Geometric phase amplification in a clock interferometer for enhanced metrology

High-precision measurements are crucial for testing the fundamental laws of nature and advancing the technological frontier. Clock interferometry, where particles with an internal clock are coherently split and recombined along two spatial paths, has sparked interest due to its fundamental implications, especially at the intersection of quantum mechanics and general relativity. Here, we demonstrate that a clock interferometer provides metrological improvement compared to its technical noise-limited counterpart using a single internal quantum state. This enhancement around a critical working point can be interpreted as a geometric phase-induced signal-to-noise ratio gain. In our experimental setup, we infer a sensitivity enhancement of 8.8 decibels when measuring a small difference between external fields. We estimate that tens of decibels of sensitivity enhancement could be attained for measurements with a higher atom flux. This opens the door to developing a superior probe for fundamental physics and a high-performance sensor for various technological applications.