Closed-loop dual-channel atomic beam interferometry beyond the half-fringe limit

Atom interferometric inertial sensors offer exceptional sensitivity but are fundamentally constrained by the periodic phase response of matter-wave interference, which imposes an intrinsic half-fringe dynamic-range limit and prevents continuous inertial tracking. In multi-axis configurations, additional cross coupling between acceleration and rotation further complicates closed-loop operation. Here we demonstrate the first dual-channel closed-loop operation of an atomic beam interferometer, realizing decoupled feedback control of acceleration- and rotation-induced phases and overcoming the half-fringe limitation. Using continuous, transversely cooled $^{87}$Rb atomic beams, the interferometric phases associated with rotation and acceleration are independently extracted, tracked across multiple fringes, and actively compensated through Raman frequency modulation. This closed-loop scheme enables unambiguous measurements up to $\pm1\,\mathrm{^{\circ}/s}$ in rotation and $\pm0.17\,\mathrm{g}$ in acceleration while maintaining high fringe contrast, corresponding to nearly two orders-of-magnitude extension beyond the conventional half-fringe limit. The sensor achieves a long-term stability of $4\times10^{-4}\,\mathrm{^{\circ}/h}$ for rotation and $4\,\mathrm{\mu g}$ for acceleration at an averaging time of $1000\,\mathrm{s}$. By converting the intrinsically periodic interferometric response into stabilized phase-encoded inertial channels, this work establishes a new operating regime for atomic beam interferometry and advances matter-wave sensors toward practical quantum inertial navigation under dynamic conditions.