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Characterization of spatial Schmidt modes in high-gain SU(1,1) interferometers

D. Scharwald1,2,3,4,* and P. R. Sharapova3

  • 1Heinz Nixdorf Institute, Paderborn University, Fürstenallee 11, 33102 Paderborn, Germany
  • 2Department of Electrical Engineering and Information Technology, Paderborn University, Warburger Straße 100, 33098 Paderborn, Germany
  • 3Department of Physics, Paderborn University, Warburger Straße 100, 33098 Paderborn, Germany
  • 4Institute for Photonic Quantum Systems (PhoQS), Paderborn University, Warburger Straße 100, 33098 Paderborn, Germany

  • *Contact author: dennis.scharwald@uni-paderborn.de
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Phys. Rev. Research 8, 033139 – Published 4 August, 2026

DOI: https://doi.org/10.1103/ph64-ts39

Abstract

Multimode quantum light has promising applications in many areas of physics, such as quantum communications and quantum computing. However, its multimode nature also makes it challenging to measure its properties. Recently [I. Barakat et al., Optica Quantum 3, 36 (2025)], a technique for the simultaneous measurement of squeezing of multiple broadband modes based on a phase-sensitive amplification approach was experimentally implemented using a setup that effectively corresponds to an SU(1,1) interferometer. Here, we aim to provide a complete theoretical analysis of the modal structure of (generally unbalanced) SU(1,1) interferometers and a detailed theoretical formal derivation of the framework for this technique. Utilizing the joint Schmidt decomposition of the transfer functions, we investigate the shape and phase profiles of the modes of the SU(1,1) interferometer and its components [parametric down-conversion (PDC) sections] for different parametric gain regimes. We discover a complicated interplay between the PDC modes and the modes of the entire interferometer, and analyze it by using their overlap coefficients as a similarity measure. Finally, we develop a rigorous processing method for the aforementioned multimode squeezing measurement technique and discuss necessary approximations to make this method experimentally feasible.

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Phys. Rev. Research 8, 033139– Published 4 August, 2026
  • Received 3 July 2025
  • Accepted 22 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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