---
_id: '63826'
abstract:
- lang: ger
text: In dieser Dissertation werden Aspekte von high-gain multimode SU(1,1) Interferometer
theoretisch untersucht. Dabei wird der Prozess der parametrischen Fluoreszenz
(PDC) mithilfe von Integro-Differentialgleichungen modelliert, welche die räumliche
Entwicklung der Ebene-Wellen-Operatoren beschreiben. Es wurde gezeigt, dass Supersensitivität
für die Phasenempfindlichkeit dieser Interferometer erreicht werden kann, sofern
die Beugung der PDC Strahlung kompensiert wird. Weiterhin führt eine Erhöhung
der parametrische Verstärkung und eine Reduktion der Schmidt-Zahl zu einer Verbesserung
der Phasenempfindlichkeit und einer Verkleinerung des Phasenbereiches, über den
die Supersensitivität erreicht werden kann. Basierend auf der Struktur der Schmidt-Moden
von SU(1,1) Interferometern wurde ein numerisches Aufbereitungsverfahren konstruiert,
welches die Messung der Stärke des Squeezing und Anti-Squeezing des Zustandes
ermöglicht, der durch den ersten Kristall des Interferometers erzeugt wird. Das
Verfahren wurde experimentell von Kooperationspartnern angewandt, wobei eine gute
Übereinstimmung mit der Theorie festgestellt wurde. Zuletzt wurden SU(1,1) Interferometer
mit Laguerre-Gauß-Moden als Pump-Strahlung für die Messung von Winkelverschiebungen
untersucht. Es zeigte sich, dass sich die quantenmechanisch bedingte Messunsicherheit
verbessert, wenn die parametrische Verstärkung oder die Indizes der Pump-Mode
erhöht werden. Das generelle Verhalten gleicht dem der Phasensensitivität.
- lang: eng
text: In this thesis, several aspects of high-gain multimode SU(1,1) interferometers
are theoretically investigated, with the focus being on metrological applications.
The parametric down-conversion (PDC) process utilized in these interferometers
is theoretically described via integro-differential equations describing spatial
evolution of the plane-wave operators. It is shown that for the phase sensitivity
of these interferometers, supersensitivity can be reached provided that proper
diffraction compensation is applied. The phase sensitivity improves if the gain
is increased or if the number of effective modes is decreased. This comes at the
cost of the phase-region width over which supersensitivity can be reached. Based
on the Schmidt mode structure of SU(1,1) interferometers, a processing method
is constructed which allows for the experimental retrieval of the levels of squeezing
and anti-squeezing of the multimode state generated by the first PDC section of
an SU(1,1) interferometer. It is then applied experimentally by collaborators
and is found to be in good agreement with the theoretical predictions. Finally,
SU(1,1) interferometers pumped with Laguerre-Gaussian beams are analyzed in the
context of angular displacement measurements. As either the gain, the OAM index
or the radial index of the pump are increased, the measurement uncertainty is
decreased, ultimately allowing for supersensitive measurements. Generally, the
behavior is the same as for the phase sensitivity.
author:
- first_name: Dennis
full_name: Scharwald, Dennis
id: '55907'
last_name: Scharwald
orcid: 0009-0007-5654-5412
citation:
ama: Scharwald D. Theoretical Investigations of Spatially Multimode High-Gain
SU(1,1) Interferometers. Universität Paderborn; 2026. doi:10.17619/UNIPB/1-2491
apa: Scharwald, D. (2026). Theoretical investigations of spatially multimode
high-gain SU(1,1) interferometers. Universität Paderborn. https://doi.org/10.17619/UNIPB/1-2491
bibtex: '@book{Scharwald_2026, place={Paderborn}, title={Theoretical investigations
of spatially multimode high-gain SU(1,1) interferometers}, DOI={10.17619/UNIPB/1-2491},
publisher={Universität Paderborn}, author={Scharwald, Dennis}, year={2026} }'
chicago: 'Scharwald, Dennis. Theoretical Investigations of Spatially Multimode
High-Gain SU(1,1) Interferometers. Paderborn: Universität Paderborn, 2026.
https://doi.org/10.17619/UNIPB/1-2491.'
ieee: 'D. Scharwald, Theoretical investigations of spatially multimode high-gain
SU(1,1) interferometers. Paderborn: Universität Paderborn, 2026.'
mla: Scharwald, Dennis. Theoretical Investigations of Spatially Multimode High-Gain
SU(1,1) Interferometers. Universität Paderborn, 2026, doi:10.17619/UNIPB/1-2491.
short: D. Scharwald, Theoretical Investigations of Spatially Multimode High-Gain
SU(1,1) Interferometers, Universität Paderborn, Paderborn, 2026.
date_created: 2026-02-01T11:59:30Z
date_updated: 2026-08-16T09:38:59Z
department:
- _id: '15'
- _id: '35'
doi: 10.17619/UNIPB/1-2491
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://digital.ub.uni-paderborn.de/hs/download/pdf/8189794
oa: '1'
page: XII, 201
place: Paderborn
publisher: Universität Paderborn
status: public
title: Theoretical investigations of spatially multimode high-gain SU(1,1) interferometers
type: dissertation
user_id: '55907'
year: '2026'
...
---
_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. Physical Review Research. 2026;8(3). doi:10.1103/ph64-ts39
apa: Scharwald, D., & Sharapova, P. (2026). Characterization of spatial Schmidt
modes in high-gain SU(1,1) interferometers. Physical Review Research, 8(3),
Article 033139. https://doi.org/10.1103/ph64-ts39
bibtex: '@article{Scharwald_Sharapova_2026, title={Characterization of spatial Schmidt
modes in high-gain SU(1,1) interferometers}, volume={8}, DOI={10.1103/ph64-ts39},
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.” Physical Review Research 8,
no. 3 (2026). https://doi.org/10.1103/ph64-ts39.
ieee: 'D. Scharwald and P. Sharapova, “Characterization of spatial Schmidt modes
in high-gain SU(1,1) interferometers,” Physical Review Research, vol. 8,
no. 3, Art. no. 033139, 2026, doi: 10.1103/ph64-ts39.'
mla: Scharwald, Dennis, and Polina Sharapova. “Characterization of Spatial Schmidt
Modes in High-Gain SU(1,1) Interferometers.” Physical Review Research,
vol. 8, no. 3, 033139, American Physical Society (APS), 2026, doi:10.1103/ph64-ts39.
short: D. Scharwald, P. Sharapova, Physical Review Research 8 (2026).
date_created: 2026-08-05T11:51:21Z
date_updated: 2026-08-12T14:29:44Z
department:
- _id: '975'
- _id: '15'
- _id: '623'
- _id: '569'
- _id: '170'
- _id: '35'
- _id: '429'
- _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'
project:
- _id: '56'
name: TRR 142 - Project Area C
- _id: '53'
name: 'TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten
zu funktionellen Strukturen'
- _id: '174'
name: 'TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen
Systemen: Eine theoretische Analyse'
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
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'
...
---
_id: '63744'
abstract:
- lang: eng
text: Orbital angular momentum (OAM) modes are an important resource used in various
branches of quantum science and technology due to their unique helical structure
and countably infinite basis. Generating light that simultaneously carries high-order
orbital angular momenta and exhibits quantum correlations is a challenging task.
In this work, we present a theoretical approach to the generation of correlated
Schmidt modes carrying OAM via parametric down-conversion (PDC) in cascaded nonlinear
systems (nonlinear interferometers) pumped by Laguerre–Gaussian beams. We demonstrate
how the number of generated modes and their population can be controlled by varying
the pump parameters, the gain of the PDC process, and the distance between the
crystals. We investigate the angular displacement measurement uncertainty of these
interferometers and demonstrate that it can overcome the classical shot noise
limit.
article_number: '016112'
article_type: original
author:
- first_name: Dennis
full_name: Scharwald, Dennis
id: '55907'
last_name: Scharwald
orcid: 0009-0007-5654-5412
- first_name: Lucas
full_name: Gehse, Lucas
last_name: Gehse
- first_name: Polina
full_name: Sharapova, Polina
id: '60286'
last_name: Sharapova
citation:
ama: Scharwald D, Gehse L, Sharapova P. Schmidt modes carrying orbital angular momentum
generated by cascaded systems pumped with Laguerre–Gaussian beams. APL Photonics.
2025;10(1). doi:10.1063/5.0229802
apa: Scharwald, D., Gehse, L., & Sharapova, P. (2025). Schmidt modes carrying
orbital angular momentum generated by cascaded systems pumped with Laguerre–Gaussian
beams. APL Photonics, 10(1), Article 016112. https://doi.org/10.1063/5.0229802
bibtex: '@article{Scharwald_Gehse_Sharapova_2025, title={Schmidt modes carrying
orbital angular momentum generated by cascaded systems pumped with Laguerre–Gaussian
beams}, volume={10}, DOI={10.1063/5.0229802},
number={1016112}, journal={APL Photonics}, publisher={AIP Publishing}, author={Scharwald,
Dennis and Gehse, Lucas and Sharapova, Polina}, year={2025} }'
chicago: Scharwald, Dennis, Lucas Gehse, and Polina Sharapova. “Schmidt Modes Carrying
Orbital Angular Momentum Generated by Cascaded Systems Pumped with Laguerre–Gaussian
Beams.” APL Photonics 10, no. 1 (2025). https://doi.org/10.1063/5.0229802.
ieee: 'D. Scharwald, L. Gehse, and P. Sharapova, “Schmidt modes carrying orbital
angular momentum generated by cascaded systems pumped with Laguerre–Gaussian beams,”
APL Photonics, vol. 10, no. 1, Art. no. 016112, 2025, doi: 10.1063/5.0229802.'
mla: Scharwald, Dennis, et al. “Schmidt Modes Carrying Orbital Angular Momentum
Generated by Cascaded Systems Pumped with Laguerre–Gaussian Beams.” APL Photonics,
vol. 10, no. 1, 016112, AIP Publishing, 2025, doi:10.1063/5.0229802.
short: D. Scharwald, L. Gehse, P. Sharapova, APL Photonics 10 (2025).
date_created: 2026-01-26T15:48:54Z
date_updated: 2026-02-01T13:19:20Z
department:
- _id: '15'
- _id: '569'
- _id: '170'
- _id: '35'
- _id: '429'
doi: 10.1063/5.0229802
intvolume: ' 10'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://pubs.aip.org/aip/app/article-pdf/doi/10.1063/5.0229802/20352749/016112_1_5.0229802.pdf
oa: '1'
project:
- _id: '53'
name: 'TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten
zu funktionellen Strukturen'
- _id: '56'
name: TRR 142 - Project Area C
- _id: '174'
name: 'TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen
Systemen: Eine theoretische Analyse'
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
publication: APL Photonics
publication_identifier:
issn:
- 2378-0967
publication_status: published
publisher: AIP Publishing
status: public
title: Schmidt modes carrying orbital angular momentum generated by cascaded systems
pumped with Laguerre–Gaussian beams
type: journal_article
user_id: '55907'
volume: 10
year: '2025'
...
---
_id: '63745'
abstract:
- lang: eng
text: Multimode squeezed light is an increasingly popular tool in photonic quantum
technologies, including sensing, imaging, and computation. Meanwhile, the existing
methods of its characterization are technically complicated, which reduces the
level of squeezing, and mostly deal with a single mode at a time. Here, for the
first time, to the best of our knowledge, we employ optical parametric amplification
to characterize multiple squeezing eigenmodes simultaneously. We retrieve the
shapes and squeezing degrees of all modes at once through direct detection followed
by modal decomposition. This method is tolerant to inefficient detection and does
not require a local oscillator. For a spectrally and spatially multimode squeezed
vacuum, we characterize eight strongest spatial modes, obtaining squeezing and
anti-squeezing values of up to −5.2 ± 0.2 dB and 8.6 ± 0.3 dB, respectively, despite
the 50% detection loss. This work, being the first exploration of an optical parametric
amplifier’s multimode capability for squeezing detection, paves the way for the
real-time detection of multimode squeezing.
article_number: '36'
article_type: original
author:
- first_name: Ismail
full_name: Barakat, Ismail
last_name: Barakat
- first_name: Mahmoud
full_name: Kalash, Mahmoud
last_name: Kalash
- 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
- first_name: Norbert
full_name: Lindlein, Norbert
last_name: Lindlein
- first_name: Maria
full_name: Chekhova, Maria
last_name: Chekhova
citation:
ama: Barakat I, Kalash M, Scharwald D, Sharapova P, Lindlein N, Chekhova M. Simultaneous
measurement of multimode squeezing through multimode phase-sensitive amplification.
Optica Quantum. 2025;3(1). doi:10.1364/opticaq.524682
apa: Barakat, I., Kalash, M., Scharwald, D., Sharapova, P., Lindlein, N., &
Chekhova, M. (2025). Simultaneous measurement of multimode squeezing through multimode
phase-sensitive amplification. Optica Quantum, 3(1), Article 36.
https://doi.org/10.1364/opticaq.524682
bibtex: '@article{Barakat_Kalash_Scharwald_Sharapova_Lindlein_Chekhova_2025, title={Simultaneous
measurement of multimode squeezing through multimode phase-sensitive amplification},
volume={3}, DOI={10.1364/opticaq.524682},
number={136}, journal={Optica Quantum}, publisher={Optica Publishing Group}, author={Barakat,
Ismail and Kalash, Mahmoud and Scharwald, Dennis and Sharapova, Polina and Lindlein,
Norbert and Chekhova, Maria}, year={2025} }'
chicago: Barakat, Ismail, Mahmoud Kalash, Dennis Scharwald, Polina Sharapova, Norbert
Lindlein, and Maria Chekhova. “Simultaneous Measurement of Multimode Squeezing
through Multimode Phase-Sensitive Amplification.” Optica Quantum 3, no.
1 (2025). https://doi.org/10.1364/opticaq.524682.
ieee: 'I. Barakat, M. Kalash, D. Scharwald, P. Sharapova, N. Lindlein, and M. Chekhova,
“Simultaneous measurement of multimode squeezing through multimode phase-sensitive
amplification,” Optica Quantum, vol. 3, no. 1, Art. no. 36, 2025, doi:
10.1364/opticaq.524682.'
mla: Barakat, Ismail, et al. “Simultaneous Measurement of Multimode Squeezing through
Multimode Phase-Sensitive Amplification.” Optica Quantum, vol. 3, no. 1,
36, Optica Publishing Group, 2025, doi:10.1364/opticaq.524682.
short: I. Barakat, M. Kalash, D. Scharwald, P. Sharapova, N. Lindlein, M. Chekhova,
Optica Quantum 3 (2025).
date_created: 2026-01-26T15:57:13Z
date_updated: 2026-02-10T22:44:44Z
department:
- _id: '15'
- _id: '569'
- _id: '170'
- _id: '35'
- _id: '429'
doi: 10.1364/opticaq.524682
intvolume: ' 3'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://opg.optica.org/opticaq/viewmedia.cfm?uri=opticaq-3-1-36&seq=0
oa: '1'
project:
- _id: '53'
name: 'TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten
zu funktionellen Strukturen'
- _id: '56'
name: TRR 142 - Project Area C
- _id: '174'
name: 'TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen
Systemen: Eine theoretische Analyse'
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
publication: Optica Quantum
publication_identifier:
issn:
- 2837-6714
publication_status: published
publisher: Optica Publishing Group
status: public
title: Simultaneous measurement of multimode squeezing through multimode phase-sensitive
amplification
type: journal_article
user_id: '55907'
volume: 3
year: '2025'
...
---
_id: '55900'
article_number: '043158'
author:
- first_name: Dennis
full_name: Scharwald, Dennis
id: '55907'
last_name: Scharwald
orcid: 0009-0007-5654-5412
- first_name: Torsten
full_name: Meier, Torsten
id: '344'
last_name: Meier
orcid: 0000-0001-8864-2072
- first_name: Polina
full_name: Sharapova, Polina
last_name: Sharapova
citation:
ama: Scharwald D, Meier T, Sharapova P. Phase sensitivity of spatially broadband
high-gain SU(1,1) interferometers. Physical Review Research. 2023;5(4).
doi:10.1103/physrevresearch.5.043158
apa: Scharwald, D., Meier, T., & Sharapova, P. (2023). Phase sensitivity of
spatially broadband high-gain SU(1,1) interferometers. Physical Review Research,
5(4), Article 043158. https://doi.org/10.1103/physrevresearch.5.043158
bibtex: '@article{Scharwald_Meier_Sharapova_2023, title={Phase sensitivity of spatially
broadband high-gain SU(1,1) interferometers}, volume={5}, DOI={10.1103/physrevresearch.5.043158},
number={4043158}, journal={Physical Review Research}, publisher={American Physical
Society (APS)}, author={Scharwald, Dennis and Meier, Torsten and Sharapova, Polina},
year={2023} }'
chicago: Scharwald, Dennis, Torsten Meier, and Polina Sharapova. “Phase Sensitivity
of Spatially Broadband High-Gain SU(1,1) Interferometers.” Physical Review
Research 5, no. 4 (2023). https://doi.org/10.1103/physrevresearch.5.043158.
ieee: 'D. Scharwald, T. Meier, and P. Sharapova, “Phase sensitivity of spatially
broadband high-gain SU(1,1) interferometers,” Physical Review Research,
vol. 5, no. 4, Art. no. 043158, 2023, doi: 10.1103/physrevresearch.5.043158.'
mla: Scharwald, Dennis, et al. “Phase Sensitivity of Spatially Broadband High-Gain
SU(1,1) Interferometers.” Physical Review Research, vol. 5, no. 4, 043158,
American Physical Society (APS), 2023, doi:10.1103/physrevresearch.5.043158.
short: D. Scharwald, T. Meier, P. Sharapova, Physical Review Research 5 (2023).
date_created: 2024-08-30T04:48:05Z
date_updated: 2026-02-01T13:21:22Z
department:
- _id: '15'
- _id: '569'
- _id: '170'
- _id: '293'
- _id: '35'
- _id: '230'
- _id: '429'
- _id: '623'
- _id: '27'
doi: 10.1103/physrevresearch.5.043158
intvolume: ' 5'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://journals.aps.org/prresearch/pdf/10.1103/PhysRevResearch.5.043158
oa: '1'
project:
- _id: '53'
name: 'TRR 142: TRR 142 - Maßgeschneiderte nichtlineare Photonik: Von grundlegenden
Konzepten zu funktionellen Strukturen'
- _id: '56'
name: 'TRR 142 - C: TRR 142 - Project Area C'
- _id: '174'
name: 'TRR 142 - C10: TRR 142 - Erzeugung und Charakterisierung von Quantenlicht
in nichtlinearen Systemen: Eine theoretische Analyse (C10*)'
- _id: '52'
name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication: Physical Review Research
publication_identifier:
issn:
- 2643-1564
publication_status: published
publisher: American Physical Society (APS)
status: public
title: Phase sensitivity of spatially broadband high-gain SU(1,1) interferometers
type: journal_article
user_id: '55907'
volume: 5
year: '2023'
...