@phdthesis{63826,
  abstract     = {{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.}},
  author       = {{Scharwald, Dennis}},
  pages        = {{XII, 201}},
  publisher    = {{Universität Paderborn}},
  title        = {{{Theoretical investigations of spatially multimode high-gain SU(1,1) interferometers}}},
  doi          = {{10.17619/UNIPB/1-2491}},
  year         = {{2026}},
}

@article{66665,
  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.}},
  author       = {{Scharwald, Dennis and Sharapova, Polina}},
  issn         = {{2643-1564}},
  journal      = {{Physical Review Research}},
  number       = {{3}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Characterization of spatial Schmidt modes in high-gain SU(1,1) interferometers}}},
  doi          = {{10.1103/ph64-ts39}},
  volume       = {{8}},
  year         = {{2026}},
}

@article{63744,
  abstract     = {{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.}},
  author       = {{Scharwald, Dennis and Gehse, Lucas and Sharapova, Polina}},
  issn         = {{2378-0967}},
  journal      = {{APL Photonics}},
  number       = {{1}},
  publisher    = {{AIP Publishing}},
  title        = {{{Schmidt modes carrying orbital angular momentum generated by cascaded systems pumped with Laguerre–Gaussian beams}}},
  doi          = {{10.1063/5.0229802}},
  volume       = {{10}},
  year         = {{2025}},
}

@article{63745,
  abstract     = {{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.}},
  author       = {{Barakat, Ismail and Kalash, Mahmoud and Scharwald, Dennis and Sharapova, Polina and Lindlein, Norbert and Chekhova, Maria}},
  issn         = {{2837-6714}},
  journal      = {{Optica Quantum}},
  number       = {{1}},
  publisher    = {{Optica Publishing Group}},
  title        = {{{Simultaneous measurement of multimode squeezing through multimode phase-sensitive amplification}}},
  doi          = {{10.1364/opticaq.524682}},
  volume       = {{3}},
  year         = {{2025}},
}

@article{55900,
  author       = {{Scharwald, Dennis and Meier, Torsten and Sharapova, Polina}},
  issn         = {{2643-1564}},
  journal      = {{Physical Review Research}},
  number       = {{4}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Phase sensitivity of spatially broadband high-gain SU(1,1) interferometers}}},
  doi          = {{10.1103/physrevresearch.5.043158}},
  volume       = {{5}},
  year         = {{2023}},
}