---
_id: '66665'
abstract:
- lang: eng
  text: 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.
article_number: '033139'
article_type: original
author:
- first_name: Dennis
  full_name: Scharwald, Dennis
  id: '55907'
  last_name: Scharwald
  orcid: 0009-0007-5654-5412
- first_name: Polina
  full_name: Sharapova, Polina
  id: '60286'
  last_name: Sharapova
citation:
  ama: Scharwald D, Sharapova P. Characterization of spatial Schmidt modes in high-gain
    SU(1,1) interferometers. <i>Physical Review Research</i>. 2026;8(3). doi:<a href="https://doi.org/10.1103/ph64-ts39">10.1103/ph64-ts39</a>
  apa: Scharwald, D., &#38; Sharapova, P. (2026). Characterization of spatial Schmidt
    modes in high-gain SU(1,1) interferometers. <i>Physical Review Research</i>, <i>8</i>(3),
    Article 033139. <a href="https://doi.org/10.1103/ph64-ts39">https://doi.org/10.1103/ph64-ts39</a>
  bibtex: '@article{Scharwald_Sharapova_2026, title={Characterization of spatial Schmidt
    modes in high-gain SU(1,1) interferometers}, volume={8}, DOI={<a href="https://doi.org/10.1103/ph64-ts39">10.1103/ph64-ts39</a>},
    number={3033139}, journal={Physical Review Research}, publisher={American Physical
    Society (APS)}, author={Scharwald, Dennis and Sharapova, Polina}, year={2026}
    }'
  chicago: Scharwald, Dennis, and Polina Sharapova. “Characterization of Spatial Schmidt
    Modes in High-Gain SU(1,1) Interferometers.” <i>Physical Review Research</i> 8,
    no. 3 (2026). <a href="https://doi.org/10.1103/ph64-ts39">https://doi.org/10.1103/ph64-ts39</a>.
  ieee: 'D. Scharwald and P. Sharapova, “Characterization of spatial Schmidt modes
    in high-gain SU(1,1) interferometers,” <i>Physical Review Research</i>, vol. 8,
    no. 3, Art. no. 033139, 2026, doi: <a href="https://doi.org/10.1103/ph64-ts39">10.1103/ph64-ts39</a>.'
  mla: Scharwald, Dennis, and Polina Sharapova. “Characterization of Spatial Schmidt
    Modes in High-Gain SU(1,1) Interferometers.” <i>Physical Review Research</i>,
    vol. 8, no. 3, 033139, American Physical Society (APS), 2026, doi:<a href="https://doi.org/10.1103/ph64-ts39">10.1103/ph64-ts39</a>.
  short: D. Scharwald, P. Sharapova, Physical Review Research 8 (2026).
date_created: 2026-08-05T11:51:21Z
date_updated: 2026-08-05T15:06:31Z
department:
- _id: '975'
- _id: '15'
- _id: '623'
- _id: '569'
- _id: '170'
- _id: '35'
- _id: '429'
- _id: '27'
- _id: '34'
- _id: '502'
doi: 10.1103/ph64-ts39
intvolume: '         8'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://journals.aps.org/prresearch/pdf/10.1103/ph64-ts39
oa: '1'
publication: Physical Review Research
publication_identifier:
  issn:
  - 2643-1564
publication_status: published
publisher: American Physical Society (APS)
status: public
title: Characterization of spatial Schmidt modes in high-gain SU(1,1) interferometers
type: journal_article
user_id: '55907'
volume: 8
year: '2026'
...