- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Disentangling Electronic and Ionic Nonlinear Polarization Effects in Bulk THz Kerr Response

Chao Shen1, Maximilian Frenzel2, Sebastian F. Maehrlein2,3,4, and Zhanybek Alpichshev1,*

  • *Contact author: alpishev@ist.ac.at
PDF

Phys. Rev. Lett. 136, 106901 – Published 9 March, 2026

DOI: https://doi.org/10.1103/1c5k-9z82

Abstract

Terahertz (THz) spectroscopy is a powerful probe of low-energy excitations in complex materials. Extending it into the nonlinear regime broadens its scope and can provide valuable insight into interactions among these modes. However, interpreting nonlinear spectra is challenging because resonant features in this case do not always reflect intrinsic material dynamics. Here, we study nonlinear THz-induced Kerr effect in a generic material LaAlO3. After detailed analysis of temporal oscillations of the Kerr signal, we identify an Eg Raman mode at 1.1 THz excited through a two-photon process, while two additional peaks (0.86 and 0.36 THz) arise from phase matching of the near-infrared probe beam with co- and counterpropagating THz pump fields, mediated by off-resonant electronic hyperpolarizability. These results demonstrate the crucial role of kinematic effects in shaping THz-induced Kerr response and establish a framework for interpreting nonlinear spectroscopies in complex materials.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (29)

  1. M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, J. Lu et al., Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial, Nature (London) 487, 345 (2012).
  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. S. Pal, N. Strkalj, C.-J. Yang, M. C. Weber, M. Trassin, M. Woerner, and M. Fiebig, Origin of terahertz soft-mode nonlinearities in ferroelectric perovskites, Phys. Rev. X 11, 021023 (2021).
  4. B. Song, X. Yang, C. Sundahl, J.-H. Kang, M. Mootz, Y. Yao, I. Perakis, L. Luo, C. Eom, and J. Wang, Ultrafast martensitic phase transition driven by intense terahertz pulses, Ultrafast Science 3, 0007 (2023).
  5. M. Basini, M. Pancaldi, B. Wehinger, M. Udina, V. Unikandanunni, T. Tadano, M. Hoffmann, A. Balatsky, and S. Bonetti, Terahertz electric-field-driven dynamical multiferroicity in SrTiO3, Nature (London) 628, 534 (2024).
  6. C. L. Johnson, B. E. Knighton, and J. A. Johnson, Distinguishing nonlinear terahertz excitation pathways with two-dimensional spectroscopy, Phys. Rev. Lett. 122, 073901 (2019).
  7. H.-W. Lin, G. Mead, and G. A. Blake, Mapping LiNbO3 phonon-polariton nonlinearities with 2D THz-THz-Raman spectroscopy, Phys. Rev. Lett. 129, 207401 (2022).
  8. T. G. H. Blank, K. A. Grishunin, K. A. Zvezdin, N. T. Hai, J. C. Wu, S.-H. Su, J.-C. A. Huang, A. K. Zvezdin, and A. V. Kimel, Two-dimensional terahertz spectroscopy of nonlinear phononics in the topological insulator MnBi2Te4, Phys. Rev. Lett. 131, 026902 (2023).
  9. Z. Zhang, J. Zhang, Z.-J. Liu, N. S. Dahod, W. Paritmongkol, N. Brown, A. Stollmann, W. S. Lee, Y.-C. Chien, Z. Dai, K. A. Nelson, W. A. Tisdale, A. M. Rappe, and E. Baldini, Discovery of enhanced lattice dynamics in a single-layered hybrid perovskite, Sci. Adv. 9, eadg4417 (2023).
  10. O. Minakova, C. Paiva, M. Frenzel, M. S. Spencer, J. M. Urban, C. Ringkamp, M. Wolf, G. Mussler, D. M. Juraschek, and S. F. Maehrlein, Direct observation of angular momentum transfer among crystal lattice modes, arXiv:2503.11626.
  11. M. Frenzel, M. Cherasse, J. M. Urban, F. Wang, B. Xiang, L. Nest, L. Huber, L. Perfetti, M. Wolf, T. Kampfrath et al., Nonlinear terahertz control of the lead halide perovskite lattice, Sci. Adv. 9, eadg3856 (2023).
  12. See Supplemental Material at http://link.aps.org/supplemental/10.1103/1c5k-9z82 for (1) the experimental setup, (2) details of sample, (3) simulation details of four-wave mixing of the 2D-TKE signal, (4) analytical treatment of THz Kerr effect, and (5) simulation details of Eg Raman phonon, which includes Ref. [13].
  13. S. F. Maehrlein, P. P. Joshi, L. Huber, F. Wang, M. Cherasse, Y. Liu, D. M. Juraschek, E. Mosconi, D. Meggiolaro, F. De Angelis et al., Decoding ultrafast polarization responses in lead halide perovskites by the two-dimensional optical Kerr effect, Proc. Natl. Acad. Sci. U.S.A. 118, e2022268118 (2021).
  14. S. Kovalev, C. Zhu, A. Reinold, M. Koch, Z. Wang, P. Pilch, A. Ghalgaoui, S. Duan, C. Li, J. Zhang et al., Terahertz electro-optic Kerr effect in LaAlO3, Opt. Lett. 50, 762 (2025).
  15. M. Basini, V. Unikandanunni, F. Gabriele, M. Cross, A. Derrico, A. Gray, M. Hoffmann, F. Forte, M. Cuoco, and S. Bonetti, Terahertz-driven parametric excitation of Raman-active phonons in LaAlO3, arXiv:2410.06748.
  16. J. Hebling, G. Almasi, I. Z. Kozma, and J. Kuhl, Velocity matching by pulse front tilting for large-area THz-pulse generation, Opt. Express 10, 1161 (2002).
  17. H. Hirori, A. Doi, F. Blanchard, and K. Tanaka, Single-cycle terahertz pulses with amplitudes exceeding 1  MV/cm generated by optical rectification in LiNbO3, Appl. Phys. Lett. 98, 091106 (2011).
  18. E. K. Salje, M. Alexe, S. Kustov, M. C. Weber, J. Schiemer, G. F. Nataf, and J. Kreisel, Direct observation of polar tweed in LaAlO3, Sci. Rep. 6, 27193 (2016).
  19. C. M. Nelson, M. Spies, L. S. Abdallah, S. Zollner, Y. Xu, and H. Luo, Dielectric function of LaAlO3 from 0.8 to 6 eV between 77 and 700 K, J. Vac. Sci. Technol. A 30, 061404 (2012).
  20. M. S. Spencer, J. M. Urban, M. Frenzel, N. S. Mueller, O. Minakova, M. Wolf, A. Paarmann, and S. F. Maehrlein, Electro-optic cavities for in-situ measurement of cavity fields, Light 14, 69 (2025).
  21. J. M. Urban, M. S. Spencer, M. Frenzel, G. Trippé-Allard, M. Cherasse, C. Berrezueta-Palacios, P. P. Joshi, A. P. Fellows, O. Minakova, E. B. Barros, L. Perfetti, S. Reich, M. Wolf, E. Deleporte, and S. F. Maehrlein, THz-driven coherent phonon fingerprints of hidden symmetry breaking in 2D layered hybrid perovskites, Adv. Mater. 38, e02204 (2026).
  22. J. Lu, X. Li, H. Y. Hwang, B. K. Ofori-Okai, T. Kurihara, T. Suemoto, and K. A. Nelson, Coherent two-dimensional terahertz magnetic resonance spectroscopy of collective spin waves, Phys. Rev. Lett. 118, 207204 (2017).
  23. C. Shen, C. Verdi, S. Babkin, M. Serbyn, and Z. Alpichshev, Nonlinear terahertz polaritonics in a quantum paraelectric, arXiv:2507.19358.
  24. L. Huber, S. F. Maehrlein, F. Wang, Y. Liu, and X.-Y. Zhu, The ultrafast Kerr effect in anisotropic and dispersive media, J. Chem. Phys. 154, 094202 (2021).
  25. D. M. Juraschek and S. F. Maehrlein, Sum-frequency ionic Raman scattering, Phys. Rev. B 97, 174302 (2018).
  26. S. Maehrlein, A. Paarmann, M. Wolf, and T. Kampfrath, Terahertz sum-frequency excitation of a Raman-active phonon, Phys. Rev. Lett. 119, 127402 (2017).
  27. G. Khalsa, N. A. Benedek, and J. Moses, Ultrafast control of material optical properties via the infrared resonant Raman effect, Phys. Rev. X 11, 021067 (2021).
  28. M. V. Abrashev, A. P. Litvinchuk, M. N. Iliev, R. L. Meng, V. N. Popov, V. G. Ivanov, R. A. Chakalov, and C. Thomsen, Comparative study of optical phonons in the rhombohedrally distorted perovskites LaAlO3 and LaMnO3, Phys. Rev. B 59, 4146 (1999).
  29. X. Li, P. Peng, H. Dammak, G. Geneste, A. Akbarzadeh, S. Prosandeev, L. Bellaiche, and D. Talbayev, Terahertz pulse induced second harmonic generation and Kerr effect in the quantum paraelectric KTaO3, Phys. Rev. B 107, 064306 (2023).

Outline

Information

Phys. Rev. Lett. 136, 106901– Published 9 March, 2026
  • Received 12 June 2025
  • Accepted 3 February 2026
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation