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