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We investigate the unconventional Bose-Einstein condensations (BEC) with theorbital degree of freedom in the 3D cubic optical lattice, which give rise tovarious exotic features absent in conventional scalar and spinor BECs. Orbitalangular momentum moments are formed on lattice sites breaking time-reversalsymmetry spontaneously. Furthermore, they exhibit orbital frustrations anddevelop a chiral ordering selected by the "order-from-disorder" mechanism.

Frustrated Bose-Einstein condensates with non-collinear orbital ordering