Paired phases of bosons in optical lattices

We describe the conditions under which bosons in optical lattices can form paired condensates, focusing on the case of bosons with spin. We show that the ground state of such a system, with sufficiently strong spin-dependent interactions, is a \textit{spin-singlet condensate}, which preserves spin-rotation symmetry. We then consider the gapped single-particle excitations across the phase transition from the insulator, and show that they have nontrivial scaling behavior, determined by coupling to the critical pair modes.