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  • Open Access

Nonlinear spectroscopy of cavity polaritons

Anqi Li1, Upendra Harbola2, and Michael Galperin3,*

  • *Contact author: mgalperin@tauex.tau.ac.il

Phys. Rev. Research 7, 033248 – Published 12 September, 2025

DOI: https://doi.org/10.1103/ccfc-1fg4

Abstract

Confinement of molecules within a cavity leads to a strong coupling between light and matter degrees of freedom, merging the two into a quasiparticle known as a polariton. Theoretical treatments of molecular polaritons generally utilize either exact diagonalization of the interacting molecule-cavity system Hamiltonian or perturbation theory to analyze intracavity light-matter interactions. The former is constrained in its capacity to account for the open nature of the molecular cavity system, while the treatment of strong interactions within perturbation theory represents a weakness of the latter. Here, we introduce a pseudoparticle nonequilibrium Green's function (PP-NEGF) formulation for molecular polariton spectroscopy. This formulation addresses the limitations of currently available approaches by accounting for all intrasystem interactions exactly and treating system-bath couplings within diagrammatic expansion and extends a recent NEGF-based formulation for nonlinear optical spectroscopy [J. Chem. Phys. 162, 074108 (2025)] to strongly interacting molecular systems. Theoretical derivations are demonstrated through numerical simulations, where we examine the impact of strong light-matter interaction on fluxes and multidimensional optical spectroscopy of cavity polaritons.

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References (54)

  1. T. Schwartz, J. A. Hutchison, C. Genet, and T. W. Ebbesen, Reversible switching of ultrastrong light-molecule coupling, Phys. Rev. Lett. 106, 196405 (2011).
  2. J. A. Hutchison, T. Schwartz, C. Genet, E. Devaux, and T. W. Ebbesen, Modifying chemical landscapes by coupling to vacuum fields, Angew. Chem. Int. Ed. 51, 1592 (2012).
  3. J. A. Hutchison, A. Liscio, T. Schwartz, A. Canaguier-Durand, C. Genet, V. Palermo, P. Samorì, and T. W. Ebbesen, Tuning the work-function via strong coupling, Adv. Mater. 25, 2481 (2013).
  4. T. Schwartz, J. A. Hutchison, J. Léonard, C. Genet, S. Haacke, and T. W. Ebbesen, Polariton dynamics under strong light–molecule coupling, ChemPhysChem 14, 125 (2013).
  5. A. W. Eddins, C. C. Beedle, D. N. Hendrickson, and J. R. Friedman, Collective coupling of a macroscopic number of single-molecule magnets with a microwave cavity mode, Phys. Rev. Lett. 112, 120501 (2014).
  6. E. Eizner, K. Akulov, T. Schwartz, and T. Ellenbogen, Temporal dynamics of localized exciton–polaritons in composite organic–plasmonic metasurfaces, Nano Lett. 17, 7675 (2017).
  7. G. G. Rozenman, K. Akulov, A. Golombek, and T. Schwartz, Long-range transport of organic exciton-polaritons revealed by ultrafast microscopy, ACS Photon. 5, 105 (2018).
  8. K. Akulov, D. Bochman, A. Golombek, and T. Schwartz, Long-distance resonant energy transfer mediated by hybrid plasmonic–photonic modes, J. Phys. Chem. C 122, 15853 (2018).
  9. B. Xiang, R. F. Ribeiro, M. Du, L. Chen, Z. Yang, J. Wang, J. Yuen-Zhou, and W. Xiong, Intermolecular vibrational energy transfer enabled by microcavity strong light–matter coupling, Science 368, 665 (2020).
  10. T.-T. Chen, M. Du, Z. Yang, J. Yuen-Zhou, and W. Xiong, Cavity-enabled enhancement of ultrafast intramolecular vibrational redistribution over pseudorotation, Science 378, 790 (2022).
  11. Z. Yang and W. Xiong, Molecular vibrational polaritons towards quantum technologies, Adv. Quantum Technol. 5, 2100163 (2022).
  12. T. E. Li, B. Cui, J. E. Subotnik, and A. Nitzan, Molecular polaritonics: Chemical dynamics under strong light–matter coupling, Annu. Rev. Phys. Chem. 73, 43 (2022).
  13. E. Orgiu, J. George, J. A. Hutchison, E. Devaux, J. F. Dayen, B. Doudin, F. Stellacci, C. Genet, J. Schachenmayer, C. Genes, G. Pupillo, P. Samorì, and T. W. Ebbesen, Conductivity in organic semiconductors hybridized with the vacuum field, Nat. Mater. 14, 1123 (2015).
  14. G. Lerario, D. Ballarini, A. Fieramosca, A. Cannavale, A. Genco, F. Mangione, S. Gambino, L. Dominici, M. De Giorgi, G. Gigli, and D. Sanvitto, High-speed flow of interacting organic polaritons, Light Sci. Appl. 6, e16212 (2017).
  15. B. Munkhbat, M. Wersäll, D. G. Baranov, T. J. Antosiewicz, and T. Shegai, Suppression of photo-oxidation of organic chromophores by strong coupling to plasmonic nanoantennas, Sci. Adv. 4, eaas9552 (2018).
  16. X. Shi, K. Ueno, T. Oshikiri, Q. Sun, K. Sasaki, and H. Misawa, Enhanced water splitting under modal strong coupling conditions, Nat. Nanotechnol. 13, 953 (2018).
  17. S. Hou, M. Khatoniar, K. Ding, Y. Qu, A. Napolov, V. M. Menon, and S. R. Forrest, Ultralong-range energy transport in a disordered organic semiconductor at room temperature via coherent exciton-polariton propagation, Adv. Mater. 32, 2002127 (2020).
  18. N. Krainova, A. J. Grede, D. Tsokkou, N. Banerji, and N. C. Giebink, Polaron photoconductivity in the weak and strong light-matter coupling regime, Phys. Rev. Lett. 124, 177401 (2020).
  19. M. Balasubrahmaniyam, A. Simkhovich, A. Golombek, G. Sandik, G. Ankonina, and T. Schwartz, From enhanced diffusion to ultrafast ballistic motion of hybrid light–matter excitations, Nat. Mater. 22, 338 (2023).
  20. R. Chikkaraddy, B. de Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, Single-molecule strong coupling at room temperature in plasmonic nanocavities, Nature (London) 535, 127 (2016).
  21. F. Benz, M. K. Schmidt, A. Dreismann, R. Chikkaraddy, Y. Zhang, A. Demetriadou, C. Carnegie, H. Ohadi, B. de Nijs, R. Esteban, J. Aizpurua, and J. J. Baumberg, Single-molecule optomechanics in “picocavities”, Science 354, 726 (2016).
  22. K. K. Lehmann and D. Romanini, The superposition principle and cavity ring‐down spectroscopy, J. Chem. Phys. 105, 10263 (1996).
  23. C. Ciuti and I. Carusotto, Input-output theory of cavities in the ultrastrong coupling regime: The case of time-independent cavity parameters, Phys. Rev. A 74, 033811 (2006).
  24. N. Moiseyev, Non-Hermitian Quantum Mechanics (Cambridge University Press, Cambridge, 2011).
  25. S. R.-K. Rodriguez, Classical and quantum distinctions between weak and strong coupling, Eur. J. Phys. 37, 025802 (2016).
  26. M. Berry, Physics of nonHermitian degeneracies, Czech. J. Phys. 54, 1039 (2004).
  27. U. Günther, I. Rotter, and B. F. Samsonov, Projective Hilbert space structures at exceptional points, J. Phys. A 40, 8815 (2007).
  28. W. D. Heiss, The physics of exceptional points, J. Phys. A 45, 444016 (2012).
  29. A. Delga, J. Feist, J. Bravo-Abad, and F. J. Garcia-Vidal, Theory of strong coupling between quantum emitters and localized surface plasmons, J. Opt. 16, 114018 (2014).
  30. T. Gao, E. Estrecho, K. Y. Bliokh, T. C. H. Liew, M. D. Fraser, S. Brodbeck, M. Kamp, C. Schneider, S. Hofling, Y. Yamamoto, F. Nori, Y. S. Kivshar, A. G. Truscott, R. G. Dall, and E. A. Ostrovskaya, Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard, Nature (London) 526, 554 (2015).
  31. M.-A. Miri and A. Alú, Exceptional points in optics and photonics, Science 363, eaar7709 (2019).
  32. M. S. Ergoktas, S. Soleymani, N. Kakenov, K. Wang, T. B. Smith, G. Bakan, S. Balci, A. Principi, K. S. Novoselov, S. K. Ozdemir, and C. Kocabas, Topological engineering of terahertz light using electrically tunable exceptional point singularities, Science 376, 184 (2022).
  33. S. Soleymani, Q. Zhong, M. Mokim, S. Rotter, R. El-Ganainy, and Ş. K. Özdemir, Chiral and degenerate perfect absorption on exceptional surfaces, Nat. Commun. 13, 599 (2022).
  34. D. Finkelstein-Shapiro, P.-A. Mante, S. Balci, D. Zigmantas, and T. Pullerits, Non-Hermitian Hamiltonians for linear and nonlinear optical response: A model for plexcitons, J. Chem. Phys. 158, 104104 (2023).
  35. S. Mukamel, A. Li, and M. Galperin, Exceptional points treatment of cavity spectroscopies, J. Chem. Phys. 158, 154106 (2023).
  36. C. Yang, X. Wei, J. Sheng, and H. Wu, Phonon heat transport in cavity-mediated optomechanical nanoresonators, Nat. Commun. 11, 4656 (2020).
  37. D. Hagenmüller, J. Schachenmayer, S. Schütz, C. Genes, and G. Pupillo, Cavity-enhanced transport of charge, Phys. Rev. Lett. 119, 223601 (2017).
  38. R. F. Ribeiro, A. D. Dunkelberger, B. Xiang, W. Xiong, B. S. Simpkins, J. C. Owrutsky, and J. Yuen-Zhou, Theory for nonlinear spectroscopy of vibrational polaritons, J. Phys. Chem. Lett. 9, 3766 (2018).
  39. B. Xiang, R. F. Ribeiro, A. D. Dunkelberger, J. Wang, Y. Li, B. S. Simpkins, J. C. Owrutsky, J. Yuen-Zhou, and W. Xiong, Two-dimensional infrared spectroscopy of vibrational polaritons, Proc. Natl. Acad. Sci. USA 115, 4845 (2018).
  40. Z. Zhang, X. Nie, D. Lei, and S. Mukamel, Multidimensional coherent spectroscopy of molecular polaritons: Langevin approach, Phys. Rev. Lett. 130, 103001 (2023).
  41. D. Gallego-Valencia, L. Mewes, J. Feist, and J. L. Sanz-Vicario, Coherent multidimensional spectroscopy in polariton systems, Phys. Rev. A 109, 063704 (2024).
  42. S. Mukamel, Principles of Nonlinear Optical Spectroscopy, Oxford Series in Optical and Imaging Sciences (Oxford University Press, New York, 1995), Vol. 6.
  43. H. K. Yadalam, S. Mukamel, and U. Harbola, Energy, particle, and photon fluxes in molecular junctions, J. Phys. Chem. Lett. 11, 1762 (2020).
  44. H. Sun, U. Harbola, S. Mukamel, and M. Galperin, Nonlinear optical spectroscopy of open quantum systems, J. Chem. Phys. 162, 074108 (2025).
  45. H. Sun, U. Harbola, S. Mukamel, and M. Galperin, Two-dimensional spectroscopy of open quantum systems: Nonequilibrium Green's function formulation, J. Phys. Chem. Lett. 16, 2008 (2025).
  46. N. E. Bickers, Review of techniques in the large-NNexpansion for dilute magnetic alloys, Rev. Mod. Phys. 59, 845 (1987).
  47. H. Aoki, N. Tsuji, M. Eckstein, M. Kollar, T. Oka, and P. Werner, Nonequilibrium dynamical mean-field theory and its applications, Rev. Mod. Phys. 86, 779 (2014).
  48. Y. Gao and M. Galperin, Optical spectroscopy of molecular junctions: Nonequilibrium Green's functions perspective, J. Chem. Phys. 144, 174113 (2016).
  49. S. Mukamel and M. Galperin, Flux-conserving diagrammatic formulation of optical spectroscopy of open quantum systems, J. Phys. Chem. C 123, 29015 (2019).
  50. D. Karlsson, R. van Leeuwen, Y. Pavlyukh, E. Perfetto, and G. Stefanucci, Fast Green's function method for ultrafast electron-boson dynamics, Phys. Rev. Lett. 127, 036402 (2021).
  51. N. S. Wingreen and Y. Meir, Anderson model out of equilibrium: Noncrossing-approximation approach to transport through a quantum dot, Phys. Rev. B 49, 11040 (1994).
  52. M. Eckstein and P. Werner, Nonequilibrium dynamical mean-field calculations based on the noncrossing approximation and its generalizations, Phys. Rev. B 82, 115115 (2010).
  53. A. Li, U. Harbola, and M. Galperin, Nonlinear spectroscopy of cavity polaritons, Zenodo, 2025, https://doi.org/10.5281/zenodo.15617698.
  54. H. Haug and A.-P. Jauho, in Quantum Kinetics in Transport and Optics of Semiconductors, 2nd rev. ed., edited by M. Cardona, P. Fulde, K. von Klitzing, and H.-J. Queisser, Springer Series in Solid-State Sciences Vol. 123 (Springer, Berlin, 2008).

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