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π-flux Dirac bosons and topological edge excitations in a bosonic chiral p-wave superfluid

We study the topological properties of elementary excitations in a staggered $p_x \pm i p_y$ Bose-Einstein condensate realized in recent orbital optical lattice experiments. The condensate wave function may be viewed as a configuration space variant of the famous $p_x+ ip_y$ momentum space order parameter of strontium ruthenate superconductors. We show that its elementary excitation spectrum possesses Dirac bosons with $π$ Berry flux. Remarkably, if we induce a population imbalance between the $p_x+ip_y$ and $p_x-ip_y$ condensate components, a gap opens up in the excitation spectrum resulting in a nonzero Chern invariant and topologically protected edge excitation modes. We give a detailed description on how our proposal can be implemented with standard experimental technology.