  We show that the ground state of disordered rotor models with quadrupolar
interactions can exhibit biaxial nematic ordering in the disorder-averaged
sense. We present a mean-field analysis of the model and demonstrate that the
biaxial phase is stable against small quantum fluctuations. We point out the
possibility of experimental realization of such rotor models using ultracold
spin-one Bose atoms in a spin-dependent and disordered optical lattice in the
limit of a large number of atoms per site and also suggest an imaging
experiment to detect the biaxial nematicity in such systems.
