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Molecules have vibrational, rotational, spin-orbit and hyperfine degrees offreedom or quantum states, each of which responds in a unique fashion toexternal electromagnetic radiation. The control over superpositions of thesequantum states is key to coherent manipulation of molecules. For example, thebetter the coherence time the longer quantum simulations can last. Theimportant quantity for controlling an ultracold molecule with laser light isits complex-valued molecular dynamic polarizability. Its real part determinesthe tweezer or trapping potential as felt by the molecule, while its imaginarypart limits the coherence time. Here, our study shows that efficient trappingof a molecule in its vibrational ground state can be achieved by selecting alaser frequency with a detuning on the order of tens of GHz relative to anelectric-dipole-forbidden molecular transition. Close proximity to this nearlyforbidden transition allows to create a sufficiently deep trapping potentialfor multiple rotational states without sacrificing coherence times among thesestates from Raman and Rayleigh scattering. In fact, we demonstrate that magictrapping conditions for multiple rotational states of the ultracold$^{23}$Na$^{87}$Rb polar molecule can be created.

Rotational magic conditions for ultracold molecules in the presence of Raman and Rayleigh scattering