[{"publication_status":"published","date_updated":"2026-08-12T14:29:44Z","article_type":"original","intvolume":"         8","title":"Characterization of spatial Schmidt modes in high-gain SU(1,1) interferometers","year":"2026","publication_identifier":{"issn":["2643-1564"]},"author":[{"full_name":"Scharwald, Dennis","first_name":"Dennis","orcid":"0009-0007-5654-5412","last_name":"Scharwald","id":"55907"},{"first_name":"Polina","last_name":"Sharapova","full_name":"Sharapova, Polina","id":"60286"}],"doi":"10.1103/ph64-ts39","article_number":"033139","main_file_link":[{"url":"https://journals.aps.org/prresearch/pdf/10.1103/ph64-ts39","open_access":"1"}],"language":[{"iso":"eng"}],"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."}],"issue":"3","publication":"Physical Review Research","type":"journal_article","department":[{"_id":"975"},{"_id":"15"},{"_id":"623"},{"_id":"569"},{"_id":"170"},{"_id":"35"},{"_id":"429"},{"_id":"34"},{"_id":"502"}],"date_created":"2026-08-05T11:51:21Z","status":"public","user_id":"55907","volume":8,"_id":"66665","publisher":"American Physical Society (APS)","project":[{"name":"TRR 142 - Project Area C","_id":"56"},{"_id":"53","name":"TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten zu funktionellen Strukturen"},{"name":"TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen Systemen: Eine theoretische Analyse","_id":"174"},{"name":"Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"citation":{"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>.","short":"D. Scharwald, P. Sharapova, Physical Review Research 8 (2026).","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>","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>.","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>","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} }","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>."},"oa":"1"},{"doi":"10.1364/oe.592467","language":[{"iso":"eng"}],"article_number":"35794","intvolume":"        34","date_updated":"2026-09-12T10:10:04Z","publication_status":"published","publication_identifier":{"issn":["1094-4087"]},"author":[{"full_name":"Braasch, M.","last_name":"Braasch","first_name":"M."},{"full_name":"Kartashova, A.","last_name":"Kartashova","first_name":"A."},{"full_name":"Krasikov, S.","first_name":"S.","last_name":"Krasikov"},{"full_name":"Goi, E.","first_name":"E.","last_name":"Goi"},{"first_name":"T.","last_name":"Pertsch","full_name":"Pertsch, T."},{"full_name":"Saravi, S.","first_name":"S.","last_name":"Saravi"}],"year":"2026","title":"Second-harmonic generation for enhancing the performance of diffractive neural networks","department":[{"_id":"975"}],"type":"journal_article","date_created":"2026-09-12T10:09:12Z","abstract":[{"text":"<jats:p>Diffractive neural networks (DNNs) are an emerging approach for the realization of photonic artificial intelligence, especially due to their suitability for machine-vision applications and high-dimensional photonic information processing at lower power consumption. However, incorporating optical nonlinear activation functions to make DNNs a feasible alternative to their electronic counterpart remains a challenge. Here, we investigate the inclusion of second-harmonic generation (SHG), as one of the simplest and most efficient types of optical nonlinearities, in DNNs. We numerically investigate the impact of SHG on the performance of classification tasks in an all-optical nonlinear DNN. Specifically, we investigate and discuss the essential requirements for an effective arrangement of a SHG activation in single and multilayer DNNs. We find that the performance, in terms of classification accuracy and class contrast, is affected strongly by the positioning of the SHG activation. Finally, we discuss and outline the constraints for including SHG in an experimental realization. Taking these constraints into account, we estimate the power-related efficiency of the nonlinear DNN system. Overall, our results provide a path towards implementing nonlinear DNNs using the SHG process.</jats:p>","lang":"eng"}],"issue":"19","publication":"Optics Express","volume":34,"user_id":"115260","_id":"67134","publisher":"Optica Publishing Group","status":"public","citation":{"mla":"Braasch, M., et al. “Second-Harmonic Generation for Enhancing the Performance of Diffractive Neural Networks.” <i>Optics Express</i>, vol. 34, no. 19, 35794, Optica Publishing Group, 2026, doi:<a href=\"https://doi.org/10.1364/oe.592467\">10.1364/oe.592467</a>.","ama":"Braasch M, Kartashova A, Krasikov S, Goi E, Pertsch T, Saravi S. Second-harmonic generation for enhancing the performance of diffractive neural networks. <i>Optics Express</i>. 2026;34(19). doi:<a href=\"https://doi.org/10.1364/oe.592467\">10.1364/oe.592467</a>","bibtex":"@article{Braasch_Kartashova_Krasikov_Goi_Pertsch_Saravi_2026, title={Second-harmonic generation for enhancing the performance of diffractive neural networks}, volume={34}, DOI={<a href=\"https://doi.org/10.1364/oe.592467\">10.1364/oe.592467</a>}, number={1935794}, journal={Optics Express}, publisher={Optica Publishing Group}, author={Braasch, M. and Kartashova, A. and Krasikov, S. and Goi, E. and Pertsch, T. and Saravi, S.}, year={2026} }","apa":"Braasch, M., Kartashova, A., Krasikov, S., Goi, E., Pertsch, T., &#38; Saravi, S. (2026). Second-harmonic generation for enhancing the performance of diffractive neural networks. <i>Optics Express</i>, <i>34</i>(19), Article 35794. <a href=\"https://doi.org/10.1364/oe.592467\">https://doi.org/10.1364/oe.592467</a>","ieee":"M. Braasch, A. Kartashova, S. Krasikov, E. Goi, T. Pertsch, and S. Saravi, “Second-harmonic generation for enhancing the performance of diffractive neural networks,” <i>Optics Express</i>, vol. 34, no. 19, Art. no. 35794, 2026, doi: <a href=\"https://doi.org/10.1364/oe.592467\">10.1364/oe.592467</a>.","short":"M. Braasch, A. Kartashova, S. Krasikov, E. Goi, T. Pertsch, S. Saravi, Optics Express 34 (2026).","chicago":"Braasch, M., A. Kartashova, S. Krasikov, E. Goi, T. Pertsch, and S. Saravi. “Second-Harmonic Generation for Enhancing the Performance of Diffractive Neural Networks.” <i>Optics Express</i> 34, no. 19 (2026). <a href=\"https://doi.org/10.1364/oe.592467\">https://doi.org/10.1364/oe.592467</a>."}},{"article_number":"023706","language":[{"iso":"eng"}],"doi":"10.1103/2hth-yy33","title":"Toward spectral engineering of squeezed light in high-gain parametric down-conversion","year":"2026","publication_identifier":{"issn":["2469-9926","2469-9934"]},"author":[{"first_name":"Jatin","last_name":"Kumar","full_name":"Kumar, Jatin"},{"full_name":"Krstić, Aleksa","first_name":"Aleksa","last_name":"Krstić"},{"full_name":"Saravi, Sina","last_name":"Saravi","first_name":"Sina"},{"last_name":"Setzpfandt","first_name":"Frank","full_name":"Setzpfandt, Frank"}],"date_updated":"2026-09-12T10:10:11Z","publication_status":"published","intvolume":"       114","date_created":"2026-09-12T10:08:24Z","type":"journal_article","department":[{"_id":"975"}],"publication":"Physical Review A","issue":"2","abstract":[{"text":"<jats:p>We investigated the spectral properties of squeezed light generated via parametric down-conversion in the high-gain regime, considering both unapodized and apodized dispersion-engineered waveguides. The gain-dependent evolution of these states is examined starting from the low-gain regime, which includes both highly correlated and nearly uncorrelated cases. For the unapodized configuration, our simulated results show a monotonic increase in spectral purity with gain, whereas for some of the apodized configuration, they exhibit a nonmonotonic dependence, initially decreasing and then recovering at higher gain. By combining Schmidt-mode analysis with a group-velocity-based interpretation, we explain why different dispersion conditions exhibit distinct gain-dependent behavior, specifically that rapid purification occurs when the pump group velocity lies between those of the signal and idler. Our study shows that the evolution of spectral purity is governed primarily by the underlying dispersion of the waveguide. These results demonstrate that dispersion engineering and parametric gain can be jointly exploited to tailor the spectral-mode structure of squeezed-light sources, enabling their optimization for a broad range of quantum applications.</jats:p>","lang":"eng"}],"_id":"67133","publisher":"American Physical Society (APS)","user_id":"115260","volume":114,"status":"public","citation":{"short":"J. Kumar, A. Krstić, S. Saravi, F. Setzpfandt, Physical Review A 114 (2026).","chicago":"Kumar, Jatin, Aleksa Krstić, Sina Saravi, and Frank Setzpfandt. “Toward Spectral Engineering of Squeezed Light in High-Gain Parametric down-Conversion.” <i>Physical Review A</i> 114, no. 2 (2026). <a href=\"https://doi.org/10.1103/2hth-yy33\">https://doi.org/10.1103/2hth-yy33</a>.","apa":"Kumar, J., Krstić, A., Saravi, S., &#38; Setzpfandt, F. (2026). Toward spectral engineering of squeezed light in high-gain parametric down-conversion. <i>Physical Review A</i>, <i>114</i>(2), Article 023706. <a href=\"https://doi.org/10.1103/2hth-yy33\">https://doi.org/10.1103/2hth-yy33</a>","ieee":"J. Kumar, A. Krstić, S. Saravi, and F. Setzpfandt, “Toward spectral engineering of squeezed light in high-gain parametric down-conversion,” <i>Physical Review A</i>, vol. 114, no. 2, Art. no. 023706, 2026, doi: <a href=\"https://doi.org/10.1103/2hth-yy33\">10.1103/2hth-yy33</a>.","ama":"Kumar J, Krstić A, Saravi S, Setzpfandt F. Toward spectral engineering of squeezed light in high-gain parametric down-conversion. <i>Physical Review A</i>. 2026;114(2). doi:<a href=\"https://doi.org/10.1103/2hth-yy33\">10.1103/2hth-yy33</a>","bibtex":"@article{Kumar_Krstić_Saravi_Setzpfandt_2026, title={Toward spectral engineering of squeezed light in high-gain parametric down-conversion}, volume={114}, DOI={<a href=\"https://doi.org/10.1103/2hth-yy33\">10.1103/2hth-yy33</a>}, number={2023706}, journal={Physical Review A}, publisher={American Physical Society (APS)}, author={Kumar, Jatin and Krstić, Aleksa and Saravi, Sina and Setzpfandt, Frank}, year={2026} }","mla":"Kumar, Jatin, et al. “Toward Spectral Engineering of Squeezed Light in High-Gain Parametric down-Conversion.” <i>Physical Review A</i>, vol. 114, no. 2, 023706, American Physical Society (APS), 2026, doi:<a href=\"https://doi.org/10.1103/2hth-yy33\">10.1103/2hth-yy33</a>."}}]