Composite fermion state of spin-orbit coupled bosons

We consider spinor Bose gas with the isotropic Rashba spin-orbit coupling in 2D. We argue that at low density its groundstate is a composite fermion state with a Chern-Simons gauge field and filling factor one. The chemical potential of such a state scales with the density as \mu \propto n^{3/2}. This is a lower energy per particle than \mu \propto n for the earlier suggested groundstate candidates: a condensate with broken time-reversal symmetry and a spin density wave state.