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(Dated: January 13, 2015)The OH molecule in its ground state presents a versatile platform for precision measurementand quantum information processing. These applications depend vitally on the accurate measure-ment of transition energies between the OH levels. Signicant sources of systematic errors in thesemeasurements are shifts based on the geometric phase arising from the magnetic and electric eldsused for manipulating OH. In this article, we present these geometric phases for elds that varyharmonically in time, as in the Ramsey technique. Our calculation of the phases is exact withinthe description provided by our recent analytic solution of an eective Stark-Zeeman Hamiltonianfor the OH ground state. This Hamiltonian has earlier been shown to model experimental dataaccurately. We nd that the OH geometric phases exhibit rich structure as a function of the eldrotation rate. Remarkably, we nd rotation rates where the geometric phase accumulated by aspecic state is zero, or where the relative geometric phase between two states vanishes. We expectthese ndings to be of importance to precision experiments on OH involving time-varying elds.More specically, our analysis quantitatively characterizes an important item in the error budgetfor precision spectroscopy of ground state OH.

Coherent cancellation of geometric phase for the OH molecule in external fields