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AVS Quantum Science

Method for phase extraction from atom interference fringes via orthogonal subspace projection

Jiaqi Lei, Junjie Jiang, Sitong Yan, Zhuo Hou, Chuan He, Rundong Xu, Lin Zhou, Jin Wang, Прудников Олег Николаевич, Valeriy I. Yudin, Mingsheng Zhan

Published Feb 26, 2026• 0 citations
Publisher

Abstract

We propose a method for extracting the phase from atom interference fringes based on orthogonal subspace projection. By projecting the shear interference fringes from an atom interferometer into an orthogonal subspace, this method characterizes and removes the atomic ensemble envelope, thereby isolating the interference phase information. We systematically investigate the phase extraction accuracy of this method under various conditions, including different atomic ensemble envelope shapes and fringe contrasts, and apply it to analyze experimental data from two practical atom interferometers. The study demonstrates that, compared to the conventional direct model fitting method, our approach more accurately extracts the interference phase under conditions involving nonideal and dynamically varying atomic ensemble envelopes as well as low-contrast fringes, thereby improving the accuracy and robustness of the atom interferometer. This makes it particularly valuable for application-oriented atom shear interferometers operating in complex environments.

DOI
10.1116/5.0312264

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We propose a method for extracting the phase from atom interference fringes based on orthogonal subspace projection. By projecting the shear interference fringes from an atom interferometer into an orthogonal subspace, this method characterizes and removes the atomic ensemble envelope, thereby isolating the interference phase information. We systematically investigate the phase extraction accuracy of this method under various conditions, including different atomic ensemble envelope shapes and fringe contrasts, and apply it to analyze experimental data from two practical atom interferometers. The study demonstrates that, compared to the conventional direct model fitting method, our approach more accurately extracts the interference phase under conditions involving nonideal and dynamically varying atomic ensemble envelopes as well as low-contrast fringes, thereby improving the accuracy and robustness of the atom interferometer. This makes it particularly valuable for application-oriented atom shear interferometers operating in complex environments.
Atom interferometry-based sensors have demonstrated remarkable precision, making them attractive for diverse applications compared to traditional sensors. However, practical experiments inevitably encounter noise, which limits precision. We investigate the performance of two commonly used methods, ellipse fitting (EF) and fringe fitting (FF), for differential phase estimation in a dual atom interferometer under various noise conditions. We comprehensively analyze the efficacy of these methods for each type of Gaussian noise, including phase noise, amplitude noise, and offset noise. Using a colored noise model, we investigate the Allan deviation results. Our investigations will offer valuable insights for future quantum sensing based on dual interferometers.
When the initial size of an atom cloud in a cold atom interferometer is negligible compared to its size after free expansion, the interferometer is approximated to a point-source interferometer and is sensitive to rotational movements by introducing an additional phase shear in the interference sequence. This sensitivity on rotation enables a vertical atom-fountain interferometer to measure angular velocity in addition to gravitational acceleration, which it is conventionally used to measure. The accuracy and precision of the angular velocity measurement depends on proper extraction of frequency and phase from spatial interference patterns detected via the imaging of the atom cloud, which is usually affected by various systematic biases and noise. To improve the measurement, a pre-fitting process based on principal component analysis is applied to the recorded raw images. The contrast of interference patterns are enhanced by 7-12 dB when the processing is present, which leads to an enhancement in the precision of angular velocity measurements from 6.3 μrad/s to 3.3 μrad/s. This technique is applicable in various instruments that involve precise extraction of frequency and phase from a spatial interference pattern.
Generally, the phase of the cold-atom interferometer is extracted from the atomic interference fringe, which can be obtained by scanning the chirp rate of the Raman lasers at a given interrogation time T. If mapping the phase shift for each T with a series of measurements, the extraction time is limited by the protocol of each T measurement, and therefore increases dramatically when doing fine mapping with a small step of T. Here we present a new method for rapid extraction of the phase shift via phase demodulation. By using this method, the systematic shifts can be mapped though the whole interference area. This method enables quick diagnostics of the potential cause of the phase shift in specific time. We demonstrate experimentally that this method is effective for the evaluation of the systematic errors of the cold atomic gravimeter. The systematic phase error induced by the quadratic Zeeman effect in the free-falling region is extracted by this method. The measured results correspond well with the theoretic prediction and also agree with the results obtained by the fringe fitting method for each T.更多还原
Generally, the phase of the cold-atom interferometer is extracted from the atomic interference fringe, which can be obtained by scanning the chirp rate of the Raman lasers at a given interrogation time T . If mapping the phase shift for each T with a series of measurements, the extraction time is limited by the protocol of each T measurement, and therefore increases dramatically when doing fine mapping with a small step of T . Here we present a new method for rapid extraction of the phase shift via phase demodulation. By using this method, the systematic shifts can be mapped though the whole interference area. This method enables quick diagnostics of the potential cause of the phase shift in specific time. We demonstrate experimentally that this method is effective for the evaluation of the systematic errors of the cold atomic gravimeter. The systematic phase error induced by the quadratic Zeeman effect in the free-falling region is extracted by this method. The measured results correspond well with the theoretic prediction and also agree with the results obtained by the fringe fitting method for each T .
Point source atom interferometry (PSI) uses the velocity distribution in a cold atom cloud to simultaneously measure one axis of acceleration and two axes of rotation from the spatial distribution of interferometer phase in an expanded cloud of atoms. Previously, the interferometer phase has been found from the phase, orientation, and period of the resulting spatial atomic interference fringe images. For practical applications in inertial sensing and precision measurement, it is important to be able to measure a wide range of system rotation rates, corresponding to interferograms with far less than one full interference fringe to very many fringes. Interferogram analysis techniques based on image processing used previously for PSI are challenging to implement for low rotation rates that generate less than one full interference fringe across the cloud. We introduce a new experimental method that is closely related to optical phase-shifting interferometry that is effective in extracting rotation values from signals consisting of fractional fringes as well as many fringes without prior knowledge of the rotation rate. The method finds the interferometer phase for each pixel in the image from four interferograms, each with a controlled Raman laser phase shift, to reconstruct the underlying atomic interferometer phase map without image processing.