Frustrated superfluids in a non-Abelian flux

We study possible superfluid states of the Rashba spin-orbit coupled (SOC) spinor bosons with the spin anisotropic interaction $\lambda$ hopping in a square lattice. The frustrations from the non-abelian flux due to the SOC leads to novel spin-bond correlated superfluids. By using a recently developed systematic "order from quantum disorder" analysis, we not only determine the true quantum ground state, but also evaluate the mass gap in the spin sector at $\lambda < 1$, especially compute the the excitation spectrum of the Goldstone mode in the spin sector at $\lambda=1$ which would be quadratic without the analysis. The analysis also leads to different critical exponents on the two sides of the 2nd order transition driven by a roton touchdown at $\lambda=1$. The intimate analogy at $\lambda=1$ with the charge neutral Goldstone mode in the pseudo-spin sector in the Bilayer quantum Hall systems at the total filling factor $\nu_T=1$ are stressed. The experimental implications and detections of these novel phenomena in cold atoms loaded on a optical lattice are presented.