Time-Reversal Symmetry Breaking of p-Orbital Bosons in a One-Dimensional Optical Lattice

We study bosons loaded in a one-dimensional optical lattice of twofold p-orbital degeneracy at each site. Our numerical simulations find an anti-ferro-orbital p(x) + ip(y), a homogeneous p(x) Mott-insulator phase, and two kinds of superfluid phases distinguished by the orbital order (anti-ferro-orbital and paraorbital). The anti-ferro-orbital order breaks time-reversal symmetry. Experimentally observable evidence is predicted for the phase transition between the two different superfluid phases. We also discover that the quantum noise measurement is able to provide a concrete evidence of time-reversal symmetry breaking in the first Mott phase.