Non-zero momentum Bose-Einstein condensation of orbital atoms

Bose-Einstein condensation (BEC) is often associated with zero momentum to which a macroscopic fraction of bosons condense. Here we propose a new class of meta-stable quantum states where bosons condense at non-zero momenta, defying the paradigm. This becomes possible when bosonic atoms are confined in the $p$-orbital Bloch bands of an optical lattice rather than the usual $s$-orbital. A recent experiment at Mainz confirmed the discovery of such an exotic BEC with alkali-metal atoms in a 3D cubic lattice with anisotropic optical potentials. Non-zero momentum suggests crystalline order. Our theoretical studies further found that such non-zero momentum BECs are also naturally orbital ordered superfluids due to the fascinating, less studied center-of-mass $p$-wave symmetry (e.g., a vortex-like $p_x+ip_y$ condensate). Varying with the geometry from standard optical lattices to double-well lattices, the interesting orderings include staggered orbital currents, stripes of angular momenta, and modulated super-current density wave. Different than a phase of coexisting orders such as supersolidity, this new class of states is characterized by a single order parameter. Work done in collaboration with J. Moore, S. Das Sarma, V. M. Stojanovic, C. Wu, and E. Zhao. \\[4pt] References:\\[0pt] [1] W. V. Liu, C. Wu, Phys. Rev. A {\bf 74}, 013607 (2006). \\[0pt] [2] C. Wu, W. V. Liu, J. Moore, S. Das Sarma, Phys. Rev. Lett. {\bf 97}, 190406 (2006). \\[0pt] [3] V. M. Stojanovic, C. Wu, W. V. Liu, S. Das Sarma, Phys. Rev. Lett. {\bf 101}, 125301 (2008). \\[0pt] [4] E. Zhao and W. V. Liu, Phys. Rev. Lett. {\bf 100}, 160403 (2008).