Realizing negative index of refraction in an ensemble of ground-state polar molecules with lasers

We propose a coherent optical method for creating negative refractive index (NRI) for a gaseous ensemble of ground-state polar molecules possessing both permanent electric and magnetic moments. Exploiting the pure rotational transition between the two lowest rotational levels of the ground vibrational state, one can generate two dressed states of mixed parity using a microwave laser. These dressed states are then used as the two lower states of a $\Lambda$-type three-level scheme using two infra-red lasers to couple them to another ro-vibrational level in the ground-state manifold. Our analytical and numerical results show that, when one of infra-red lasers used as a probe and the other as a control field with a fixed detuning, there are two distinct probe detuning regimes where the system can exhibit NRI with figure of merit reaching as high as 10. The first regime dubbed as NRI-I is the red-detuned side of the probe field and away from the two-photon or dark-state resonance. The other regime called as NRI-II is close to the dark-state resonance or electro-magnetically induced transparency (EIT). While the first regime has a broad frequency span the second one has relatively narrow width. We interpret our results in terms of the proximity of EIT, quantum interference and dispersive behavior of the system.