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

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.

💡 Research Summary

The paper proposes and numerically validates a digital closed‑loop thermal atomic‑beam interferometer designed for inertial navigation. Traditional cold‑atom interferometers offer high precision but suffer from limited bandwidth (a few hertz) due to long interrogation times. Thermal atomic beams, with much higher longitudinal velocities, can provide bandwidths of several hundred hertz, yet they introduce two major challenges: (1) the need for three spatially separated Raman beam pairs makes the interferometer sensitive to arbitrary phase differences between the beams, and (2) the broad velocity distribution limits dynamic range and prevents absolute acceleration measurement.

To overcome these issues, the authors adapt the digital closed‑loop concept from fiber‑optic gyroscopes. The key idea is to synchronize a digital phase bias with the mean atomic transit time through the interferometer. An electro‑optic modulator (EOM) applies alternating phase shifts of ±ΔΦ/2 to Raman beam B, producing two fluorescence intensity measurements (I_up and I_down). From these, the interferometer phase ϕ is directly extracted without lock‑in detection. By feeding back the two‑photon detuning δ, the system maintains ϕ≈0, thereby keeping the sensor in a pseudo‑inertial frame.

In addition, a momentum‑k reversal (k‑reversal) is performed every two transit‑time cycles by shifting the RF frequencies driving the three EOMs by ±ω_D, where ω_D is the Doppler shift for the most probable atomic velocity. This generates four interferometer phases: ϕ_R, ϕ_L, ϕ_R(kr), and ϕ_L(kr). Combining these phases cancels the arbitrary laser‑path‑length terms (Δl_A, Δl_B, Δl_C) and mirror motion (ΔL), suppressing path‑length noise by roughly five orders of magnitude. Consequently, the remaining phase contains only the inertial contributions from acceleration a and rotation Ω.

The closed‑loop feedback maps the acceleration and rotation onto the detuning corrections δ_a and δ_Ω, which are read out as independent signals, eliminating cross‑coupling. Numerical simulations using a 170 °C ^85Rb beam, a 100 mm interferometer arm, an atomic flux of 10⁸ atoms s⁻¹, 200 mW Raman power, and 50 % detection efficiency predict noise‑limited sensitivities of 3 µm s⁻² Hz⁻¹ᐟ² (velocity random walk) and 15 µdeg h⁻¹ᐟ² (angular random walk). These figures surpass the performance of state‑of‑the‑art inertial measurement units used in modern navigation systems.

The authors also demonstrate that the digital closed‑loop architecture yields a bandwidth exceeding 500 Hz and a dynamic range on the order of 10⁴ g·deg s⁻¹, fulfilling the stringent requirements of GPS‑denied navigation (underwater, underground, or aerospace). By providing an absolute, self‑calibrated reference based on atomic transition frequencies, the sensor reduces long‑term drift and scale‑factor errors inherent to conventional mechanical or optical gyroscopes.

Overall, the work establishes a viable pathway toward compact, high‑performance, dual‑axis inertial sensors that combine the intrinsic accuracy of atom interferometry with the speed and robustness required for real‑time navigation. Potential applications extend beyond navigation to precision gravimetry, geodesy, and fundamental physics experiments such as tests of general relativity and searches for dark‑sector forces.