Engineering field-insensitive molecular clock transitions for symmetry violation searches

Molecules are a powerful platform to probe fundamental symmetry violations beyond the Standard Model, as they offer both large amplification factors and robustness against systematic errors. As experimental sensitivities improve, it is important to develop new methods to suppress sensitivity to external electromagnetic fields, as limits on the ability to control these fields are a major experimental concern. Here we show that sensitivity to both external magnetic and electric fields can be simultaneously suppressed using engineered radio frequency, microwave, or two-photon transitions that maintain large amplification of CP-violating effects. By performing a clock measurement on these transitions, CP-violating observables including the electron electric dipole moment, nuclear Schiff moment, and magnetic quadrupole moment can be measured with suppression of external field sensitivity of $\gtrsim$100 generically, and even more in many cases. Furthermore, the method is compatible with traditional Ramsey measurements, offers internal co-magnetometry, and is useful for systems with large angular momentum commonly present in molecular searches for nuclear CP-violation.