We study bosons in the first excited Bloch band of a double-well optical lattice, recently realized at NIST. By calculating the relevant parameters from a realistic nonseparable lattice potential, we find that in the most favorable cases the boson li
fetime in the first excited band can be several orders of magnitude longer than the typical nearest-neighbor tunnelling timescales, in contrast to that of a simple single-well lattice. In addition, for sufficiently small lattice depths the excited band has minima at nonzero momenta incommensurate with the lattice period, which opens a possibility to realize an exotic superfluid state that spontaneously breaks the time-reversal, rotational, and translational symmetries. We discuss possible experimental signatures of this novel state.
Recently, a homogeneous superfluid state with a single gapless Fermi surface was predicted to be the ground state of an ultracold Fermi gas with spin population imbalance in the regime of molecular Bose-Einstein condensation. We study vortices in thi
s novel state using a symmetry-based effective field theory, which captures the low-energy physics of gapless fermions and superfluid phase fluctuations. This theory is applicable to all spin-imbalanced ultracold Fermi gases in the superfluid regime, regardless of whether the original fermion pairing interaction is weak or strong. We find a remarkable, unconventional form of the interaction between vortices. The presence of gapless fermions gives rise to a spatially oscillating potential, akin to the RKKY indirect-exchange interaction in non-magnetic metals. We compare the parameters of the effective theory to the experimentally measurable quantities and further discuss the conditions for the verification of the predicted new feature. Our study opens up an interesting question as to the nature of the vortex lattice resulting from the competition between the usual repulsive logarithmic (2D Coulomb) and predominantly attractive fermion-induced interactions.
