D-wave bosonic pair in an optical lattice

We present a bosonic model, in which two bosons may form a bound pair with d-wave symmetry via the four-site ring exchange interaction. A d-wave pairing superfluid as well as a d-wave density wave (DDW) state, are proposed to be achievable in this system. This exotic bosonic system can be realized in the BEC zone of a two-dimensional attractive p-band spinless fermionic system. By the mean field approach, we find that at low densities, the d-wave pairs may condensate, leading to a d-wave bosonic paired superfluid. At some particular filling factors, a novel phase, d-wave density wave state, emerges. We study this DDW state and its corresponding quantum phase transition in a two-leg ladder by the time-evolving block decimation (TEBD) method.