Abstract
The ultrafast dynamics of electrons in solid-state systems have garnered considerable attention recently, driven by technological advancements in the generation of short laser pulses from femtosecond down to attosecond durations. Techniques such as high-order harmonic generation (HHG) and attosecond transient absorption and reflection spectroscopy (ATAS and ATRS) provide valuable insights into sub-cycle dynamics, rendering the interaction of solids with intense laser fields a pivotal area of research. However, discrepancies in the explanation of the underlying mechanisms remain, requiring further analysis. This Perspective focuses on the relationship between the above techniques, highlighting their efficacy in probing charge dynamics induced by intense laser pulses in solid-state systems. We emphasize the importance of unified theoretical frameworks to advance our understanding of the strong-field attoscience of solids, while recognizing points of disparity between theoretical descriptions and experimental findings. By drawing attention to the complementary nature of HHG and both ATAS and ATRS, and by illustrating the key applications enabled by them, this Perspective aims to motivate stronger collaborations and concerted efforts to bridge the existing gaps between theory and experiment and propel the field forward.
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References
Agostini, P., Fabre, F., Mainfray, G., Petite, G. & Rahman, N. K. Free–free transitions following six-photon ionization of xenon atoms. Phys. Rev. Lett. 42, 1127–1130 (1979).
Voronov, G. S. & Delone, N. B. Ionization of the xenon atom by the electric field of ruby laser emission. JETP Lett. 1, 66–68 (1965).
Voronov, G. S. & Delone, N. B. Many-photon ionization of the xenon atom by ruby laser radiation. Sov. Phys. JETP 23, 54–58 (1966).
Chin, S. L., Farkas, G. & Yergeau, F. Observation of Kr and Xe ions created by intense nanosecond CO2 laser pulses. J. Phys. B At. Mol. Opt. Phys. 16, L223 (1983).
Krause, J. L., Schafer, K. J. & Kulander, K. C. High-order harmonic generation from atoms and ions in the high intensity regime. Phys. Rev. Lett. 68, 3535–3538 (1992).
Lewenstein, M., Balcou, P., Ivanov, M. Y., L’Huillier, A. & Corkum, P. B. Theory of high-harmonic generation by low-frequency laser fields. Phys. Rev. A 49, 2117–2132 (1994).
Krausz, F. & Ivanov, M. Attosecond physics. Rev. Mod. Phys. 81, 163–234 (2009).
Drescher, M. et al. X-ray pulses approaching the attosecond frontier. Science 291, 1923–1927 (2001).
Antoine, P., L’Huillier, A. & Lewenstein, M. Attosecond pulse trains using high-order harmonics. Phys. Rev. Lett. 77, 1234–1237 (1996).
Paul, P. M. et al. Observation of a train of attosecond pulses from high harmonic generation. Science 292, 1689–1692 (2001).
Geneaux, R., Marroux, H. J. B., Guggenmos, A., Neumark, D. M. & Leone, S. R. Transient absorption spectroscopy using high harmonic generation: a review of ultrafast X-ray dynamics in molecules and solids. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 377, 20170463 (2019).
Ghimire, S. et al. Observation of high-order harmonic generation in a bulk crystal. Nat. Phys. 7, 138–141 (2011).
Luu, T. T. et al. Extreme ultraviolet high-harmonic spectroscopy of solids. Nature 521, 498–502 (2015).
Bauer, D. & Hansen, K. K. High-harmonic generation in solids with and without topological edge states. Phys. Rev. Lett. 120, 177401 (2018).
Garg, M., Kim, H. Y. & Goulielmakis, E. Ultimate waveform reproducibility of extreme-ultraviolet pulses by high-harmonic generation in quartz. Nat. Photonics 12, 291–296 (2018).
Schiffrin, A. et al. Optical-field-induced current in dielectrics. Nature 493, 70–74 (2013).
Schultze, M. et al. Controlling dielectrics with the electric field of light. Nature 493, 75–78 (2013).
Mashiko, H., Oguri, K., Yamaguchi, T., Suda, A. & Gotoh, H. Petahertz optical drive with wide-bandgap semiconductor. Nat. Phys. 12, 741–745 (2016).
Sommer, A. et al. Attosecond nonlinear polarization and light-matter energy transfer in solids. Nature 534, 86–90 (2016).
Garg, M. et al. Multi-petahertz electronic metrology. Nature 538, 359–363 (2016).
Higuchi, T., Heide, C., Ullmann, K., Weber, H. B. & Hommelhoff, P. Light-field-driven currents in graphene. Nature 550, 224–228 (2017).
Chen, L., Zhang, Y., Chen, G. & Franco, I. Stark control of electrons along nanojunctions. Nat. Commun. 9, 2070 (2018).
Ossiander, M. et al. The speed limit of optoelectronics. Nat. Commun. 13, 1620 (2022).
Gaynor, J. D. et al. Solid state core-exciton dynamics in NaCl observed by tabletop attosecond four-wave mixing spectroscopy. Phys. Rev. B 103, 245140 (2021).
Wang, Y. H., Steinberg, H., Jarillo-Herrero, P. & Gedik, N. Observation of Floquet-Bloch states on the surface of a topological insulator. Science 342, 453–457 (2013).
Goulielmakis, E. & Brabec, T. High harmonic generation in condensed matter. Nat. Photonics 16, 411–421 (2022).
Di Palo, N. et al. Attosecond absorption and reflection spectroscopy of solids. APL Photonics 9, 020901 (2024).
Ghimire, S. et al. Strong-field and attosecond physics in solids. J. Phys. B At. Mol. Opt. Phys. 47, 204030 (2014).
Li, J. et al. Attosecond science based on high harmonic generation from gases and solids. Nat. Commun. 11, 2748 (2020).
Golde, D., Meier, T. & Koch, S. W. High harmonics generated in semiconductor nanostructures by the coupled dynamics of optical inter- and intraband excitations. Phys. Rev. B 77, 075330 (2008).
Vampa, G. et al. Theoretical analysis of high-harmonic generation in solids. Phys. Rev. Lett. 113, 073901 (2014).
Jürgens, P. et al. Origin of strong-field-induced low-order harmonic generation in amorphous quartz. Nat. Phys. 16, 1035–1039 (2020).
Brunel, F. Harmonic generation due to plasma effects in a gas undergoing multiphoton ionization in the high-intensity limit. J. Opt. Soc. Am. B 7, 521–526 (1990).
Li, L. et al. Reciprocal-space-trajectory perspective on high-harmonic generation in solids. Phys. Rev. Lett. 122, 193901 (2019).
Pellegrini, C., Marinelli, A. & Reiche, S. The physics of X-ray free-electron lasers. Rev. Mod. Phys. 88, 015006 (2016).
Maroju, P. K. et al. Attosecond pulse shaping using a seeded free-electron laser. Nature 578, 386–391 (2020).
Duris, J. et al. Tunable isolated attosecond X-ray pulses with gigawatt peak power from a free-electron laser. Nat. Photonics 14, 30–36 (2020).
Malyzhenkov, A. et al. Single- and two-color attosecond hard X-ray free-electron laser pulses with nonlinear compression. Phys. Rev. Res. 2, 042018 (2020).
Guo, Z. et al. Experimental demonstration of attosecond pump-probe spectroscopy with an X-ray free-electron laser. Nat. Photonics 18, 691–697 (2024).
Agostini, P. & DiMauro, L. F. The physics of attosecond light pulses. Rep. Prog. Phys. 67, 813 (2004).
Lakhotia, H. et al. Laser picoscopy of valence electrons in solids. Nature 583, 55–59 (2020).
Vampa, G. et al. All-optical reconstruction of crystal band structure. Phys. Rev. Lett. 115, 193603 (2015).
You, Y. S., Cunningham, E., Reis, D. A. & Ghimire, S. Probing periodic potential of crystals via strong-field re-scattering. J. Phys. B At. Mol. Opt. Phys. 51, 114002 (2018).
Nefedova, V. E. et al. Enhanced extreme ultraviolet high-harmonic generation from chromium-doped magnesium oxide. Appl. Phys. Lett. 118, 201103 (2021).
Mrudul, M. S., Tancogne-Dejean, N., Rubio, A. & Dixit, G. High-harmonic generation from spin-polarised defects in solids. npj Comput. Mater. 6, 1–9 (2020).
Uzan, A. J. et al. Attosecond spectral singularities in solid-state high-harmonic generation. Nat. Photonics 14, 183–187 (2020).
Baykusheva, D. et al. All-optical probe of three-dimensional topological insulators based on high-harmonic generation by circularly polarized laser fields. Nano Lett. 21, 8970–8978 (2021).
Bai, Y. et al. High-harmonic generation from topological surface states. Nat. Phys. 17, 311–315 (2021).
Heide, C. et al. Probing topological phase transitions using high-harmonic generation. Nat. Photonics 16, 620–624 (2022).
Zürch, M. et al. Direct and simultaneous observation of ultrafast electron and hole dynamics in germanium. Nat. Commun. 8, 15734 (2017).
Jiang, C.-M. et al. Characterization of photo-induced charge transfer and hot carrier relaxation pathways in spinel cobalt oxide (Co3O4). J. Phys. Chem. C 118, 22774–22784 (2014).
Vura-Weis, J. et al. Femtosecond M2,3-edge spectroscopy of transition-metal oxides: photoinduced oxidation state change in α-Fe2O3. J. Phys. Chem. Lett. 4, 3667–3671 (2013).
Chang, H.-T. et al. Coupled valence carrier and core-exciton dynamics in WS2 probed by few-femtosecond extreme ultraviolet transient absorption spectroscopy. Phys. Rev. B 104, 064309 (2021).
Garratt, D. et al. Direct observation of ultrafast exciton localization in an organic semiconductor with soft X-ray transient absorption spectroscopy. Nat. Commun. 13, 3414 (2022).
Géneaux, R. et al. Attosecond time-domain measurement of core-level-exciton decay in magnesium oxide. Phys. Rev. Lett. 124, 207401 (2020).
Neufeld, O., Zhang, J., De Giovannini, U., Hübener, H. & Rubio, A. Probing phonon dynamics with multidimensional high harmonic carrier-envelope-phase spectroscopy. Proc. Natl Acad. Sci. USA 119, e2204219119 (2022).
Jager, M. F. et al. Tracking the insulator-to-metal phase transition in VO2 with few-femtosecond extreme UV transient absorption spectroscopy. Proc. Natl Acad. Sci. USA 114, 9558–9563 (2017).
Bionta, M. R. et al. Tracking ultrafast solid-state dynamics using high harmonic spectroscopy. Phys. Rev. Res. 3, 023250 (2021).
Morrison, V. R. et al. A photoinduced metal-like phase of monoclinic VO2 revealed by ultrafast electron diffraction. Science 346, 445–448 (2014).
Géneaux, R., Chang, H.-T., Schwartzberg, A. M. & Marroux, H. J. B. Source noise suppression in attosecond transient absorption spectroscopy by edge-pixel referencing. Opt. Express 29, 951–960 (2021).
Golde, D., Kira, M., Meier, T. & Koch, S. W. Microscopic theory of the extremely nonlinear terahertz response of semiconductors. Phys. Status Solidi B 248, 863–866 (2011).
Picón, A., Plaja, L. & Biegert, J. Attosecond X-ray transient absorption in condensed-matter: a core-state-resolved Bloch model. New J. Phys. 21, 043029 (2019).
Cistaro, G. et al. Theoretical approach for electron dynamics and ultrafast spectroscopy (EDUS). J. Chem. Theory Comput. 19, 333–348 (2023).
Yu, C., Hansen, K. K. & Madsen, L. B. Enhanced high-order harmonic generation in donor-doped band-gap materials. Phys. Rev. A 99, 013435 (2019).
Pemmaraju, C. D. Simulation of attosecond transient soft X-ray absorption in solids using generalized Kohn-Sham real-time time-dependent density functional theory. New J. Phys. 22, 083063 (2020).
Wu, M., Ghimire, S., Reis, D. A., Schafer, K. J. & Gaarde, M. B. High-harmonic generation from Bloch electrons in solids. Phys. Rev. A 91, 043839 (2015).
Jürß, H. & Bauer, D. High-harmonic generation in Su-Schrieffer-Heeger chains. Phys. Rev. B 99, 195428 (2019).
Yu, C., Iravani, H. & Madsen, L. B. Crystal-momentum-resolved contributions to multiple plateaus of high-order harmonic generation from band-gap materials. Phys. Rev. A 102, 033105 (2020).
Li, L., Lan, P., Zhu, X. & Lu, P. High harmonic generation in solids: particle and wave perspectives. Rep. Prog. Phys. 86, 116401 (2023).
Vampa, G., McDonald, C. R., Orlando, G., Corkum, P. B. & Brabec, T. Semiclassical analysis of high harmonic generation in bulk crystals. Phys. Rev. B 91, 064302 (2015).
Kohn, W. & Sham, L. J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133–A1138 (1965).
Silva, R. E. F., Martín, F. & Ivanov, M. High harmonic generation in crystals using maximally localized Wannier functions. Phys. Rev. B 100, 195201 (2019).
Yue, L. & Gaarde, M. B. Structure gauges and laser gauges for the semiconductor Bloch equations in high-order harmonic generation in solids. Phys. Rev. A 101, 053411 (2020).
Yue, L. & Gaarde, M. B. Introduction to theory of high-harmonic generation in solids: tutorial. J. Opt. Soc. Am. B 39, 535 (2022).
Houston, W. V. Acceleration of electrons in a crystal lattice. Phys. Rev. 57, 184–186 (1940).
Krieger, J. B. & Iafrate, G. J. Time evolution of Bloch electrons in a homogeneous electric field. Phys. Rev. B 33, 5494–5500 (1986).
Yue, L. & Gaarde, M. B. Imperfect recollisions in high-harmonic generation in solids. Phys. Rev. Lett. 124, 153204 (2020).
Wannier, G. H. The structure of electronic excitation levels in insulating crystals. Phys. Rev. 52, 191–197 (1937).
Marzari, N., Mostofi, A. A., Yates, J. R., Souza, I. & Vanderbilt, D. Maximally localized Wannier functions: theory and applications. Rev. Mod. Phys. 84, 1419–1475 (2012).
Parks, A. M. et al. Wannier quasi-classical approach to high harmonic generation in semiconductors. Optica 7, 1764 (2020).
Osika, E. N. et al. Wannier-Bloch approach to localization in high-harmonics generation in solids. Phys. Rev. X 7, 021017 (2017).
Brown, G. G., Jiménez-Galán, A., Silva, R. E. F. & Ivanov, M, Real-space perspective on dephasing in solid-state high harmonic generation. Phys. Rev. Res. 6, 043005 (2024).
Vampa, G. et al. Linking high harmonics from gases and solids. Nature 522, 462–464 (2015).
Hohenleutner, M. et al. Real-time observation of interfering crystal electrons in high-harmonic generation. Nature 523, 572–575 (2015).
Huttner, U., Schuh, K., Moloney, J. V. & Koch, S. W. Similarities and differences between high-harmonic generation in atoms and solids. J. Opt. Soc. Am. B 33, C22 (2016).
Schubert, O. et al. Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations. Nat. Photonics 8, 119–123 (2014).
Higuchi, T., Stockman, M. I. & Hommelhoff, P. Strong-field perspective on high-harmonic radiation from bulk solids. Phys. Rev. Lett. 113, 213901 (2014).
McDonald, C. R., Vampa, G., Corkum, P. B. & Brabec, T. Interband Bloch oscillation mechanism for high-harmonic generation in semiconductor crystals. Phys. Rev. A 92, 033845 (2015).
Thorpe, A., Boroumand, N., Parks, A. M., Goulielmakis, E. & Brabec, T. High harmonic generation in solids: real versus virtual transition channels. Phys. Rev. B 107, 075135 (2023).
Moulet, A. et al. Soft X-ray excitonics. Science 357, 1134–1138 (2017).
Schultze, M. et al. Attosecond band-gap dynamics in silicon. Science 346, 1348–1352 (2014).
Lucchini, M. et al. Attosecond dynamical Franz-Keldysh effect in polycrystalline diamond. Science 353, 916–919 (2016).
Schlaepfer, F. et al. Attosecond optical-field-enhanced carrier injection into the GaAs conduction band. Nat. Phys. 14, 560–564 (2018).
Mashiko, H. et al. Multi-petahertz electron interference in Cr:Al2O3 solid-state material. Nat. Commun. 9, 1468 (2018).
Buades, B. et al. Attosecond state-resolved carrier motion in quantum materials probed by soft X-ray XANES. Appl. Phys. Rev. 8, 011408 (2021).
Volkov, M. et al. Floquet-Bloch resonances in near-petahertz electroabsorption spectroscopy of SiO2. Phys. Rev. B 107, 184304 (2023).
Inzani, G. et al. Field-driven attosecond charge dynamics in germanium. Nat. Photonics 17, 1059–1065 (2023).
Lucchini, M. et al. Unravelling the intertwined atomic and bulk nature of localised excitons by attosecond spectroscopy. Nat. Commun. 12, 1021 (2021).
Kobayashi, Y. et al. Floquet engineering of strongly driven excitons in monolayer tungsten disulfide. Nat. Phys. 19, 171–176 (2023).
Jensen, S. V. B., Madsen, L. B., Rubio, A. & Tancogne-Dejean, N. High-harmonic spectroscopy of strongly bound excitons in solids. Phys. Rev. A 109, 063104 (2024).
Portella, M. T., Bigot, J.-Y., Schoenlein, R. W., Cunningham, J. E. & Shank, C. V. k-space carrier dynamics in GaAs. Appl. Phys. Lett. 60, 2123–2125 (1992).
Waldermann, F. C. et al. Measuring phonon dephasing with ultrafast pulses using Raman spectral interference. Phys. Rev. B 78, 155201 (2008).
Orlando, G., Ho, T.-S. & Chu, S.-I. Macroscopic effects on high-order harmonic generation in disordered semiconductors. J. Opt. Soc. Am. B 36, 1873 (2019).
Luu, T. T. & Wörner, H. J. High-order harmonic generation in solids: a unifying approach. Phys. Rev. B 94, 115164 (2016).
Brown, G. G., Jiménez-Galán, A., Silva, R. E. F. & Ivanov, M. Ultrafast dephasing in solid-state high-harmonic generation: macroscopic origin revealed by real-space dynamics. J. Opt. Soc. Am. B 41, B40–B46 (2024).
Abadie, C. Q., Wu, M. & Gaarde, M. B. Spatiotemporal filtering of high harmonics in solids. Opt. Lett. 43, 5339 (2018).
Floss, I. et al. Ab initio multiscale simulation of high-order harmonic generation in solids. Phys. Rev. A 97, 011401 (2018).
Navarrete, F., Ciappina, M. F. & Thumm, U. Crystal-momentum-resolved contributions to high-order harmonic generation in solids. Phys. Rev. A 100, 033405 (2019).
Vampa, G. et al. Attosecond synchronization of extreme ultraviolet high harmonics from crystals. J. Phys. B At. Mol. Opt. Phys. 53, 144003 (2020).
Jeong, T.-I. et al. Deterministic nanoantenna array design for stable plasmon-enhanced harmonic generation. Nanophotonics 12, 619–629 (2023).
Butet, J., Brevet, P.-F. & Martin, O. J. F. Optical second harmonic generation in plasmonic nanostructures: from fundamental principles to advanced applications. ACS Nano 9, 10545–10562 (2015).
Kim, K.-H., Husakou, A. & Herrmann, J. High-order harmonic generation employing field enhancement by metallic fractal rough surfaces. Opt. Express 19, 20910–20915 (2011).
Wu, X.-Y., Liang, H., Kong, X.-S., Gong, Q. & Peng, L.-Y. Enhancement of high-order harmonic generation in two-dimensional materials by plasmonic fields. Phys. Rev. A 103, 043117 (2021).
Vampa, G. et al. Plasmon-enhanced high-harmonic generation from silicon. Nat. Phys. 13, 659–662 (2017).
Cox, J. D., Marini, A. & de Abajo, F. J. G. Plasmon-assisted high-harmonic generation in graphene. Nat. Commun. 8, 14380 (2017).
Han, S. et al. High-harmonic generation by field enhanced femtosecond pulses in metal-sapphire nanostructure. Nat. Commun. 7, 13105 (2016).
Han, S. High-harmonic generation using a single dielectric nanostructure. Photonics 9, 427 (2022).
Liu, H. et al. Enhanced high-harmonic generation from an all-dielectric metasurface. NaPhys. 14, 1006–1010 (2018).
Ciappina, M. F. et al. Attosecond physics at the nanoscale. Rep. Prog. Phys. 80, 054401 (2017).
Pattanayak, A., S, M. M. & Dixit, G. Influence of vacancy defects in solid high-order harmonic generation. Phys. Rev. A 101, 013404 (2020).
Iravani, H., Hansen, K. K. & Madsen, L. B. Effects of vacancies on high-order harmonic generation in a linear chain with band gap. Phys. Rev. Res. 2, 013204 (2020).
Queisser, H. J. & Haller, E. E. Defects in semiconductors: some fatal, some vital. Science 281, 945–950 (1998).
Vines, L., Monakhov, E. & Kuznetsov, A. Defects in semiconductors. J. Appl. Phys. 132, 150401 (2022).
Coutinho, J., Markevich, V. P. & Peaker, A. R. Characterisation of negative-U defects in semiconductors. J. Condens. Matter Phys. 32, 323001 (2020).
Tuomisto, F. (ed.) Characterisation and Control of Defects in Semiconductors (IET, 2019).
Xu, S. et al. The defect-state-assisted enhancement of high harmonic generation in bulk ZnO. Appl. Phys. Lett. 122, 182105 (2023).
Summers, A. M. et al. Realizing attosecond core-level X-ray spectroscopy for the investigation of condensed matter systems. Ultrafast Sci. 3, 0004 (2023).
Azoury, D. et al. Electronic wavefunctions probed by all-optical attosecond interferometry. Nat. Photonics 13, 54–59 (2019).
Knowles, K. E., Koch, M. D. & Shelton, J. L. Three applications of ultrafast transient absorption spectroscopy of semiconductor thin films: spectroelectrochemistry, microscopy, and identification of thermal contributions. J. Mater. Chem. C 6, 11853–11867 (2018).
Keimer, B. & Moore, J. E. The physics of quantum materials. Nat. Phys. 13, 1045–1055 (2017).
Zong, A., Nebgen, B. R., Lin, S.-C., Spies, J. A. & Zuerch, M. Emerging ultrafast techniques for studying quantum materials. Nat. Rev. Mater. 8, 224–240 (2023).
Bowlan, P., Martinez-Moreno, E., Reimann, K., Elsaesser, T. & Woerner, M. Ultrafast terahertz response of multilayer graphene in the nonperturbative regime. Phys. Rev. B 89, 041408 (2014).
Yoshikawa, N., Tamaya, T. & Tanaka, K. High-harmonic generation in graphene enhanced by elliptically polarized light excitation. Science 356, 736–738 (2017).
Zhang, Y. et al. Orientation dependence of high-order harmonic generation in graphene. Phys. Rev. A 104, 033110 (2021).
Mrudul, M. S. & Dixit, G. High-harmonic generation from monolayer and bilayer graphene. Phys. Rev. B 103, 094308 (2021).
Feng, Y. et al. Semiclassical analysis of ellipticity dependence of harmonic yield in graphene. Phys. Rev. A 104, 043525 (2021).
Murakami, Y., Eckstein, M. & Werner, P. High-harmonic generation in Mott insulators. Phys. Rev. Lett. 121, 057405 (2018).
Silva, R. E. F., Jiménez-Galán, A., Amorim, B., Smirnova, O. & Ivanov, M. Topological strong-field physics on sub-laser-cycle timescale. Nat. Photonics 13, 849–854 (2019).
Chacón, A. et al. Circular dichroism in higher-order harmonic generation: heralding topological phases and transitions in Chern insulators. Phys. Rev. B 102, 134115 (2020).
Schmid, C. P. et al. Tunable non-integer high-harmonic generation in a topological insulator. Nature 593, 385–390 (2021).
Pattanayak, A., Pujari, S. & Dixit, G. Role of Majorana fermions in high-harmonic generation from Kitaev chain. Sci. Rep. 12, 6722 (2022).
Baldelli, N., Bhattacharya, U., González-Cuadra, D., Lewenstein, M. & Graß, T. Detecting Majorana zero modes via strong field dynamics. ACS Omega 7, 47424–47430 (2022).
Silva, R. E. F., Blinov, I. V., Rubtsov, A. N., Smirnova, O. & Ivanov, M. High-harmonic spectroscopy of ultrafast many-body dynamics in strongly correlated systems. Nat. Photonics 12, 266–270 (2018).
Roy, A., Bera, S. & Saha, K. Nonlinear dynamical response of interacting bosons to synthetic electric field. Phys. Rev. Res. 2, 043133 (2020).
Uchida, K. et al. High-order harmonic generation and its unconventional scaling law in the Mott-insulating Ca2RuO4. Phys. Rev. Lett. 128, 127401 (2022).
Murakami, Y., Uchida, K., Koga, A., Tanaka, K. & Werner, P. Anomalous temperature dependence of high-harmonic generation in Mott insulators. Phys. Rev. Lett. 129, 157401 (2022).
Alcalà, J. et al. High-harmonic spectroscopy of quantum phase transitions in a high-Tc superconductor. Proc. Natl Acad. Sci. USA 119, e2207766119 (2022).
Cistaro, G., Plaja, L., Martín, F. & Picón, A. Attosecond X-ray transient absorption spectroscopy in graphene. Phys. Rev. Res. 3, 013144 (2021).
Shao, Z., Cao, X., Luo, H. & Jin, P. Recent progress in the phase-transition mechanism and modulation of vanadium dioxide materials. NPG Asia Mater. 10, 581–605 (2018).
Sala, S., Förster, J. & Saenz, A. Ultracold-atom quantum simulator for attosecond science. Phys. Rev. A 95, 011403 (2017).
Senaratne, R. et al. Quantum simulation of ultrafast dynamics using trapped ultracold atoms. Nat. Commun. 9, 2065 (2018).
Argüello-Luengo, J. et al. Analog simulation of high-harmonic generation in atoms. PRX Quantum 5, 010328 (2024).
Kolesik, M. & Moloney, J. V. Numerical discreteness and dephasing in high-harmonic calculations in solids. Phys. Rev. B 108, 115433 (2023).
Borsch, M., Meierhofer, M., Huber, R. & Kira, M. Lightwave electronics in condensed matter. Nat. Rev. Mater. 8, 668–687 (2023).
Emelina, A. S., Emelin, M. Y. & Ryabikin, M. Y. Wavelength scaling laws for high-order harmonic yield from atoms driven by mid- and long-wave infrared laser fields. J. Opt. Soc. Am. B 36, 3236–3245 (2019).
Wan, Z. et al. Wavelength scaling of high harmonic yields and cutoff energies in solids driven by mid-infrared pulses. Opt. Express 31, 30294–30304 (2023).
Hassan, M. T. et al. Optical attosecond pulses and tracking the nonlinear response of bound electrons. Nature 530, 66–70 (2016).
Chini, M., Zhao, K. & Chang, Z. The generation, characterization and applications of broadband isolated attosecond pulses. Nat. Photonics 8, 178–186 (2014).
Li, B. et al. Resonance-enhanced solid high-order harmonic generation by a chirped laser pulse. Opt. Commun. 511, 128020 (2022).
Zhong, S. et al. High harmonic generation and application for photoemission spectroscopy in condensed matter. Mater. Futures 1, 032201 (2022).
Weissenbilder, R. et al. How to optimize high-order harmonic generation in gases. Nat. Rev. Phys. 4, 713–722 (2022).
Klas, R. et al. Ultra-short-pulse high-average-power megahertz-repetition-rate coherent extreme-ultraviolet light source. PhotoniX 2, 4 (2021).
Comby, A. et al. Cascaded harmonic generation from a fiber laser: a milliwatt XUV source. Opt. Express 27, 20383–20396 (2019).
Park, J., Subramani, A., Kim, S. & Ciappina, M. F. Recent trends in high-order harmonic generation in solids. Adv. Phys. X 7, 2003244 (2022).
Lu, J., Cunningham, E. F., You, Y. S., Reis, D. A. & Ghimire, S. Interferometry of dipole phase in high harmonics from solids. Nat. Photonics 13, 96–100 (2019).
Yang, Y. et al. High-harmonic generation from an epsilon-near-zero material. Nat. Phys. 15, 1022–1026 (2019).
Yang, H. et al. High-harmonic generation in polycrystalline CdTe nano-films via macroscopic investigations. Opt. Express 30, 47733–47743 (2022).
Kaplan, C. J. et al. Femtosecond tracking of carrier relaxation in germanium with extreme ultraviolet transient reflectivity. Phys. Rev. B 97, 205202 (2018).
Xia, P. et al. Nonlinear propagation effects in high harmonic generation in reflection and transmission from gallium arsenide. Opt. Express 26, 29393–29400 (2018).
Leshchenko, V. et al. Kramers-Kronig relation in attosecond transient absorption spectroscopy. Optica 10, 142–146 (2023).
Brahms, C., Belli, F. & Travers, J. C. Resonant dispersive wave emission in hollow capillary fibers filled with pressure gradients. Opt. Lett. 45, 4456–4459 (2020).
Catoire, F. et al. Complex structure of spatially resolved high-order-harmonic spectra. Phys. Rev. A 94, 063401 (2016).
Ghimire, S. & Reis, D. A. High-harmonic generation from solids. Nat. Phys. 15, 10–16 (2019).
Higley, D. J. et al. Femtosecond X-ray induced changes of the electronic and magnetic response of solids from electron redistribution. Nat. Commun. 10, 1–9 (2019).
Kohrell, F. et al. A solid-state high harmonic generation spectrometer with cryogenic cooling. Rev. Sci. Instrum. 95, 023906 (2024).
Han, Y.-C. & Madsen, L. B. Comparison between length and velocity gauges in quantum simulations of high-order harmonic generation. Phys. Rev. A 81, 063430 (2010).
Runge, E. & Gross, E. K. U. Density-functional theory for time-dependent systems. Phys. Rev. Lett. 52, 997–1000 (1984).
Sundaram, B. & Milonni, P. W. High-order harmonic generation: simplified model and relevance of single-atom theories to experiment. Phys. Rev. A 41, 6571–6573 (1990).
Wu, M., Chen, S., Camp, S., Schafer, K. J. & Gaarde, M. B. Theory of strong-field attosecond transient absorption. J. Phys. B At. Mol. Opt. Phys. 49, 062003 (2016).
Acknowledgements
The authors express their gratitude to C.F.d.M. Faria and the organizers of the Quantum Battles in Attoscience 2023 (particularly to K. Hamilton and L. Rodríguez) at the University College of London for bringing them together and providing the opportunity to present their perspectives on the attoscience of solids. S.M.C. acknowledges support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant TReSFiDS No. 886092. K.M.K. acknowledges PhD funding from the Royal Society URF/R1/191759. F.O.N. gratefully acknowledges funding by the German Research Foundation, SFB 1477 ‘Light-Matter Interactions at Interfaces’, project number 441234705. J.R.-D. acknowledges support from the Secretaria d’Universitats i Recerca del Departament d’Empresa i Coneixement de la Generalitat de Catalunya, the European Social Fund (L’FSE inverteix en el teu futur)–FEDER, the Government of Spain (Severo Ochoa CEX2019-000910-S and TRANQI), Fundació Cellex, Fundació Mir-Puig, Generalitat de Catalunya (CERCA programme) and the ERC AdG CERQUTE.
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Cavaletto, S.M., Kowalczyk, K.M., Navarrete, F.O. et al. The attoscience of strong-field-driven solids. Nat Rev Phys 7, 38–49 (2025). https://doi.org/10.1038/s42254-024-00784-3
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DOI: https://doi.org/10.1038/s42254-024-00784-3


