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Preservation and destruction of the purity of two-photon states in the interaction with a classical nanoscatterer

Álvaro Nodar1,*, Ruben Esteban1,2, Carlos Maciel-Escudero1,3,†, Jon Lasa-Alonso1,2,‡, Javier Aizpurua1,2,4,5, and Gabriel Molina-Terriza1,2,4,§

  • *Present address: Global Data Quantum, Alameda Rekalde 18, 7 izq., 48009 Bilbao, Bizkaia.
  • †Present address: Department of Physics, Philipps-Universität Marburg, 35032 Marburg, Germany.
  • ‡Present address: Basic Sciences Department, Mondragon Unibertsitatea, Olagorta Kalea 26, 48014 Bilbao, Spain.
  • §Contact author: gabriel.molina@ehu.eus
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Phys. Rev. Research 8, 013189 – Published 20 February, 2026

DOI: https://doi.org/10.1103/hb1h-jw72

Abstract

The optical resonances supported by nanostructures offer the possibility to enhance the interaction between matter and quantum states of light. On the other hand, due to abrupt changes in the optical response the quantum states of light can be significantly affected by the interaction. In this work, we provide a framework to study the scattering of quantum states of light (with information encoded in their helicity) by a nanostructure. We analyze the purity of the scattered output quantum state and find that the purity of the incident state can be lost when it interacts with the optical resonances of the nanostructure. To explain the loss of quantum purity, we develop a physical picture based on time delays and frequency shifts between the output two-photon modes. The framework and analysis proposed in this work establish a tool to address the interaction between quantum light and nanoenvironments.

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References (46)

  1. W. H. Zurek, Decoherence, einselection, and the quantum origins of the classical, Rev. Mod. Phys. 75, 715 (2003).
  2. Y.-S. Kim, J.-C. Lee, O. Kwon, and Y.-H. Kim, Protecting entanglement from decoherence using weak measurement and quantum measurement reversal, Nat. Phys. 8, 117 (2012).
  3. M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, Communication with spatially modulated light through turbulent air across Vienna, New J. Phys. 16, 113028 (2014).
  4. M. Krenn, M. Malik, T. Scheidl, R. Ursin, and A. Zeilinger, Quantum communication with photons, Opt. Time 18, 455 (2016).
  5. M. Aspelmeyer, H. R. Bohm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, et al., Long-distance free-space distribution of quantum entanglement, Science 301, 621 (2003).
  6. T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, Quantum computers, Nature (London) 464, 45 (2010).
  7. M. A. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, New York, 2002).
  8. M.-A. Lemonde, N. Didier, and A. A. Clerk, Enhanced nonlinear interactions in quantum optomechanics via mechanical amplification, Nat. Commun. 7, 11338 (2016).
  9. L. Novotny and N. Van Hulst, Antennas for light, Nat. Photon. 5, 83 (2011).
  10. F. Benz, M. K. Schmidt, A. Dreismann, R. Chikkaraddy, Y. Zhang, A. Demetriadou, C. Carnegie, H. Ohadi, B. De Nijs, R. Esteban, et al., Single-molecule optomechanics in “picocavities”, Science 354, 726 (2016).
  11. A. Krasnok, M. Caldarola, N. Bonod, and A. Alú, Spectroscopy and biosensing with optically resonant dielectric nanostructures, Adv. Opt. Mater. 6, 1701094 (2018).
  12. J. Lasa-Alonso, D. R. Abujetas, Á. Nodar, J. A. Dionne, J. J. Sáenz, G. Molina-Terriza, J. Aizpurua, and A. García-Etxarri, Surface-enhanced circular dichroism spectroscopy on periodic dual nanostructures, ACS Photonics 7, 2978 (2020).
  13. O. J. Farías, V. D’Ambrosio, C. Taballione, F. Bisesto, S. Slussarenko, L. Aolita, L. Marrucci, S. P. Walborn, and F. Sciarrino, Resilience of hybrid optical angular momentum qubits to turbulence, Sci. Rep. 5, 8424 (2015).
  14. A. H. Ibrahim, F. S. Roux, M. McLaren, T. Konrad, and A. Forbes, Orbital-angular-momentum entanglement in turbulence, Phys. Rev. A 88, 012312 (2013).
  15. S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. 't Hooft, and J. P. Woerdman, Experimental demonstration of fractional orbital angular momentum entanglement of two photons, Phys. Rev. Lett. 95, 240501 (2005).
  16. S. Franke-Arnold, L. Allen, and M. Padgett, Advances in optical angular momentum, Laser Photonics Rev. 2, 299 (2008).
  17. G. Molina-Terriza, A. Vaziri, J. Řeháček, Z. Hradil, and A. Zeilinger, Triggered qutrits for quantum communication protocols, Phys. Rev. Lett. 92, 167903 (2004).
  18. G. Molina-Terriza, J. P. Torres, and L. Torner, Twisted photons, Nat. Phys. 3, 305 (2007).
  19. J. Lasa-Alonso, M. Molezuelas-Ferreras, J. M. Varga, A. García-Etxarri, G. Giedke, and G. Molina-Terriza, Symmetry-protection of multiphoton states of light, New J. Phys. 22, 123010 (2020).
  20. A. Büse, M. L. Juan, N. Tischler, V. D’Ambrosio, F. Sciarrino, L. Marrucci, and G. Molina-Terriza, Symmetry protection of photonic entanglement in the interaction with a single nanoaperture, Phys. Rev. Lett. 121, 173901 (2018).
  21. N. Tischler, C. Rockstuhl, and K. Słowik, Quantum optical realization of arbitrary linear transformations allowing for loss and gain, Phys. Rev. X 8, 021017 (2018).
  22. S. M. Barnett, J. Jeffers, A. Gatti, and R. Loudon, Quantum optics of lossy beam splitters, Phys. Rev. A 57, 2134 (1998).
  23. B. Vest, M.-C. Dheur, É. Devaux, A. Baron, E. Rousseau, J.-P. Hugonin, J.-J. Greffet, G. Messin, and F. Marquier, Anti-coalescence of bosons on a lossy beam splitter, Science 356, 1373 (2017).
  24. S. Fan, Ş. E. Kocabaş, and J.-T. Shen, Input-output formalism for few-photon transport in one-dimensional nanophotonic waveguides coupled to a qubit, Phys. Rev. A 82, 063821 (2010).
  25. C. Cohen-Tannoudji, B. Diu, and F. Laloë, Quantum Mechanics: Basic Concepts, Tools, and Applications (Wiley, Weinheim, Germany, 2019), Vol. 1.
  26. A. Akimov, A. Mukherjee, C. Yu, D. Chang, A. Zibrov, P. Hemmer, H. Park, and M. Lukin, Generation of single optical plasmons in metallic nanowires coupled to quantum dots, Nature (London) 450, 402 (2007).
  27. J. M. Varga, J. Lasa-Alonso, M. Molezuelas-Ferreras, N. Tischler, and G. Molina-Terriza, Bandwidth control of the biphoton wavefunction exploiting spatio-temporal correlations, Opt. Commun. 504, 127461 (2022).
  28. N. Tischler, A. Buese, L. G. Helt, M. L. Juan, N. Piro, J. Ghosh, M. J. Steel, and G. Molina-Terriza, Measurement and shaping of biphoton spectral wave functions, Phys. Rev. Lett. 115, 193602 (2015).
  29. J. B. Altepeter, E. R. Jeffrey, and P. G. Kwiat, Photonic state tomography, Adv. At. Mol. Opt. Phys. 52, 105 (2005).
  30. R. Matloob, R. Loudon, S. M. Barnett, and J. Jeffers, Electromagnetic field quantization in absorbing dielectrics, Phys. Rev. A 52, 4823 (1995).
  31. R. Matloob and R. Loudon, Electromagnetic field quantization in absorbing dielectrics. II, Phys. Rev. A 53, 4567 (1996).
  32. I. Białynicki-Birula, On the wave function of the photon, Acta Phys. Pol. A 86, 97 (1994).
  33. J. C. Schotland, A. Cazé, and T. B. Norris, Scattering of entangled two-photon states, Opt. Lett. 41, 444 (2016).
  34. J. Olmos-Trigo, C. Sanz-Fernández, D. R. Abujetas, J. Lasa-Alonso, N. de Sousa, A. García-Etxarri, J. A. Sánchez-Gil, G. Molina-Terriza, and J. J. Sáenz, Kerker conditions upon lossless, absorption, and optical gain regimes, Phys. Rev. Lett. 125, 073205 (2020).
  35. X. Zambrana-Puyalto, I. Fernandez-Corbaton, M. Juan, X. Vidal, and G. Molina-Terriza, Duality symmetry and Kerker conditions, Opt. Lett. 38, 1857 (2013).
  36. J. Lasa-Alonso, J. Olmos-Trigo, A. García-Etxarri, and G. Molina-Terriza, Correlations between helicity and optical losses within general electromagnetic scattering theory, Mater. Adv. 3, 4179 (2022).
  37. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998), Vol 3.
  38. X. Zambrana-Puyalto, X. Vidal, and G. Molina-Terriza, Excitation of single multipolar modes with engineered cylindrically symmetric fields, Opt. Express 20, 24536 (2012).
  39. C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  40. R. Rangarajan, M. Goggin, and P. Kwiat, Optimizing type-I polarization-entangled photons, Opt. Express 17, 18920 (2009).
  41. A. E. Siegman, Lasers (University Science Books, 1986).
  42. E. W. Weisstein, Associated Laguerre polynomial, https://mathworld.wolfram.com/.
  43. N. Tischler, X. Zambrana-Puyalto, and G. Molina-Terriza, The role of angular momentum in the construction of electromagnetic multipolar fields, Eur. J. Phys. 33, 1099 (2012).
  44. M. Rose, Elementary theory of angular momentum, Structure of Matter Series (Wiley, 1957).
  45. L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge University Press, 2012).
  46. Á. Nodar, R. Esteban, C. Maciel-Escudero, J. Lasa-Alonso, J. Aizpurua, and G. Molina-Terriza, Research data supporting “Preservation and destruction of the purity of two-photon states in the interaction with a classical nanoscatterer” [Data set] (2026), DIGITAL.CSIC, http://doi.org/10.20350/DIGITALCSIC/17893.

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Phys. Rev. Research 8, 013189– Published 20 February, 2026
  • Received 7 November 2022
  • Accepted 21 December 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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