Pendular trapping conditions for ultracold polar molecules enforced by external electric fields

We theoretically investigate trapping conditions for ultracold polar molecules in optical lattices, when external magnetic and electric fields are simultaneously applied. Our results are based on an accurate electronic-structure calculation of the polar ${}^{23}$Na${}^{40}$K polar molecule in its absolute ground state combined with a calculation of its rovibrational-hyperfine motion. We find that an electric field strength of $5.26(15)$ kV/cm and an angle of ${54.7}^{\circ }$ between this field and the polarization of the optical laser lead to a trapping design for ${}^{23}$Na${}^{40}$K molecules where decoherences due laser-intensity fluctuations and fluctuations in the direction of its polarization are kept to a minimum. One standard deviation systematic and statistical uncertainties are given in parenthesis. Under such conditions pairs of hyperfine-rotational states of $v=0$ molecules, used to induce tunable dipole-dipole interactions between them, experience ultrastable, matching trapping forces.