Noncyclic geometric phase in three-level Ramsey interferometry for enhanced metrology

Abstract

In a standard two-level Ramsey interferometer, the accumulated signal phase is linearly mapped to the readout phase. Here, we introduce three-level Ramsey interferometry, in which projected interference between internal paths reshapes this mapping through a noncyclic geometric phase response. Near a geodesic-closure transition, a small accumulated signal phase produces a sharply amplified readout-phase shift. We quantify the accompanying gain--visibility tradeoff and identify a finite operating window in which the amplified response can yield a net signal-to-noise-ratio gain in the presence of additional technical phase noise. A controllable Ramsey phase offset further positions this high-slope response at a chosen operating point, making the local enhancement accessible without requiring a large signal-induced phase. More broadly, these results establish a multilevel Ramsey route to enhanced phase sensitivity in quantum platforms, in which two signal-collecting internal paths interfere to produce a controllable noncyclic geometric response.