Interaction induced ferro-electricity in the rotational states of polar molecules

We show that a ferro-electric quantum phase transition can be driven by the dipolar interaction of polar molecules in the presence a micro-wave field. The obtained ferro-electricity crucially depends on the harmonic confinement potential, and the resulting dipole moment persists even when the external field is turned off adiabatically. The transition is shown to be second order for fermions and for bosons of a smaller permanent dipole moment, but is first order for bosons of a larger moment. Our results suggest the possibility of manipulating the microscopic rotational state of polar molecules by tuning the trap's aspect ratio (and other mesoscopic parameters), even though the later's energy scale is smaller than the former's by six orders of magnitude.