Fault-tolerant hyper-Ramsey spectroscopy of ultra-narrow clock transitions with dynamical decoupling

Abstract

A probe laser field that interrogates an atomic transition also shifts it. Although Hyper-Ramsey (HR) spectroscopy was developed to mitigate these light-induced frequency shifts, the technique remains sensitive to probe intensity fluctuations. In this work, we introduce a novel class of dynamically decoupled hyper-Ramsey (DDHR) sequences that utilize a modified refocusing pulse to effectively eliminate this residual sensitivity. This three-pulse interferometric protocol significantly enhances the contrast of quantum interference fringes while providing robust immunity against probe-induced frequency shifts, even in the presence of external field inhomogeneities. We experimentally validate both HR and DDHR protocols on the NQCH and \textcolor{blue}{IQM} superconducting quantum processor, demonstrating an error scaling that is rigorously consistent with theoretical simulations of the optical clock regime. DDHR spectroscopy yields superior suppression of residual probe-induced frequency shifts compared to the standard HR scheme under probe amplitude fluctuation and decoherence. Furthermore, we demonstrate that the implementation of composite refocusing pulses, derived from a Pascal binomial tree architecture, gives substantial resilience against technical pulse area imperfections. Ultimately, fault-tolerant, dynamically decoupled hyper-clocks will offer a promising experimental platform for the evaluation of advanced, NMR-inspired DDHR sequences of multiple refocusing pulses holding significant potential for high-precision matter/antimatter quantum sensing and rigorous tests of fundamental physics within harsh electromagnetic environments.