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Sensors

Enhanced Readout from Spatial Interference Fringes in a Point-Source Cold Atom Inertial Sensor

Jing Wang, Junze Tong, Wenbin Xie, Ziqian Wang, Yafei Feng, Xiaolong Wang

Published May 25, 2023• 3 citations
Publisher

Abstract

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.

DOI
10.3390/s23115071

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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.
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.
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.
Light pulse atom interferometry can be used to realize high-performance sensors of accelerations and rotations. In order to broaden the range of applications of these sensors, it is desirable to reduce their size and complexity. Point source interferometry (PSI) is a promising technique for accomplishing both of these goals. With PSI, rotations are measured by detecting the orientation and frequency of spatial fringe patterns in the atomic state. These spatial fringes are primarily due to a correlation between an atom's initial velocity and its final position, which is created by the expansion of a cold atom cloud. However, the fringe patterns are also influenced by the structure of the initial atomic distribution. We summarize several methods that can be used to investigate the relationship between the spatial fringe pattern and the initial atomic distribution. This relationship will need to be understood in detail to realize an accurate gyroscope based on PSI.
Ultra-cold atoms provide ideal platforms for interferometry. The macroscopic matter-wave property of ultra-cold atoms leads to large coherent length and long coherent time, which enable high accuracy and sensitivity to measurement. Here, we review our efforts to improve the performance of the interferometer. We demonstrate a shortcut method for manipulating ultra-cold atoms in an optical lattice. Compared with traditional ones, this shortcut method can reduce the manipulation time by up to three orders of magnitude. We construct a matter-wave Ramsey interferometer for trapped motional quantum states and significantly increase its coherence time by one order of magnitude with an echo technique based on this method. Efforts have also been made to enhance the resolution by multimode scheme. Application of a noise-resilient multi-component interferometer shows that increasing the number of paths could sharpen the peaks in the time-domain interference fringes, which leads to a resolution nearly twice compared with that of a conventional double-path two-mode interferometer. With the shortcut method mentioned above, improvement of the momentum resolution could also be fulfilled, which leads to atomic momentum patterns less than 0.6 ℏkL . To identify and remove systematic noises, we introduce the methods based on the principal component analysis (PCA) that reduce the noise in detection close to the 1 / 2 of the photon-shot noise and separate and identify or even eliminate noises. Furthermore, we give a proposal to measure precisely the local gravity acceleration within a few centimeters based on our study of ultracold atoms in precision measurements.
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.