Realizing the Strongly Correlated $d$-Wave Mott-Insulator State in a Fermionic Cold-Atom Optical Lattice

We show that a new state of matter, the $d$-wave Mott-insulator state ($d$-Mott state) (introduced recently by [H. Yao, W. F. Tsai, and S. A. Kivelson, Phys. Rev. B 76, 161104 (2007)]), which is characterized by a nonzero expectation value of a local plaquette operator embedded in an insulating state, can be engineered using ultracold atomic fermions in two-dimensional double-well optical lattices. We characterize and analyze the parameter regime where the $d$-Mott state is stable. We predict the testable signatures of the state in the time-of-flight measurements.