Theory of coherent-oscillations generation in terahertz pump-probe spectroscopy: From phonons to electronic collective modes
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Time-resolved spectroscopies using intense THz pulses appear as a promising tool to address collective electronic excitations in condensed matter. In particular, recent experiments showed the possibility to selectively excite collective modes emerging across a phase transition, as is the case for superconducting and charge-density-wave (CDW) systems. One possible signature of these excitations is the emergence of coherent oscillations of the differential probe field in pump-probe protocols. While the analogy with the case of phonon modes suggests that the basic underlying mechanism should be a sum-frequency stimulated Raman process, a general theoretical scheme able to describe the experiments and to define the relevant optical quantity is still lacking. Here we provide this scheme by showing that coherent oscillations as a function of the pump-probe time delay can be linked to the convolution in the frequency domain between the squared pump field and a Raman-like nonlinear optical kernel. This approach is applied and discussed in a few paradigmatic examples: ordinary phonons in an insulator, and collective charge and Higgs fluctuations across a superconducting and a CDW transition. Our results not only account very well for the existing experimental data in a wide variety of systems, but they also offer a useful perspective to design future experiments in emerging materials.
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Two peaks of comparable amplitudes are expected when accounting for the electronic nonlinear response associated with χ(3), namely the third-order susceptibility tensor.
“Two peaks of comparable amplitudes are, on the other hand, expected when accounting for the electronic nonlinear response associated with χ(3), namely the third-order susceptibility tensor22.”
From Terahertz electric-field-driven dynamical multiferroicity in SrTiO3 (2024) · cites this paper as [22]
Section I (page unavailable) describes the nonlinear electronic current as controlled by a third-order tensor, supporting the χ(3) characterization. It also identifies peaks in the squared pump-field spectrum, but does not predict that two peaks in the electronic nonlinear response have comparable amplitudes; their response depends on the nonlinear kernel and resonance conditions. (LLM, conf=0.85)
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Grasset, R., Katsumi, K., Massat, P., Wen, H., Chen, X., Gallais, Y., & Shimano, R. (2022) · npj Quantum Materials · doi:10.1038/s41535-021-00411-9 · Cited by 21 · see citing works
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THz non-linear optical response in cuprates: predominance of the BCS response over the Higgs mode
Udina, M., Fiore, J., Cea, T., Castellani, C., Seibold, G., & Benfatto, L. (2022) · Faraday Discussions · doi:10.1039/d2fd00016d · Cited by 19 · see citing works
Self-citationCurrent-assisted Raman activation of the Higgs mode in superconductors
Puviani, M. B., Schwarz, L., Zhang, X.-X., Kaiser, S., & Manske, D. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.101.220507 · Cited by 17 · see citing works
Perspective on Terahertz Applications of Molecular Crystals
Sinko, A. S., Ozheredov, I. A., Rudneva, E. B., Львовна, М. В., Kozlova, N. N., Lobova, N., Voloshin, A. E., Coutaz, J., & Shkurinov, A. P. (2022) · Electronics · doi:10.3390/electronics11172731 · Cited by 16 · see citing works
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Self-citationTerahertz ionic Kerr effect: Two-phonon contribution to the nonlinear optical response in insulators
Basini, M., Udina, M., Pancaldi, M., Unikandanunni, V., Bonetti, S., & Benfatto, L. (2024) · Physical Review B · doi:10.1103/physrevb.109.024309 · Cited by 14 · see citing works
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Properties and challenges of hot-phonon physics in metals: MgB2 and other compounds
Cappelluti, E., Caruso, F., & Novko, D. (2022) · Progress in Surface Science · doi:10.1016/j.progsurf.2022.100664 · Cited by 13 · see citing works
Quench-drive spectroscopy and high-harmonic generation in BCS superconductors
Puviani, M. B., Haenel, R., & Manske, D. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.107.094501 · Cited by 13 · see citing works
Terahertz electric-field driven dynamical multiferroicity in SrTiO$_3$
Basini, M., Pancaldi, M., Wehinger, B., Udina, M., Tadano, T., Hoffmann, M. C., Balatsky, A. V., & Bonetti, S. (2022) · Institutional Repositories DataBase (IRDB) · doi:10.48550/arxiv.2210.01690 · Cited by 12 · see citing works
Self-citationInvestigating Josephson plasmons in layered cuprates via nonlinear terahertz spectroscopy
Fiore, J., Sellati, N., Gabriele, F., Castellani, C., Seibold, G., Udina, M., & Benfatto, L. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.l060504 · Cited by 12 · see citing works
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Nonequilibrium dynamics from BCS to the bosonic limit
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Allerbeck, J., Deckert, T., & Brida, D. (2025) · Ultrafast Science · doi:10.34133/ultrafastscience.0095 · Cited by 10 · see citing works
Dispersion of optical constants of Si:PbGeO crystal in the terahertz range
Bilyk, V. R., Brekhov, K. A., Agranat, M. B., & Мишина, Е. Д. (2023) · Russian Technological Journal · doi:10.32362/2500-316x-2023-11-3-38-45 · Cited by 9 · see citing works
Chirped amplitude mode in photoexcited superconductors
Blommel, T., Kaye, J., Murakami, Y., Gull, E., & Golež, D. (2025) · Physical review. B./Physical review. B · doi:10.1103/physrevb.111.094502 · Cited by 8 · see citing works
Optical second harmonic generation: role of symmetry and local resonances (review)
Михайловна, Б. И., Dolgova, T. V., Kolmychek, I. A., Maydykovskiy, A. I., Мишина, Е. Д., Murzina, T. V., & Fedyanin, A. A. (2022) · Quantum Electronics · doi:10.1070/qel18037 · Cited by 8 · see citing works
Terahertz 2D coherent spectroscopy for probing and controlling multicorrelations in quantum matter
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Ferroelectric switching by (sub)-picosecond electromagnetic pulse
Мишина, Е. Д., Bilyk, V. R., Sherstyuk, N. É., & Sigov, A. S. (2021) · Ferroelectrics · doi:10.1080/00150193.2021.1916345 · Cited by 6 · see citing works
Dynamical phase transition in a strongly hybridized phonon-triplon chain
Yarmohammadi, M. (2025) · Physical review. B./Physical review. B · doi:10.1103/c3tb-h5hv · Cited by 5 · see citing works
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Selective Excitation of Collective Modes in Multiband Superconductor MgB 2
Yuan, J., Shi, L. Y., Xu, T., Wang, Y., Gan, Z., Wang, H., Wu, T., Wu, D., Dong, T., & Wang, N. (2025) · Physical Review Letters · doi:10.1103/b5h4-ppdf · Cited by 4 · see citing works
Adiabatic transition from a BCS superconductor to a Fermi liquid and phase dynamics
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Ultrafast excitation and topological soliton formation in incommensurate charge density wave states
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Udina, M., & Paul, I. (2026) · Physical Review Letters · doi:10.1103/gnpt-5ffq · Cited by 1 · see citing works
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Measuring intrinsic relaxation rates in superconductors using nonlinear response
Tseng, W.-E., & Nandkishore, R. (2026) · Physical review. B./Physical review. B · doi:10.1103/3j2n-tvvr
Two-dimensional terahertz spectroscopy in electronic systems: A many-body diagrammatic approach
Fiore, J., Sellati, N., Udina, M., & Benfatto, L. (2026) · Physical review. B./Physical review. B · doi:10.1103/8ffz-rtyf
Self-citationResonant chiral dressing by amplitude fluctuations in a ferroaxial electronic crystal
Barantani, F., Peng, X., Boström, E. V., Gao, F. Y., You, W., Klein, P., Glier, T. E., Fava, S., Kim, D., Shin, D., et al. (2026) · Nature Physics · doi:10.1038/s41567-026-03241-3
Self-citationSuperconductivity mediated by nematic fluctuations: The dispersion of collective modes
Anonymous, & Chubukov, A. V. (2026) · Physical review. B./Physical review. B · doi:10.1103/dn6s-8b5y
- Authors
- Udina, M., Cea, T., & Benfatto, L.
- Affiliations
- Sapienza University of Rome (IT)
- IMDEA Nanoscience (ES)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2019-10-17
- Volume
- 100
- Issue
- 16
- ISSN
- 2469-9950 (ISSN-L)
- 2469-9969
- OpenAlex
- W2961109485
- Cited by
- 55
- References
- 77
- Citations by year
- 2026: 7 · 2025: 5 · 2024: 10 · 2023: 4 · 2022: 11 · 2021: 10 · 2020: 7 · 2019: 1
- FWCI
- 2.61
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical review. B./Physical review. B (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- IRIS Research product catalog (Sapienza University of Rome) (submittedVersion, other-oa)
- Archivio Istituzionale della Ricerca - Università degli Studi dell Aquila (submittedVersion)
- arXiv (Cornell University)
- Funders
- Ministero degli Affari Esteri e della Cooperazione Internazionale (PGR04879)
- Ministero dell’Istruzione, dell’Università e della Ricerca (PRIN 2017Z8TS5B)
- European Commission (CNECTICT-604391)
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Terahertz technology and applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Laser-Matter Interactions and Applications
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Physics of Superconductivity and Magnetism
- Keywords
- coherent oscillations, collective electronic excitations, phonons, superconducting transition, charge-density-wave transition, charge fluctuations, phase transitions, time-resolved spectroscopy
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