Theoretical Proposal of a Digital Closed-Loop Thermal Atomic-Beam Interferometer for High-Bandwidth, Wide-Dynamic-Range, and Simultaneous Absolute Acceleration-Rotation Sensing

TL;DR

The paper addresses the need for high-bandwidth, wide-dynamic-range inertial sensing that simultaneously measures acceleration and rotation with an absolute reference. It introduces a digital closed-loop scheme for a thermal atomic-beam Mach–Zehnder interferometer, inspired by fiber-optic gyroscopes, that synchronizes phase biasing with momentum-kick reversal to extract four interferometer phases and suppress laser-path errors. The authors show how closed-loop two-photon detuning maintains a pseudo-inertial frame and eliminates cross-coupling, enabling real-time, decoupled readout of acceleration and angular velocity. They validate the approach with numerical simulations for $^{85}$Rb at a $170^\circ$C oven, predicting $3\ \mu\mathrm{m}/\mathrm{s}^2/\sqrt{\mathrm{Hz}}$ velocity random walk and $15\ \mu\mathrm{deg}/\sqrt{\mathrm{h}}$ angular random walk for a 100 mm arm, and discuss potential integration into a full quantum inertial-navigation system.

Abstract

We present a theoretical proposal and simulation study of a digital closed-loop thermal atomic-beam interferometer for inertial navigation applications. The scheme synchronizes phase biasing with momentum-kick reversal through the atomic transit time, extracting four interferometric phases to suppress Raman beam path-length errors, while two-photon detuning feedback maintains a pseudo-inertial frame and eliminates cross-coupling. The interferometer enables simultaneous measurements of acceleration and rotation based on an absolute, atom-interferometric reference, with high bandwidth and a wide dynamic range. Numerical simulations verify that acceleration and angular velocity can be measured simultaneously and independently in real time without cross-coupling, demonstrating the absolute, decoupled nature of the proposed measurement scheme. We further evaluate the noise-limited performance of the sensor and obtain sensitivities of $3{\rm μm / s^2 / \sqrt{Hz}}$ (velocity random walk) and $15{\rm μdeg / \sqrt{h}}$ (angular random walk) for a ${170}^{\circ}$ $^{85}$Rb beam and an interferometer arm length of 100~mm, surpassing the performance of sensors currently used in state-of-the-art inertial navigation systems.

Figures (9)

• Figure 1: Atom interferometer with counter-propagating beams: (a) Level diagram of stimulated Raman transitions; (b) interferometer configuration.
• Figure 2: Counter-propagating atomic beam interferometer for digital closed-loop operation. Phase modulation at angular frequency $\omega_{\rm{m}}$ applied to the electro-optic modulator (EOM) produces sidebands at $\omega_0 \pm \omega_{\rm{m}}$ relative to the carrier angular frequency $\omega_0$. Varying $\omega_{\rm{m}}$ induces interferometer area reversal, as illustrated in (a) and (b).
• Figure 3: Timing diagram of the digital closed-loop operation. The atomic transit time at the most probable velocity $v_{\rm mp}$ through the interferometer is used as the unit. The phase $\Phi_{\rm B}$ of EO-B in Fig. \ref{['fig_mirror_scheme']} is alternately biased by $\pm \Delta \Phi/2$, which, through the Raman process induced by Raman beam B, results in a phase shift of $\pm 2 \Delta \Phi$ imparted to the atom interferometer. At twice this period, the RF frequencies driving the three EOMs are alternately shifted to perform $k$-reversal.
• Figure 4: Digital closed loop utilizing the four phase outputs of the interferometer. (a) Timing chart of the two-photon detuning of the Raman light under constant angular velocity and acceleration. (b) Block diagram of the digital closed loop under time-varying acceleration and angular velocity. Here, $\phi_a^{\mathrm{(open)}}$ and $\phi_\Omega^{\mathrm{(open)}}$ denote the values of $\phi_a$ and $\phi_\Omega$ obtained in the open-loop configuration under constant acceleration and angular velocity.
• Figure 5: Simulated interference signal for an oven temperature of $170\,^\circ\mathrm{C}$ and an atomic beam inclination of $\theta = 0.2^\circ$. The horizontal axis denotes the phase of Raman beam A among the three beams forming the interferometer.