Geometric Phase-Induced Stückelberg Interference in an Optical Lattice Clock.

We theoretically investigate geometric Stückelberg interferometry in a doubly driven optical lattice clock (OLC). By tuning the relative phase between the two driving fields, we control the relative sign of the effective coupling strengths at the avoided crossings. Within the adiabatic-impulse model, we analyze the time evolution of the two-level system, where nonadiabatic transitions occur only near the crossing points and adiabatic evolution takes place between them. We show that, besides the usual dynamical phase and the Stokes phase, a gauge-invariant noncyclic geometric phase contributes to the final transition probability. This geometric contribution yields a stable π-phase shift in the Stückelberg interference fringes. Moreover, we demonstrate that, under realistic experimental conditions, this geometric Stückelberg interferometer remains insensitive to inhomogeneities in atom-light coupling arising from the finite temperature of the atomic ensemble. Our results provide a general framework for engineering and detecting geometric phases on the OLC platform.