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Multiphoton, multimode state classification for nonlinear optical circuits

Denis A. Kopylov1,2,*, Christian Offen1,3, Laura Ares1,2, Boris Wembe3, Sina Ober-Blöbaum3, Torsten Meier1,2, Polina R. Sharapova2, and Jan Sperling1,2

  • 1Institute for Photonic Quantum Systems (PhoQS), Paderborn University, Warburger Straße 100, D-33098 Paderborn, Germany
  • 2Department of Physics, Paderborn University, Warburger Straße 100, D-33098 Paderborn, Germany
  • 3Department of Mathematics, Paderborn University, Warburger Straße 100, D-33098 Paderborn, Germany

  • *Contact author: denis.kopylov@uni-paderborn.de
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Phys. Rev. Research 7, 033062 – Published 15 July, 2025

DOI: https://doi.org/10.1103/sv6z-v1gk

Abstract

We introduce a new classification of multimode states with a fixed number of photons. This classification is based on the factorizability of homogeneous multivariate polynomials and is invariant under unitary transformations. The classes physically correspond to field excitations in terms of single and multiple photons, each of which is in an arbitrary irreducible superposition of quantized modes. We further show how the transitions between classes are rendered possible by photon addition, photon subtraction, and photon-projection nonlinearities. We explicitly put forward a design for a multilayer interferometer in which the states for different classes can be generated with state-of-the-art experimental techniques. Limitations of the proposed designs are analyzed using the introduced classification, providing a benchmark for the robustness of certain states and classes.

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Phys. Rev. Research 7, 033062– Published 15 July, 2025
  • Received 10 February 2025
  • Accepted 13 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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