additional gapless mode in the critical region. We propose experiments to test our theory.
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http://arxiv.org/abs/1205.3178
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