Atomic Fermi-Bose mixtures in inhomogeneous and random lattices: From Fermi glass to quantum spin glass and quantum percolation

The interactions of atomic fermi-bose mixtures in random and inhomogeneous lattices were analyzed. It was found that in inhomogeneous lattices, interactions and tunneling could be controlled at the local level and different regimes could be accessed. Effective Hamiltonians were derived to explain the low temperature physics of the system. It was observed that the control led to the achievement of fermi-glass, fermi spin glass and quantum percolation regime involving bare and composite fermions in random lattices.