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By leveraging the hyperfine interaction between the rotational and nuclearspin degrees of freedom, we demonstrate extensive magnetic control over theelectric dipole moments, electric dipolar interactions, and ac Stark shifts ofground-state alkali-dimer molecules such as KRb$(X^1\Sigma)$. The control isenabled by narrow avoided crossings and the highly ergodic character ofmolecular eigenstates at low magnetic fields, offering a general and robust wayof continuously tuning the intermolecular electric dipolar interaction forapplications in quantum simulation and sensing.

Magnetically tunable electric dipolar interactions of ultracold polar molecules in the quantum ergodic regime