Unconventional Bose-Einstein condensation in high orbital bands

We perform the theoretical study on unconventional Bose-Einstein condensations (UBEC) in higher orbital bands of optical lattices observed by Hemmerich's group. These exotic states of bosons are non-zero condensation wavevectors, and thus beyond the ``no-node'' paradigm. We have studied various effects on UBECs including lattice asymmetry and interactions. The interplay between the kinetic and interaction energies gives rise to two different UBECs with the real and complex-valued condensation wavefunctions, respectively. The latter spontaneously breaks time-reversal symmetry, which is impossible in usual BEC systems.