Theory of Multimode Squeezed Light Generation in Lossy Media

Denis A. Kopylov; Torsten Meier; Polina R. Sharapova

doi:10.22331/q-2025-02-04-1621

Theory of Multimode Squeezed Light Generation in Lossy Media

Denis A. Kopylov^1,2, Torsten Meier^1,2, and Polina R. Sharapova¹

¹Department of Physics, Paderborn University, Warburger Straße 100, D-33098 Paderborn, Germany
²Institute for Photonic Quantum Systems (PhoQS), Paderborn University, Warburger Straße 100, D-33098 Paderborn, Germany

Published:	2025-02-04, volume 9, page 1621
Editor:	Elizabeth Agudelo
Eprint:	arXiv:2403.05259v4
Doi:	https://doi.org/10.22331/q-2025-02-04-1621
Citation:	Quantum 9, 1621 (2025).

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Abstract

A unified theoretical approach to describe the properties of multimode squeezed light generated in a lossy medium is presented. This approach is valid for Markovian environments and includes both a model of discrete losses based on the beamsplitter approach and a generalized continuous loss model based on the spatial Langevin equation. For an important class of Gaussian states, we derive master equations for the second-order correlation functions and illustrate their solution for both frequency-independent and frequency-dependent losses. Studying the mode structure, we demonstrate that in a lossy environment no broadband basis without quadrature correlations between the different broadband modes exists. Therefore, various techniques and strategies to introduce broadband modes can be considered. We show that the Mercer expansion and the Williamson-Euler decomposition do not provide modes in which the maximal squeezing contained in the system can be measured. In turn, we find a new broadband basis that maximizes squeezing in the lossy system and present an algorithm to construct it.

► BibTeX data

@article{Kopylov2025theoryofmultimode,
  doi = {10.22331/q-2025-02-04-1621},
  url = {https://doi.org/10.22331/q-2025-02-04-1621},
  title = {Theory of {M}ultimode {S}queezed {L}ight {G}eneration in {L}ossy {M}edia},
  author = {Kopylov, Denis A. and Meier, Torsten and Sharapova, Polina R.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1621},
  month = feb,
  year = {2025}
}

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Cited by

[1] Denis A. Kopylov, Michael Stefszky, Torsten Meier, Christine Silberhorn, and Polina R. Sharapova, "Spectral and temporal properties of type-II parametric down-conversion: The impact of losses during state generation", Physical Review Research 7 3, 033122 (2025).

[2] Xing Heng, Lingchen Zhang, Qingyun Yin, Wei Liu, Lulu Tang, Yueyang Zhai, and Kai Wei, "Quantum-Enhanced Sensing with Squeezed Light: From Fundamentals to Applications", Applied Sciences 15 18, 10179 (2025).

[3] Denis A. Kopylov, Torsten Meier, and Polina R. Sharapova, "Bipartite entanglement extracted from multimode squeezed light generated in lossy waveguides", APL Quantum 2 4, 046116 (2025).

[4] Dmitri B. Horoshko, Shivang Srivastava, Filip Sośnicki, Michał Mikołajczyk, Michał Karpiński, Benjamin Brecht, and Mikhail I. Kolobov, "Time-resolved second-order autocorrelation function of parametric down-conversion", Physical Review A 112 2, 023703 (2025).

[5] D. B. Horoshko and V. S. Shchesnovich, "Isoenergetic model for optical down-conversion and error-specific limits of the parametric approximation", Physical Review A 112 3, 033706 (2025).

[6] Emanuel Hubenschmid and Guido Burkard, "Time-domain field correlation measurements enable tomography of highly multimode quantum states of light", Communications Physics 9 1, 89 (2026).

[7] Nicolás Quesada, "What’s my phase again? Computing the vacuum-to-vacuum amplitude of quadratic bosonic evolution", Proceedings of the Royal Society A Mathematical Physical and Engineering Science 481 2327, 20250599 (2025).

[8] D. Scharwald and P. R. Sharapova, "Characterization of spatial Schmidt modes in high-gain SU(1,1) interferometers", Physical Review Research 8 3, 033139 (2026).

[9] Youngbin Kim, Seongjin Jeon, and Young-Ik Sohn, "Simulating quantum light in lossy microring resonators driven by strong pulses", Physical Review Applied 23 5, 054045 (2025).

[10] Emil R. Hellebek, Klaus Mølmer, and Anders S. Sørensen, "Characterization of the multimode nature of single-photon sources based on spontaneous parametric down-conversion", Physical Review A 110 2, 023728 (2024).

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