TY - JOUR AB - We introduce a new platform for quantum simulation of many-body systems based on nonspherical atoms or molecules with zero dipole moments but possessing a significant value of electric quadrupole moments. We consider a quadrupolar Fermi gas trapped in a 2D square optical lattice, and show that the peculiar symmetry and broad tunability of the quadrupole-quadrupole interaction results in a rich phase diagram encompassing unconventional BCS and charge density wave phases, and opens up a perspective to create a topological superfluid. Quadrupolar species, such as metastable alkaline-earth atoms and homonuclear molecules, are stable against chemical reactions and collapse and are readily available in experiment at high densities. AU - Bhongale, Satyan AU - Mathey, Ludwig AU - Zhao, Erhai AU - Yelin, Susanne AU - Lemeshko, Mikhail ID - 2204 IS - 15 JF - Physical Review Letters TI - Quantum phases of quadrupolar fermi gases in optical lattices VL - 110 ER -