  In a cold atom gas subject to a 2D spin-dependent optical lattice potential
with hexagonal symmetry, trapped atoms undergo orbital motion around the
potential minima. Such atoms are elementary quantum rotors. We develop the
theory of such quantum rotors. Wave functions, energies, and degeneracies are
determined for both bosonic and fermionic atoms, and magnetic dipole
transitions between the states are elucidated. Quantum rotors in optical
lattices with precisely one atom per unit cell can be used as high precision
rotation sensors, accelerometers, and magnetometers.
