Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2609.28050

Theory of Airy-Beam Wavefront Sensing

Surya Kamal

physics.opticsquant-phSubmitted Sep 23, 2026• Announced Sep 24, 2026
arXivHTMLPDF

Abstract

A new wavefront sensing framework based on the interference of counter-accelerating Airy beams is presented. An engineered cubic phase function transforms a single Gaussian beam into two coherent Airy beams with opposite transverse accelerations, which self-recombine during free-space propagation to form an interference pattern encoding the aberrated incident wavefront. Numerical simulations demonstrate accurate recovery of the aberrated exit-pupil phase across the aberration sets considered, with a root-mean-square phase reconstruction error below $10^{-6} \mathrm{\;rad}$ for the aberration set shown and consistently low errors for the other sets, while maintaining accurate recovery in the presence of measurement noise. The approach eliminates collection optics and enables a compact wavefront-sensing architecture for applications where conventional interferometric systems are difficult to implement, including electron-optical systems, augmented and virtual reality systems.

Comments
6 pages, 5 figures

Related papers

Phase Dynamics of Self-Accelerating Bose-Einstein Condensates

Maximilian L. D. D. Pellner, Georgi Gary Rozenman

Self-accelerating Airy matter waves offer a clean setting to access the intrinsic cubic-in-time phase. Here we reconstruct the relative phase of simulated Airy-shaped Bose-Einstein condensates from interference fringes in free space, a regime approached in microgravity. The cubic phase dynamics are quantified via approximately debiased, windowed polynomial fits with systematics-aware uncertainty estimates that account for window-induced correlations. We compare two physically feasible phase-extraction methods, heterodyne-based and density-based, and show that an Airy-Gaussian geometry yields substantially improved robustness to fit-window selection relative to an Airy-Airy collision. In the weakly interacting regime, the extracted cubic coefficient responds linearly to leading order to the effective interaction strength, its shift from the noninteracting value providing a calibrated probe of weak mean-field nonlinearities in self-accelerating condensates.

cond-mat.quant-gasCross-listedarXiv:2602.01406•Feb 3, 2026•0 citations

Principal Component Analysis for Spatial Phase Reconstruction in Atom Interferometry

Stefan J. Seckmeyer, Holger Ahlers, Jan-Niclas Kirsten-Siemß +4 more

Atom interferometers are sensitive to a wide range of forces by encoding their signals in interference patterns of matter waves. To estimate the magnitude of these forces, the underlying phase shifts they imprint on the atoms must be extracted. Up until now, extraction algorithms typically rely on a fixed model of the patterns' spatial structure, which if inaccurate can lead to systematic errors caused by, for example, wavefront aberrations of the used lasers. In this paper we employ an algorithm based on Principal Component Analysis, which is capable of characterizing the spatial phase structure and per image phase offsets of an atom interferometer from a set of images. The algorithm does so without any prior knowledge about the specific spatial pattern as long as this pattern is the same for all images in the set. On simulated images with atom projection noise we show the algorithm's reconstruction performance follows distinct scaling laws, i.e., it is inversely-proportional to the square-root of the number atoms or the number of images respectively, which allows a projection of its performance for experiments. We also successfully extract the spatial phase patterns of two experimental data sets from an atom gravimeter. This algorithm is a first step towards a better understanding and complex spatial phase patterns, e.g., caused by inhomogeneous laser fields in atom interferometry.

arXiv:2405.05150•May 8, 2024•1 citation

A general method for evaluation of effective Raman wavefront and phase shift in atom interferometry

Yukun Luo, Jie You, Yingying Li +4 more

Atom interferometry is an advanced optical manipulation tool of atoms in precision measurement field. Wavefront aberrations of the Raman beam have become one of the major obstacles impeding the improvement of measurement accuracy. Beforehand measurement of laser wavefront is impractical due to the further wavefront deterioration during optical mounting. In this work, we present a general method for evaluating the effective Raman wavefront that atoms experience and the corresponding phase shift of interferometric fringes. The method extracts the effective Zernike polynomial terms and reconstructs the wavefront using optimal estimation theory. The evaluation accuracy and convergence speed are discussed by simulation. The results predict the method adaptability and provide strong support on analytical and numerical reference for wavefront error compensation.

Optical Manipulation and Structured Materials Conference (OMC)•Jun 15, 2020•2 citations

Position-correlated biphoton wavefront sensing for quantum adaptive imaging

Yi Zheng, Zhao-Di Liu, Jian‐Shun Tang +3 more

Quantum imaging with spatially entangled photons offers advantages such as enhanced spatial resolution, robustness against noise, and counterintuitive phenomena, while a biphoton spatial aberration generally degrades its performance. Biphoton aberration correction has been achieved by using classical beams to detect the aberration source or scanning the correction phase on biphotons if the source is unreachable. Here, a new method named position-correlated biphoton Shack-Hartmann wavefront sensing is introduced, where the phase pattern added on photon pairs with a strong position correlation is reconstructed from their position centroid distribution at the back focal plane of a microlens array. Experimentally, biphoton phase measurement and adaptive imaging against the disturbance of a plastic film are demonstrated. This single-shot method is a more direct and efficient approach toward quantum adaptive optics, suitable for integration into quantum microscopy, remote imaging, and communication.

arXiv:2504.21573•Light Science & Applications•Sep 8, 2025•8 citations

Recovery of phase constant from two-photon interference pattern by phase retrieval algorithm

Yuhang Lei, Wen Kui Zhao, Liang Cui +1 more

For a HOM interferometer with two independent incident pulses, the interference pattern can be affected by adding a dispersion medium on one of the incident directions, but there hasn't been a method to reconstruct the phase constant of the medium from the interference pattern. To solve it, we adapted two phase retrieval algorithms and used them to recover the phase difference function between the two incident fields, from which the phase constant can be derived. Through simulations, we verified the convergence, accuracy, and robustness of the algorithms, indicating that this phase recovery process can be completed well with negligible error. Our research finds a new application direction for the phase recovery algorithm, provides an algorithmic tool for high-order dispersion measurement using two-photon interference, and paves the way for a higher resolution and phase-sensitive quantum tomography.

arXiv:2310.07988•Oct 12, 2023•0 citations

REFLECTION AND TRANSMISSION OF SELF-ACCELERATING WAVE PACKETS

Glenn Dusing

Airy beams have been studied in an optical context since their discovery in the late 1970s and have found numerous applications in technologies such as microscopy and optical trapping. Many of these applications are based on the wave packets’ unique features such as zero or minimal diffraction, self-acceleration, and self-healing. Recently, Airy beams have been produced using electrons and these matter waves exhibit many of the same unique characteristics of their optical counterparts. We use our Path Integral Quantum Trajectory (PIQTr) model to present a study of the reflection and transmission of matter Airy wave packets. Like the more familiar Gaussian wave packets, Airy beams have a Gaussian momentum distribution. However, despite this similarity, Airy beams show unique features for transmission and reflection.

•Jan 1, 2019•0 citations
A new wavefront sensing framework based on the interference of counter-accelerating Airy beams is presented. An engineered cubic phase function transforms a single Gaussian beam into two coherent Airy beams with opposite transverse accelerations, which self-recombine during free-space propagation to form an interference pattern encoding the aberrated incident wavefront. Numerical simulations demonstrate accurate recovery of the aberrated exit-pupil phase across the aberration sets considered, with a root-mean-square phase reconstruction error below 10−6  rad10^{-6} \mathrm{\;rad}10−6rad for the aberration set shown and consistently low errors for the other sets, while maintaining accurate recovery in the presence of measurement noise. The approach eliminates collection optics and enables a compact wavefront-sensing architecture for applications where conventional interferometric systems are difficult to implement, including electron-optical systems, augmented and virtual reality systems.
Self-accelerating Airy matter waves offer a clean setting to access the intrinsic cubic-in-time phase. Here we reconstruct the relative phase of simulated Airy-shaped Bose-Einstein condensates from interference fringes in free space, a regime approached in microgravity. The cubic phase dynamics are quantified via approximately debiased, windowed polynomial fits with systematics-aware uncertainty estimates that account for window-induced correlations. We compare two physically feasible phase-extraction methods, heterodyne-based and density-based, and show that an Airy-Gaussian geometry yields substantially improved robustness to fit-window selection relative to an Airy-Airy collision. In the weakly interacting regime, the extracted cubic coefficient responds linearly to leading order to the effective interaction strength, its shift from the noninteracting value providing a calibrated probe of weak mean-field nonlinearities in self-accelerating condensates.
Atom interferometers are sensitive to a wide range of forces by encoding their signals in interference patterns of matter waves. To estimate the magnitude of these forces, the underlying phase shifts they imprint on the atoms must be extracted. Up until now, extraction algorithms typically rely on a fixed model of the patterns' spatial structure, which if inaccurate can lead to systematic errors caused by, for example, wavefront aberrations of the used lasers. In this paper we employ an algorithm based on Principal Component Analysis, which is capable of characterizing the spatial phase structure and per image phase offsets of an atom interferometer from a set of images. The algorithm does so without any prior knowledge about the specific spatial pattern as long as this pattern is the same for all images in the set. On simulated images with atom projection noise we show the algorithm's reconstruction performance follows distinct scaling laws, i.e., it is inversely-proportional to the square-root of the number atoms or the number of images respectively, which allows a projection of its performance for experiments. We also successfully extract the spatial phase patterns of two experimental data sets from an atom gravimeter. This algorithm is a first step towards a better understanding and complex spatial phase patterns, e.g., caused by inhomogeneous laser fields in atom interferometry.
Atom interferometry is an advanced optical manipulation tool of atoms in precision measurement field. Wavefront aberrations of the Raman beam have become one of the major obstacles impeding the improvement of measurement accuracy. Beforehand measurement of laser wavefront is impractical due to the further wavefront deterioration during optical mounting. In this work, we present a general method for evaluating the effective Raman wavefront that atoms experience and the corresponding phase shift of interferometric fringes. The method extracts the effective Zernike polynomial terms and reconstructs the wavefront using optimal estimation theory. The evaluation accuracy and convergence speed are discussed by simulation. The results predict the method adaptability and provide strong support on analytical and numerical reference for wavefront error compensation.
Quantum imaging with spatially entangled photons offers advantages such as enhanced spatial resolution, robustness against noise, and counterintuitive phenomena, while a biphoton spatial aberration generally degrades its performance. Biphoton aberration correction has been achieved by using classical beams to detect the aberration source or scanning the correction phase on biphotons if the source is unreachable. Here, a new method named position-correlated biphoton Shack-Hartmann wavefront sensing is introduced, where the phase pattern added on photon pairs with a strong position correlation is reconstructed from their position centroid distribution at the back focal plane of a microlens array. Experimentally, biphoton phase measurement and adaptive imaging against the disturbance of a plastic film are demonstrated. This single-shot method is a more direct and efficient approach toward quantum adaptive optics, suitable for integration into quantum microscopy, remote imaging, and communication.
For a HOM interferometer with two independent incident pulses, the interference pattern can be affected by adding a dispersion medium on one of the incident directions, but there hasn't been a method to reconstruct the phase constant of the medium from the interference pattern. To solve it, we adapted two phase retrieval algorithms and used them to recover the phase difference function between the two incident fields, from which the phase constant can be derived. Through simulations, we verified the convergence, accuracy, and robustness of the algorithms, indicating that this phase recovery process can be completed well with negligible error. Our research finds a new application direction for the phase recovery algorithm, provides an algorithmic tool for high-order dispersion measurement using two-photon interference, and paves the way for a higher resolution and phase-sensitive quantum tomography.
Airy beams have been studied in an optical context since their discovery in the late 1970s and have found numerous applications in technologies such as microscopy and optical trapping. Many of these applications are based on the wave packets’ unique features such as zero or minimal diffraction, self-acceleration, and self-healing. Recently, Airy beams have been produced using electrons and these matter waves exhibit many of the same unique characteristics of their optical counterparts. We use our Path Integral Quantum Trajectory (PIQTr) model to present a study of the reflection and transmission of matter Airy wave packets. Like the more familiar Gaussian wave packets, Airy beams have a Gaussian momentum distribution. However, despite this similarity, Airy beams show unique features for transmission and reflection.