  We determine trapping conditions for ultracold polar molecules, where pairs
of internal states experience identical trapping potentials. Such conditions
could ensure that detrimental effects of inevitable inhomogeneities across an
ultracold sample are significantly reduced. In particular, we investigate the
internal rovibronic and hyperfine quantum states of ultracold fermionic
ground-state $^{40}$K$^{87}$Rb polar molecules, when static magnetic, static
electric, and trapping laser fields are simultaneously applied. Understanding
the effect of changing the relative orientation or polarization of these three
fields is of crucial importance for creation of decoherence-free subspaces
built from two or more rovibronic states. Moreover, we evaluate the induced
dipole moment of the molecule in the presence of these fields, which will allow
control of interactions between molecules in different sites of an optical
lattice and study the influence of the interaction anisotropy on the ability to
entangle polar molecules.
