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

Abstract

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 $4\,\mathrm{μg}$ 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.

Figures (4)

• Figure 1: Concept of closed-loop atom-interferometric inertial sensing beyond the conventional half-fringe limitation. (a) Closed-loop architecture of a Raman Mach–Zehnder (MZ) atom-interferometer inertial sensor enabling simultaneous and decoupled feedback control of acceleration and rotation. (b) In closed-loop operation, the interferometric phase is locked at the mid-fringe point, avoiding the intrinsic half-fringe ambiguity and suppressing fringe-decay effects, thereby extending the usable dynamic range. (c) Independent control of acceleration- and rotation-induced phase shifts realized through modulation of the Raman detunings. (d–f) Evolution of open-loop interferometric readout and its unambiguous range. (d) Conventional open-loop readout exhibits an intrinsic half-fringe limitation due to the sinusoidal phase dependence of the interference signal. (e) Quadrature demodulation enables direct phase retrieval and provides a linear response over a full interference period. (f) Phase unwrapping allows operation across multiple interference periods, further extending the open-loop unambiguous range, but remains susceptible to fringe decay caused by velocity dispersion. Shaded regions in (d)–(f) indicate the corresponding unambiguous measurement ranges.
• Figure 2: Phase control demonstration for dual-channel closed-loop operation. (a,b) Interferometric amplitude (a) and extracted phase of the left interferomter (b) versus Raman detuning $f_r$ under varying rotation inputs. (c,d) Corresponding amplitude (c) and phase (d) versus $\delta f$ under different acceleration inputs. Quadrature demodulation provides simultaneous amplitude and linear phase readout.
• Figure 3: Dynamic-range extension under closed-loop operation. (a) Rotation calibration comparing open-loop (phase output) and closed-loop (frequency-encoded output) operation. Lower panel: corresponding normalized fringe contrast. (b) Acceleration calibration (upper) and associated fringe contrast (lower). Inset: comparison of open-loop operation with and without phase unwrapping.
• Figure 4: Long-term stability of the dual-axis inertial sensor. Allan deviation of rotation (a) and acceleration (b) measured over 25,000 s. Dashed lines indicate a $1/\sqrt{\tau}$ dependence, where $\tau$ is the averaging time.