Robust nuclear spin entanglement via dipolar interactions in polar molecules

We propose a general protocol for on-demand generation of robust entangled states of nuclear and/or electron spins of ultracold polar molecules using strong and tunable electric dipolar interactions. By encoding the effective spin-1/2 degree of freedom into molecular spin-rotational states, we derive spin-spin interactions of the Ising type, and show how to use these interactions to create long-lived cluster states of the nuclear spin sublevels of KRb($^1\Sigma$) molecules in their ground rotational states. We also show that by inducing an avoided crossing of molecular energy levels with an external dc magnetic field (for $^2\Sigma$ molecules like YO) one can engineer XXZ-type couplings between the spin-rotational states with magnetically tunable spin coupling constants $J_z$ and $J_\perp$, enabling efficient magnetic control over electric dipolar interactions.