  We show that conical intersections can be created in laboratory coordinates
by dressing a parabolic trap for ultracold atoms or molecules with a
combination of optical and static magnetic fields. The resulting ring trap can
support single-particle states with half-integer rotational quantization and
many-particle states with persistent flow. Two well-separated atomic or
molecular states are brought into near-resonance by an optical field and tuned
across each other with an inhomogeneous magnetic field. Conical intersections
occur at the nodes in the optical field.
