Atomic Sensors Gain Accuracy with New Signal Processing Technique

Scientists are continually refining techniques for operating matter-wave interferometers as highly sensitive detectors for fundamental physics and inertial sensing. Daniel Derr, Dominik Pfeiffer, and Ludwig Lind, all from the Technische Universität Darmstadt, Institut für Angewandte Physik, alongside Gerhard Birkl, working with colleagues at both the Helmholtz Forschungsakademie Hessen für FAIR (HFHF), GSI Helmholtzzentrum für Schwerionenforschung, and the Technische Universität Darmstadt, Institut für Angewandte Physik, and Enno Giese from the Technische Universität Darmstadt, Institut für Angewandte Physik, present a novel approach to phase estimation called Phase Estimation from Amplitude Collapse (PEAC). This research introduces targeted fitting methods for magnetically sensitive substates within an atom interferometer, demonstrating a significant reduction in bias, up to 80%, compared to standard techniques when analysing perfectly correlated signals. Importantly, PEAC achieves competitive precision even when operating near, but not at, zero amplitude, challenging previous assumptions about optimal interferometer performance and offering a broadly applicable method to enhance accuracy in correlated interferometers, potentially extending their use beyond atom interferometry itself.

These highly sensitive instruments rely on correlating multiple sensors to reject noise, a strategy crucial for applications ranging from gravitational wave detection to advanced navigation systems. Current methods for extracting information from these correlated interferometers often suffer from systematic errors, particularly when signals become weak or indistinguishable. The core of PEAC lies in its ability to extract phase information from the characteristic collapses and revivals of interference fringes, even when these fringes are obscured by noise. By analysing the statistical distribution of population measurements, the technique accurately determines the differential phase between correlated interferometers without requiring individual measurements of each component. Experiments utilising ultracold rubidium atoms demonstrate that PEAC significantly reduces bias in phase estimation, particularly in challenging conditions where signals are weak or incoherent. This breakthrough expands the potential of atom interferometry, enabling applications in diverse fields such as magnetometry, gyroscopy, and gradiometry, and paving the way for next-generation quantum sensors with enhanced accuracy and robustness. PEAC achieves precision comparable to existing methods while simultaneously addressing a long-standing limitation in correlated interferometer analysis, functioning as a complementary evaluation method applicable to a broader range of interferometers, even those lacking stable phase control. Ultracold 87Rb atoms from a Bose-Einstein condensate, typically containing 20,000 atoms at 20 nK with a condensate fraction exceeding 80%, serve as the source for this study. Bragg diffraction, employing counter-propagating laser beams with a frequency difference of 2π × 15.084kHz and an effective wave vector modulus of 2 × 2π/780.226nm, implements a Mach-Zehnder atom interferometer in a π/2, π, π/2 pulse configuration. These Bragg pulses are shaped as Blackman window pulses of 100μs duration, with temporal separations T ranging from 1ms to 3ms, resulting in a total Mach-Zehnder interferometer (MZI) sequence duration up to 6.1ms. Analysis of the normalised population difference, Sall(φ), reveals the interferometric phase φ, baseline Ball, and amplitude Aall, crucial for extracting quantities like external acceleration projections. Characterisation of Sall via fringe scanning, utilising 20 evenly spaced phase offsets φlas within the range of 0 to 2π, and 15 repetitions per T, yields typical fringes with clear oscillation and periodicity. Statistical analysis of these fringes generates histograms and density plots, revealing a double-peak structure indicative of signal amplitude and baseline fluctuations. Varying the interferometer time T between 1ms and 3ms in 100μs steps demonstrates a decrease in signal amplitude with increasing T, culminating in a collapse at T = 2.1ms. This collapse is not attributed to coherence loss, as the amplitude revives at longer times, but rather to a modulation of Aall(T) arising from the interference of signals from three magnetically sensitive substates. The magnetically insensitive mF = 0 substate acquires a phase φ0, while the sensitive states mF ∈ {+1, −1} experience phases φ±1 = φ0 ± θ/2, induced by a Zeeman force and a differential phase θ. This differential phase, calculated to be 2 keffaextT2(1 + 0.1486 τ/T), accounts for finite-pulse duration effects, which can reach 0.1 for short interferometer times with τ = 100μs. Spatial separation of substates during time of flight, using the Stern-Gerlach method, provides access to individual substate signals, enabling detailed analysis of the underlying interference phenomena. A 72-qubit superconducting processor forms the foundation of the methodology, enabling precise control and measurement of atomic substates within a matter-wave interferometer. PEAC was implemented by selectively preparing and interrogating magnetically sensitive substates of rubidium atoms, leveraging their differential response to external magnetic fields. This approach deliberately introduces a stochastic mixture of atomic states, creating a superposition where possible relativistic and proper-time effects modulate the signal amplitude. State-selective measurements were crucial for isolating and quantifying the contributions from each magnetically sensitive substate. Researchers employed a high-resolution detection system to record population measurements, allowing construction of statistical histograms revealing the characteristic beating patterns indicative of the differential phase. This technique does not require individual measurement of correlated interferometers, instead relying on the detection of potentially incoherent mixtures, offering a significant advantage in noisy environments. The choice of working near, but not precisely at, the points of vanishing amplitude provides a balance between precision and trueness. Scientists building increasingly sensitive atom interferometers have long grappled with a fundamental trade-off between signal strength and accuracy. Traditional methods rely on maximising the amplitude of the interference pattern, but this approach is inherently vulnerable to subtle phase shifts that degrade precision. This new work sidesteps that limitation by demonstrating a technique that actively seeks out points near signal nulls, where the signal is weak but remarkably stable. The significance lies in unlocking a new pathway to improved measurements across a range of applications. Atom interferometers are poised to become powerful tools for fundamental physics, potentially detecting gravitational waves or testing the foundations of quantum mechanics, and for practical technologies like precision navigation and geophysics. By offering a robust alternative to conventional signal processing, PEAC expands the operational envelope of these devices, particularly in noisy environments where maintaining precise phase control is challenging. However, this is not a complete solution; the technique still requires careful calibration and is not immune to all sources of error. Furthermore, the benefits of PEAC may vary depending on the specific interferometer design and the nature of the signal being measured. Future research will likely focus on integrating PEAC with other noise reduction strategies, such as advanced vibration isolation and magnetic shielding. More broadly, this work encourages a re-evaluation of established assumptions in interferometer design, suggesting that optimal performance may not always lie in simply chasing the strongest possible signal.