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  • Open Access

Multicolor Phonon Excitation in Terahertz Cavities

Omer Yaniv1,* and Dominik M. Juraschek1,2,†

  • *Contact author: yaniv@mail.tau.ac.il
  • †Contact author: d.m.juraschek@tue.nl
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Phys. Rev. Lett. 135, 246901 – Published 9 December, 2025

DOI: https://doi.org/10.1103/fwr7-6jj6

Abstract

Driving materials using light with more than one frequency component is an emerging technique, enabled by advanced pulse-shaping capabilities in recent years. Here, we translate this technique to lattice vibrations by exciting multicolor phonons using terahertz cavities. In contrast to light, phonon frequencies are determined by the crystal structure and cannot readily be changed. We overcome this problem by tuning the frequencies of phonon polaritons in terahertz cavities to achieve the desired frequency ratios necessary for phononic Lissajous figures. This methodology enables dynamical crystallographic symmetry breaking and the creation of staggered phonon angular momentum and magnetic moment patterns.

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References (61)

  1. T. Nova, A. Disa, M. Fechner, and A. Cavalleri, Metastable ferroelectricity in optically strained SrTiO3, Science 364, 1075 (2019).
  2. X. Li, T. Qiu, J. Zhang, E. Baldini, J. Lu, A. M. Rappe, and K. A. Nelson, Terahertz field–induced ferroelectricity in quantum paraelectric SrTiO3, Science 364, 1079 (2019).
  3. M. Henstridge, M. Först, E. Rowe, M. Fechner, and A. Cavalleri, Nonlocal nonlinear phononics, Nat. Phys. 18, 457 (2022).
  4. M. Kwaaitaal, D. G. Lourens, C. S. Davies, and A. Kirilyuk, Epsilon-near-zero regime as the key to ultrafast control of functional properties of solids, arXiv:2305.11714.
  5. A. S. Disa, M. Fechner, T. F. Nova, B. Liu, M. Först, D. Prabhakaran, P. G. Radaelli, and A. Cavalleri, Polarizing an antiferromagnet by optical engineering of the crystal field, Nat. Phys. 16, 937 (2020).
  6. D. Afanasiev, J. R. Hortensius, B. A. Ivanov, A. Sasani, E. Bousquet, Y. M. Blanter, R. V. Mikhaylovskiy, A. V. Kimel, and A. D. Caviglia, Ultrafast control of magnetic interactions via light-driven phonons, Nat. Mater. 20, 607 (2021).
  7. A. Stupakiewicz, C. S. Davies, K. Szerenos, D. Afanasiev, K. S. Rabinovich, A. V. Boris, A. Caviglia, A. V. Kimel, and A. Kirilyuk, Ultrafast phononic switching of magnetization, Nat. Phys. 17, 489 (2021).
  8. A. S. Disa, J. Curtis, M. Fechner, A. Liu, A. Hoegen, M. Först, T. F. Nova, P. Narang, A. Maljuk, A. V. Boris, B. Keimer, and A. Cavalleri, Photo-induced high-temperature ferromagnetism in YTiO3, Nature (London) 617, 73 (2023).
  9. M. Mitrano, A. Cantaluppi, D. Nicoletti, S. Kaiser, A. Perucchi, S. Lupi, P. Di Pietro, D. Pontiroli, M. Riccò, S. R. Clark, D. Jaksch, and A. Cavalleri, Possible light-induced superconductivity in K3C60 at high temperature, Nature (London) 530, 461 (2016).
  10. S. Fava, G. De Vecchi, G. Jotzu, M. Buzzi, T. Gebert, Y. Liu, B. Keimer, and A. Cavalleri, Magnetic field expulsion in optically driven YBa2Cu3O6.48, Nature (London) 632, 75 (2024).
  11. T. F. Nova, A. Cartella, A. Cantaluppi, M. Först, D. Bossini, R. V. Mikhaylovskiy, A. V. Kimel, R. Merlin, and A. Cavalleri, An effective magnetic field from optically driven phonons, Nat. Phys. 13, 132 (2017).
  12. D. M. Juraschek, M. Fechner, A. V. Balatsky, and N. A. Spaldin, Dynamical multiferroicity, Phys. Rev. Mater. 1, 014401 (2017).
  13. D. M. Juraschek and N. A. Spaldin, Orbital magnetic moments of phonons, Phys. Rev. Mater. 3, 064405 (2019).
  14. R. M. Geilhufe, V. Juričić, S. Bonetti, J.-X. Zhu, and A. V. Balatsky, Dynamically induced magnetism in KTaO3, Phys. Rev. Res. 3, L022011 (2021).
  15. D. M. Juraschek, T. Neuman, and P. Narang, Giant effective magnetic fields from optically driven chiral phonons in 4f paramagnets, Phys. Rev. Res. 4, 013129 (2022).
  16. J. Luo, T. Lin, J. Zhang, X. Chen, E. R. Blackert, R. Xu, B. I. Yakobson, and H. Zhu, Large effective magnetic fields from chiral phonons in rare-earth halides, Science 382, 698 (2023).
  17. M. Basini, M. Pancaldi, B. Wehinger, M. Udina, V. Unikandanunni, T. Tadano, M. C. Hoffmann, A. V. Balatsky, and S. Bonetti, Terahertz electric-field driven dynamical multiferroicity in SrTiO3, Nature (London) 628, 534 (2024).
  18. C. S. Davies, F. G. N. Fennema, A. Tsukamoto, I. Razdolski, A. V. Kimel, and A. Kirilyuk, Phononic switching of magnetization by the ultrafast Barnett effect, Nature (London) 628, 540 (2024).
  19. D. Shin, H. Hübener, U. De Giovannini, H. Jin, A. Rubio, and N. Park, Phonon-driven spin-Floquet magneto-valleytronics in MoS2, Nat. Commun. 9, 638 (2018).
  20. H. Hübener, U. De Giovannini, and A. Rubio, Phonon driven Floquet matter, Nano Lett. 18, 1535 (2018).
  21. S. Chaudhary, A. Haim, Y. Peng, and G. Refael, Phonon-induced Floquet topological phases protected by space-time symmetries, Phys. Rev. Res. 2, 043431 (2020).
  22. T. Oka and H. Aoki, Photovoltaic Hall effect in graphene, Phys. Rev. B 79, 081406(R) (2009).
  23. Y. H. Wang, H. Steinberg, P. Jarillo-Herrero, and N. Gedik, Observation of Floquet-Bloch states on the surface of a topological insulator, Science 342, 453 (2013).
  24. T. Oka and S. Kitamura, Floquet engineering of quantum materials, Annu. Rev. Condens. Matter Phys. 10, 387 (2019).
  25. O. Neufeld, D. Podolsky, and O. Cohen, Floquet group theory and its application to selection rules in harmonic generation, Nat. Commun. 10, 405 (2019).
  26. O. Neufeld, N. Tancogne-Dejean, U. De Giovannini, H. Hübener, and A. Rubio, Light-driven extremely nonlinear bulk photogalvanic currents, Phys. Rev. Lett. 127, 126601 (2021).
  27. K. Sandholzer, A. S. Walter, J. Minguzzi, Z. Zhu, K. Viebahn, and T. Esslinger, Floquet engineering of individual band gaps in an optical lattice using a two-tone drive, Phys. Rev. Res. 4, 013056 (2022).
  28. A. Castro, U. De Giovannini, S. A. Sato, H. Hübener, and A. Rubio, Floquet engineering the band structure of materials with optimal control theory, Phys. Rev. Res. 4, 033213 (2022).
  29. Y. Wang, A. S. Walter, G. Jotzu, and K. Viebahn, Topological Floquet engineering using two frequencies in two dimensions, Phys. Rev. A 107, 043309 (2023).
  30. P. Strobel and M. Daghofer, From linear to circular polarized light: Floquet engineering in Kitaev-Heisenberg materials with Lissajous figures, Phys. Rev. B 108, 035132 (2023).
  31. Y. Murakami, M. Schüler, R. Arita, and P. Werner, Suppression of heating by multicolor driving protocols in Floquet-engineered strongly correlated systems, Phys. Rev. B 108, 035151 (2023).
  32. Y. Chen, Z. Zhu, and K. Viebahn, Mitigating higher-band heating in Floquet-Hubbard lattices via two-tone driving, arXiv:2410.12308.
  33. Y. Chen, A. Elben, A. Rubio, and G. Refael, Bosonic entanglement and quantum sensing from energy transfer in two-tone Floquet systems, Phys. Rev. Res. 7, 043014 (2025).
  34. R. Peña, F. Torres, and G. Romero, Steering spin fluctuations in lattice systems via two-tone Floquet engineering, Phys. Scr. 100, 015122 (2025).
  35. O. Neufeld, Degree of time-reversal and dynamical symmetry breaking in electromagnetic fields and its connection to Floquet engineering, ACS Photonics 12, 2151 (2025).
  36. M. A. Sentef, M. Ruggenthaler, and A. Rubio, Cavity quantum-electrodynamical polaritonically enhanced electron-phonon coupling and its influence on superconductivity, Sci. Adv. 4, eaau6969 (2018).
  37. Y. Ashida, A. Imamoglu, J. Faist, D. Jaksch, A. Cavalleri, and E. Demler, Quantum electrodynamic control of matter: Cavity-enhanced ferroelectric phase transition, Phys. Rev. X 10, 041027 (2020).
  38. G. Jarc, S. Y. Mathengattil, F. Giusti, M. Barnaba, A. Singh, A. Montanaro, F. Glerean, E. M. Rigoni, S. D. Zilio, S. Winnerl, and D. Fausti, Tunable cryogenic terahertz cavity for strong light–matter coupling in complex materials, Rev. Sci. Instrum. 93, 033102 (2022).
  39. D. M. Juraschek, T. Neuman, J. Flick, and P. Narang, Cavity control of nonlinear phononics, Phys. Rev. Res. 3, L032046 (2021).
  40. R. A. Evarestov and A. V. Bandura, First-principles calculations on the four phases of BaTiO3, J. Comput. Chem. 33, 1123 (2012).
  41. G. Kresse and J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6, 15 (1996).
  42. G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
  43. A. Togo, L. Chaput, and I. Tanaka, Distributions of phonon lifetimes in Brillouin zones, Phys. Rev. B 91, 094306 (2015).
  44. H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13, 5188 (1976).
  45. G. I. Csonka, J. P. Perdew, A. Ruzsinszky, P. H. T. Philipsen, S. Lebègue, J. Paier, O. A. Vydrov, and J. G. Ángyán, Assessing the performance of recent density functionals for bulk solids, Phys. Rev. B 79, 155107 (2009).
  46. I. B. Ouni, D. Chapron, H. Aroui, and M. D. Fontana, Thermal behavior of high-frequency optical phonons in tetragonal BaTiO3 single crystal, Appl. Phys. A 122, 480 (2016).
  47. See Supplemental Material at http://link.aps.org/supplemental/10.1103/fwr7-6jj6 for a view of the phonon eigenvectors along the c axis; a derivation of the cavity phonon polariton branches; extended polariton dispersion; Lissajous figures in phonon amplitude, polarization, and real space; discussion of multicolor phonons from branches 3 and 4; and Lissajous figures of other frequency ratios.
  48. Y. Ren, C. Xiao, D. Saparov, and Q. Niu, Phonon magnetic moment from electronic topological magnetization, Phys. Rev. Lett. 127, 186403 (2021).
  49. D. Saparov, B. Xiong, Y. Ren, and Q. Niu, Lattice dynamics with molecular Berry curvature: Chiral optical phonons, Phys. Rev. B 105, 064303 (2022).
  50. R. M. Geilhufe and W. Hergert, Electron magnetic moment of transient chiral phonons in KTaO3, Phys. Rev. B 107, L020406 (2023).
  51. X.-W. Zhang, Y. Ren, C. Wang, T. Cao, and D. Xiao, Gate-tunable phonon magnetic moment in bilayer graphene, Phys. Rev. Lett. 130, 226302 (2023).
  52. J. Bonini, S. Ren, D. Vanderbilt, M. Stengel, C. E. Dreyer, and S. Coh, Frequency splitting of chiral phonons from broken time-reversal symmetry in CrI3, Phys. Rev. Lett. 130, 086701 (2023).
  53. N. Shabala and R. M. Geilhufe, Phonon inverse Faraday effect from electron-phonon coupling, Phys. Rev. Lett. 133, 266702 (2024).
  54. L. Klebl, A. Schobert, M. Eckstein, G. Sangiovanni, A. V. Balatsky, and T. O. Wehling, Ultrafast pseudomagnetic fields from electron-nuclear quantum geometry, Phys. Rev. Lett. 134, 016705 (2025).
  55. S. Chaudhary, D. M. Juraschek, M. Rodriguez-Vega, and G. A. Fiete, Giant effective magnetic moments of chiral phonons from orbit-lattice coupling, Phys. Rev. B 110, 094401 (2024).
  56. W. Chen, X.-W. Zhang, Y. Su, T. Cao, D. Xiao, and S.-Z. Lin, Gauge theory of giant phonon magnetic moment in doped Dirac semimetals, Phys. Rev. B 111, 035126 (2025).
  57. H. P. Ojeda Collado, M. H. Michael, J. Skulte, A. Rubio, and L. Mathey, Equilibrium parametric amplification in Raman-cavity hybrids, Phys. Rev. Lett. 133, 116901 (2024).
  58. E. V. Boström, M. H. Michael, C. Eckhardt, and A. Rubio, Equilibrium non-linear phononics by electric field fluctuations of terahertz cavities, arXiv:2409.19063.
  59. H. Hübener, U. D. Giovannini, C. Schäfer, J. Andberger, M. Ruggenthaler, J. Faist, and A. Rubio, Engineering quantum materials with chiral optical cavities, Nat. Mater. 20, 438 (2021).
  60. F. Schlawin, D. M. Kennes, and M. A. Sentef, Cavity quantum materials, Appl. Phys. Rev. 9, 011312 (2022).
  61. O. Yaniv and D. M. Juraschek, Multicolor phonon excitation in terahertz cavities, Zenodo, 10.5281/zenodo.17571335 (2025).

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Phys. Rev. Lett. 135, 246901– Published 9 December, 2025
  • Received 23 April 2025
  • Accepted 27 October 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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