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Ultrafast high-harmonic spectroscopy of solids

Nature Physics volume 20, pages 1546–1557 (2024)Cite this article

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Abstract

High-harmonic spectroscopy, an ultrafast all-optical technique initially conceptualized in atomic and molecular systems, has now emerged as a powerful platform for studying the structure and dynamics of condensed matter. Unlike that in the gas phase, solid-state high-harmonic generation relies on the fundamental response from high atomic density and periodicity, leading to interband transitions and coherent driving of electrons and holes in their respective bands. These mechanisms make high-harmonic spectroscopy particularly sensitive to the electronic band structure, topological properties and many-body correlations in condensed media. An advantage of high-harmonic spectroscopy over other spectroscopic methods is its ability to probe ultrafast phenomena, capturing femto- to attosecond dynamics of multi-band and strongly correlated electron interactions in solids. In this Review, we discuss the latest experimental and theoretical advances in ultrafast high-harmonic spectroscopy of solids and provide perspectives for future research in this field.

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Fig. 1: Overview of ultrafast HHS.
Fig. 2: Microscopic mechanism of HHG in momentum space.
Fig. 3: HHG from 2D materials.
Fig. 4: Probing topologically protected materials.
Fig. 5: HHG in strongly correlated materials.
Fig. 6: Time-resolved HHS.

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References

  1. McPherson, A. et al. Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases. J. Opt. Soc. Am. B 4, 595–601 (1987).

    ADS  Google Scholar 

  2. Ferray, M. et al. Multiple-harmonic conversion of 1064 nm radiation in rare gases. J. Phys. B 21, L31–L35 (1988).

    Google Scholar 

  3. Hentschel, M. et al. Attosecond metrology. Nature 414, 509–513 (2001).

    ADS  Google Scholar 

  4. Paul, P. M. et al. Observation of a train of attosecond pulses from high harmonic generation. Science 292, 1689–1692 (2001).

    ADS  Google Scholar 

  5. Corkum, P. B. Plasma perspective on strong field multiphoton ionization. Phys. Rev. Lett. 71, 1994–1997 (1993).

    ADS  Google Scholar 

  6. Itatani, J. et al. Tomographic imaging of molecular orbitals. Nature 432, 867–871 (2004).

    ADS  Google Scholar 

  7. Wörner, H. J. et al. Charge migration and charge transfer in molecular systems. Struct. Dyn. 4, 061508 (2017).

    Google Scholar 

  8. Ghimire, S. & Reis, D. A. High-harmonic generation from solids. Nat. Phys. 15, 10–16 (2019).

    Google Scholar 

  9. Goulielmakis, E. & Brabec, T. High harmonic generation in condensed matter. Nat. Photon. 16, 411–421 (2022).

    ADS  Google Scholar 

  10. Ghimire, S. et al. Observation of high-order harmonic generation in a bulk crystal. Nat. Phys. 7, 138–141 (2011).

    Google Scholar 

  11. Vampa, G. et al. Theoretical analysis of high-harmonic generation in solids. Phys. Rev. Lett. 113, 073901 (2014).

    ADS  Google Scholar 

  12. Schubert, O. et al. Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations. Nat. Photon. 8, 119–123 (2014).

    ADS  Google Scholar 

  13. Luu, T. T. et al. Extreme ultraviolet high-harmonic spectroscopy of solids. Nature 521, 498–502 (2015).

    ADS  Google Scholar 

  14. 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).

    ADS  Google Scholar 

  15. Vampa, G. et al. All-optical reconstruction of crystal band structure. Phys. Rev. Lett. 115, 193603 (2015).

    ADS  Google Scholar 

  16. Uzan-Narovlansky, A. J. et al. Observation of interband Berry phase in laser-driven crystals. Nature 626, 66–71 (2024).

    ADS  Google Scholar 

  17. Heide, C. et al. Probing electron-hole coherence in strongly driven 2D materials using high-harmonic generation. Optica 9, 512–516 (2022).

    ADS  Google Scholar 

  18. You, Y. S., Reis, D. A. & Ghimire, S. Anisotropic high-harmonic generation in bulk crystals. Nat. Phys. 13, 345–349 (2016).

    Google Scholar 

  19. You, Y. S. et al. High-harmonic generation in amorphous solids. Nat. Commun. 8, 724 (2017).

    ADS  Google Scholar 

  20. Lakhotia, H. et al. Laser picoscopy of valence electrons in solids. Nature 583, 55–59 (2020).

    ADS  Google Scholar 

  21. Morimoto, Y. et al. Asymmetric single-cycle control of valence electron motion in polar chemical bonds. Optica 8, 382 (2021).

    ADS  Google Scholar 

  22. Liu, H. et al. High-harmonic generation from an atomically thin semiconductor. Nat. Phys. 13, 262–265 (2017).

    ADS  Google Scholar 

  23. Yoshikawa, N., Tamaya, T. & Tanaka, K. High-harmonic generation in graphene enhanced by elliptically polarized light excitation. Science 356, 736–738 (2017).

    ADS  MathSciNet  Google Scholar 

  24. Kruchinin, S. Y., Krausz, F. & Yakovlev, V. S. Colloquium: strong-field phenomena in periodic systems. Rev. Mod. Phys. 90, 21002 (2018).

    MathSciNet  Google Scholar 

  25. Heide C., Boolakee, T., Higuchi, T. & Hommelhoff, P. Adiabaticity parameters for the categorization of light–matter interaction: from weak to strong driving. Phys. Rev. A https://doi.org/10.1103/physreva.104.023103 (2021).

  26. Ndabashimiye, G. et al. Solid-state harmonics beyond the atomic limit. Nature 534, 520–523 (2016).

    ADS  Google Scholar 

  27. Yue, L. & Gaarde, M. B. Introduction to theory of high-harmonic generation in solids: tutorial. J. Opt. Soc. Am. B 39, 535–555 (2022).

    ADS  Google Scholar 

  28. Uzan-Narovlansky, A. J. et al. Observation of light-driven band structure via multiband high-harmonic spectroscopy. Nat. Photon. 16, 428–432 (2022).

    ADS  Google Scholar 

  29. Luu, T. T. & Wörner, H. J. Measurement of the Berry curvature of solids using high-harmonic spectroscopy. Nat. Commun. 9, 916 (2018).

    ADS  Google Scholar 

  30. Bai, Y. et al. High-harmonic generation from topological surface states. Nat. Phys. 17, 311–315 (2021).

    Google Scholar 

  31. Baykusheva, D. et al. Strong-field physics in three-dimensional topological insulators. Phys. Rev. A 103, 23101 (2021).

    ADS  Google Scholar 

  32. 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).

    ADS  Google Scholar 

  33. Schmid, C. P. et al. Tunable non-integer high-order harmonic generation in a topological insulator. Nature 593, 385–390 (2021).

    ADS  Google Scholar 

  34. Heide, C. et al. Probing topological phase transitions using high-harmonic generation. Nat. Photonics 16, 620–624 (2022).

    ADS  Google Scholar 

  35. Neufeld, O., Tancogne-Dejean, N., Hübener, H., De Giovannini, U. & Rubio, A. Are there universal signatures of topological phases in high-harmonic generation? Probably not. Phys. Rev. 13, 31011 (2023).

    Google Scholar 

  36. Jürß, C. & Bauer, D. Helicity flip of high-order harmonic photons in Haldane nanoribbons. Phys. Rev. A 102, 043105 (2020).

    ADS  Google Scholar 

  37. 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).

    ADS  Google Scholar 

  38. Silva, R. E. F., Jiménez-Galán, Á., Amorim, B., Smirnova, O. & Ivanov, M. Topological strong-field physics on sub-laser-cycle timescale. Nat. Photon. 13, 849–854 (2019).

    ADS  Google Scholar 

  39. 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. Photon. 12, 266 (2018).

    ADS  Google Scholar 

  40. Tancogne-Dejean, N., Sentef, M. A. & Rubio, A. Ultrafast modification of Hubbard U in a strongly correlated material: ab initio high-harmonic generation in NiO. Phys. Rev. Lett. 121, 097402 (2018).

    ADS  Google Scholar 

  41. Imai, S., Ono, A. & Ishihara, S. High harmonic generation in a correlated electron system. Phys. Rev. Lett. 124, 157404 (2020).

    ADS  Google Scholar 

  42. Shao, C. et al. High-harmonic generation approaching quantum critical point of strongly correlated systems. Phys. Rev. Lett. 128, 047401 (2022).

    ADS  Google Scholar 

  43. Pizzi, A., Gorlach, A., Rivera, N., Nunnenkamp, A. & Kaminer, I. Light emission from strongly driven many-body systems. Nat. Phys. 19, 551–561 (2023).

    Google Scholar 

  44. Zhang, J. et al. High-harmonic spectroscopy probes lattice dynamics. Nat. Photon. https://doi.org/10.1038/s41566-024-01457-4 (2024).

    Article  Google Scholar 

  45. Mondal, A. et al. High-harmonic spectroscopy of low-energy electron-scattering dynamics in liquids. Nat. Phys. 19, 1813–1820 (2023).

    Google Scholar 

  46. Chang, Z. et al. Intense infrared lasers for strong-field science. Adv. Opt. Photon. 14, 652–782 (2022).

    Google Scholar 

  47. Vampa, G. et al. Linking high harmonics from gases and solids. Nature 522, 462–464 (2015).

    ADS  Google Scholar 

  48. You, Y. S. et al. Laser waveform control of extreme ultraviolet high harmonics from solids. Opt. Lett. 42, 1816–1819 (2017).

    ADS  Google Scholar 

  49. 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).

    ADS  Google Scholar 

  50. Tancogne-Dejean, N., Eich, F. & Rubio, A. Effect of spin–orbit coupling on the high harmonics from the topological Dirac semimetal Na3Bi. npj Comput. Mater. 8, 145 (2022).

    ADS  Google Scholar 

  51. Reislöhner, J., Kim, D., Babushkin, I. & Pfeiffer, A. N. Onset of Bloch oscillations in the almost-strong-field regime. Nat. Commun. 13, 7716 (2022).

    ADS  Google Scholar 

  52. Li, L., Lan, P., Zhu, X. & Lu, P. Huygens–Fresnel picture for high harmonic generation in solids. Phys. Rev. Lett. 127, 223201 (2021).

    ADS  Google Scholar 

  53. Qian, C. et al. Role of shift vector in high-harmonic generation from noncentrosymmetric topological insulators under strong laser fields. Phys. Rev. X 12, 021030 (2022).

    Google Scholar 

  54. Yue, L. & Gaarde, M. B. Characterizing anomalous high-harmonic generation in solids. Phys. Rev. Lett. 130, 166903 (2023).

    ADS  Google Scholar 

  55. Uzan-Narovlansky, A. J. et al. Revealing the interplay between strong field selection rules and crystal symmetries. Phys. Rev. Lett. 131, 223802 (2023).

    ADS  Google Scholar 

  56. Yue, L. & Gaarde, M. B. Imperfect recollisions in high-harmonic generation in solids. Phys. Rev. Lett. 124, 153204 (2020).

    ADS  Google Scholar 

  57. Brown, G. G., Jiménez-Galán, Á., Silva, R. E. F. & Ivanov, M. Ultrafast dephasing in solid-state high harmonic generation: macroscopic origin revealed by real-space dynamics [invited]. J. Opt. Soc. Am. B 41, B40 (2024).

    Google Scholar 

  58. 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).

    Google Scholar 

  59. Floss, I. et al. Ab initio multiscale simulation of high-order harmonic generation in solids. Phys. Rev. A 97, 011401 (2018).

    ADS  Google Scholar 

  60. Xia, P. et al. Nonlinear propagation effects in high harmonic generation in reflection and transmission from gallium arsenide. Opt. Express 26, 29393 (2018).

    ADS  Google Scholar 

  61. Heide, C. et al. High-harmonic generation from artificially stacked 2D crystals. Nanophotonics 12, 255–261 (2023).

    Google Scholar 

  62. Yamada, S., Otobe, T., Freeman, D., Kheifets, A. & Yabana, K. Propagation effects in high-harmonic generation from dielectric thin films. Phys. Rev. B https://doi.org/10.1103/physrevb.107.035132 (2023).

  63. Lu, J., Cunningham, E. F., You, Y. S., Reis, D. A. & Ghimire, S. Interferometry of dipole phase in high harmonics from solids. Nat. Photon. 13, 96–100 (2019).

    ADS  Google Scholar 

  64. Mak, K. F., Lee, C., Hone, J., Shan, J. & Heinz, T. F. Atomically thin MoS2: a new direct-gap semiconductor. Phys. Rev. Lett. 105, 136805 (2010).

    ADS  Google Scholar 

  65. Raja, A. et al. Coulomb engineering of the bandgap and excitons in two-dimensional materials. Nat. Commun. 8, 15251 (2017).

    ADS  Google Scholar 

  66. Bolotin, K. I., Ghahari, F., Shulman, M. D., Stormer, H. L. & Kim, P. Observation of the fractional quantum Hall effect in graphene. Nature 462, 196–199 (2009).

    ADS  Google Scholar 

  67. Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005).

    ADS  Google Scholar 

  68. Xie, H. et al. Evidence of non-collinear spin texture in magnetic moiré superlattices. Nat. Phys. 19, 1150–1155 (2023).

    Google Scholar 

  69. Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).

    ADS  Google Scholar 

  70. Kobayashi, Y., et al. Polarization flipping of even-order harmonics in monolayer transition-metal dichalcogenides. Ultrafast Sci. https://doi.org/10.34133/2021/9820716 (2021).

  71. Udono, M., Sugimoto, K., Kaneko, T. & Ohta, Y. Excitonic effects on high-harmonic generation in Mott insulators. Phys. Rev. B 105, L241108 (2022).

    ADS  Google Scholar 

  72. Kobayashi, Y. et al. Floquet engineering of strongly driven excitons in monolayer tungsten disulfide. Nat. Phys. 19, 171–176 (2023).

    Google Scholar 

  73. Barré, E. et al. Optical absorption of interlayer excitons in transition-metal dichalcogenide heterostructures. Science 376, 406–410 (2022).

    ADS  Google Scholar 

  74. Molinero, E. B., Datta, A., Calderón, M. J., Bascones, E. & Silva, R. E. F. High-harmonic generation with a twist: all-optical characterization of magic-angle twisted bilayer graphene. Optica 11, 171–175 (2024).

    ADS  Google Scholar 

  75. Shi, J. et al. Giant room-temperature nonlinearities in a monolayer Janus topological semiconductor. Nat. Commun. 14, 4953 (2023).

    ADS  Google Scholar 

  76. Baudisch, M. et al. Ultrafast nonlinear optical response of Dirac fermions in graphene. Nat. Commun. 9, 1018 (2018).

    ADS  Google Scholar 

  77. Sato, S. A., Hirori, H., Sanari, Y., Kanemitsu, Y. & Rubio, A. High-order harmonic generation in graphene: nonlinear coupling of intraband and interband transitions. Phys. Rev. B 103, L041408 (2021).

    ADS  Google Scholar 

  78. Liu, C., Zheng, Y., Zeng, Z. & Li, R. Driving-laser ellipticity dependence of high-order harmonic generation in graphene. Phys. Rev. A 97, 063412 (2018).

    ADS  Google Scholar 

  79. Du, T.-Y. & Ma, C. Temperature-induced dephasing in high-order harmonic generation from solids. Phys. Rev. A 105, 053125 (2022).

    ADS  Google Scholar 

  80. Cha, S. et al. Gate-tunable quantum pathways of high harmonic generation in graphene. Nat. Commun. 13, 6630 (2022).

    ADS  Google Scholar 

  81. Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).

    ADS  Google Scholar 

  82. Reimann, J. et al. Subcycle observation of lightwave-driven Dirac currents in a topological surface band. Nature 562, 396–400 (2018).

    ADS  Google Scholar 

  83. Soifer, H. et al. Band-resolved imaging of photocurrent in a topological insulator. Phys. Rev. Lett. 122, 167401 (2019).

    ADS  Google Scholar 

  84. Bauer, D. & Hansen, K. K. High-harmonic generation in solids with and without topological edge states. Phys. Rev. Lett. 120, 177401 (2018).

    ADS  Google Scholar 

  85. Graml, M., Nitsch, M., Seith, A., Evers, F. & Wilhelm, J. Influence of chirp and carrier-envelope phase on noninteger high-harmonic generation. Phys. Rev. B 107, 054305 (2023).

    ADS  Google Scholar 

  86. Brahlek, M. et al. Topological-metal to band-insulator transition in (Bi1−xInx)2Se3 thin films. Phys. Rev. Lett. 109, 186403 (2012).

    ADS  Google Scholar 

  87. Lv, Y.-Y. et al. High-harmonic generation in Weyl semimetal β-WP2 crystals. Nat. Commun. 12, 6437 (2021).

    ADS  Google Scholar 

  88. Basov, D. N., Averitt, R. D. & Hsieh, D. Towards properties on demand in quantum materials. Nat. Mater. 16, 1077–1088 (2017).

    ADS  Google Scholar 

  89. Basov, D. N., Averitt, R. D., van der Marel, D., Dressel, M. & Haule, K. Electrodynamics of correlated electron materials. Rev. Mod. Phys. 83, 471–541 (2011).

    ADS  Google Scholar 

  90. Lv, Y. Y. et al. Solid-state high harmonic spectroscopy for all-optical band structure probing of high-pressure quantum states. Proc. Natl Acad. Sci. USA 12, e2316775121 (2021).

    Google Scholar 

  91. Kraus, P. M., Zürch, M., Cushing, S. K., Neumark, D. M. & Leone, S. R. The ultrafast X-ray spectroscopic revolution in chemical dynamics. Nat. Rev. Chem. 2, 82–94 (2018).

    Google Scholar 

  92. Neufeld, O. & Cohen, O. Probing ultrafast electron correlations in high harmonic generation. Phys. Rev. Res. 2, 033037 (2023).

    Google Scholar 

  93. Alam, D., Ud Din, N., Chini, M. & Turkowski, V. Electron–electron interactions and high-order harmonics in solids. Phys. Rev. B 106, 235124 (2022).

    ADS  Google Scholar 

  94. Orthodoxou, C., Zäir, A. & Booth, G. H. High harmonic generation in two-dimensional Mott insulators. npj Quantum Mater. 6, 76 (2021).

    ADS  Google Scholar 

  95. Baykusheva, D. R. et al. Ultrafast renormalization of the on-site Coulomb repulsion in a cuprate superconductor. Phys. Rev. X 12, 011013 (2022).

    Google Scholar 

  96. Álcala, J., Bhattacharya, U. & Biegert, J. High-harmonic spectroscopy of quantum phase transition in a high-Tc superconductor. Proc. Natl Acad. Sci. USA 119, e2207766119 (2022).

    Google Scholar 

  97. 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).

    ADS  Google Scholar 

  98. Uchida, K. et al. High-order harmonic generation and its unconventional scaling law in the Mott-insulating Ca2RuO4. Phys. Rev. Lett. 128, 127401 (2022).

    ADS  Google Scholar 

  99. Murakami, Y., Eckstein, M. & Werner, P. High-harmonic generation in Mott insulators. Phys. Rev. Lett. 121, 57405 (2018).

    ADS  Google Scholar 

  100. Murakami, Y. & Werner, P. Nonequilibrium steady states of electric field driven Mott insulators. Phys. Rev. B 98, 075102 (2018).

    ADS  Google Scholar 

  101. Kofuji, A. & Peters, R. Unconventional gap dependence of high-order harmonic generation in the extremely strong light–matter-coupling regime. Phys. Rev. A 108, 023521 (2023).

    ADS  Google Scholar 

  102. Valmispild, V. N. et al. Sub-cycle multidimensional spectroscopy of strongly correlated materials. Nat. Photon. 18, 432–439 (2024).

    ADS  Google Scholar 

  103. Wang, Y. et al. Optical control of high-harmonic generation at the atomic thickness. Nano Lett. 22, 8455–8462 (2022).

    ADS  Google Scholar 

  104. Peterka, P. et al. High harmonic generation in monolayer MoS2 controlled by resonant and near-resonant pulses on ultrashort time scales. APL Photon. https://doi.org/10.1063/5.0158995 (2023).

  105. Suthar, P., Trojánek, F., Malý, P., Derrien., T. J.-Y. & Kozák, M. Momentum-dependent intraband high harmonic generation in a photodoped indirect semiconductor. Commun. Phys. https://doi.org/10.1038/s42005-024-01593-x (2024).

  106. Li, S. et al. High-order harmonic generation from a thin film crystal perturbed by a quasi-static terahertz field. Nat. Commun. 14, 2603 (2023).

    ADS  Google Scholar 

  107. Bionta, M. R. et al. Tracking ultrafast solid-state dynamics using high harmonic spectroscopy. Phys. Rev. Res. https://doi.org/10.1103/physrevresearch.3.023250 (2021).

  108. Rana, N. & Dixit, G. Probing phonon-driven symmetry alterations in graphene via high-order-harmonic spectroscopy. Phys. Rev. A 106, 053116 (2022).

    ADS  Google Scholar 

  109. Lucchini, M. et al. Attosecond dynamical Franz–Keldysh effect in polycrystalline diamond. Science 353, 916–919 (2016).

    ADS  Google Scholar 

  110. Neufeld, O. et al. Time- and angle-resolved photoelectron spectroscopy of strong-field light-dressed solids: prevalence of the adiabatic band picture. Phys. Rev. Res. 4, 033101 (2022).

    Google Scholar 

  111. Tyulnev, I. et al. Valleytronics in bulk MoS2 with a topologic optical field. Nature 628, 746–751 (2024).

    ADS  Google Scholar 

  112. Mitra, S. et al. Light-wave-controlled Haldane model in monolayer hexagonal boron nitride. Nature https://doi.org/10.1038/s41586-024-07244-z (2024).

  113. Jiménez-Galán, Á., Zhavoronkov, N., Schloz, M., Morales, F. & Ivanov, M. Time-resolved high harmonic spectroscopy of dynamical symmetry breaking in bi-circular laser fields: the role of Rydberg states. Opt. Express 25, 22880 (2017).

    ADS  Google Scholar 

  114. Jiménez-Galán, Á., Silva, R. E. F., Smirnova, O. & Ivanov, M. Lightwave control of topological properties in 2D materials for sub-cycle and non-resonant valley manipulation. Nat. Photon. 14, 728–732 (2020).

    ADS  Google Scholar 

  115. 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).

    ADS  Google Scholar 

  116. Choi, S. et al. Observation of discrete time-crystalline order in a disordered dipolar many-body system. Nature 543, 221–225 (2017).

    ADS  Google Scholar 

  117. Takeda, K. S. et al. Ultrafast electron–electron scattering in metallic phase of 2H-NbSe2 probed by high harmonic generation. Phys. Rev. Lett. 132, 186901 (2024).

    ADS  Google Scholar 

  118. A. Gindl, et al. Attosecond control of solid-state high harmonic generation using ω–3ω fields. Preprint at https://arxiv.org/abs/2310.07254 (2023).

  119. Garg, M., Kim, H. Y. & Goulielmakis, E. Ultimate waveform reproducibility of extreme-ultraviolet pulses by high-harmonic generation in quartz. Nat. Photon. 12, 291–296 (2018).

    ADS  Google Scholar 

  120. Keathley, P. D., Jensen, S. V. B., Yeung, M., Bionta, M. R. & Madsen, L. B. Uncovering extreme nonlinear dynamics in solids through time-domain field analysis. Phys. Rev. B 107, 054302 (2023).

    ADS  Google Scholar 

  121. Neufeld, O., Yancogne-Dejean, N., De Giovanni, U., Hübener, H. & Rubio, A. Attosecond magnetization dynamics in non-magnetic materials driven by intense femtosecond lasers. npj Comput. Mater. 9, 39 (2023).

    ADS  Google Scholar 

  122. Vampa, G. et al. Characterization of high-harmonic emission from ZnO up to 11 eV pumped with a Cr:ZnS high-repetition-rate source. Opt. Lett. 44, 259–262 (2019).

    ADS  Google Scholar 

  123. Steinleitner, P. et al. Single-cycle infrared waveform control. Nat. Photon. 16, 512–518 (2022).

    ADS  Google Scholar 

  124. Wirth, A. et al. Synthesized light transients. Science 334, 195–200 (2011).

    ADS  Google Scholar 

  125. Purschke, D. N. et al. Microscopic mechanisms of high-order wave mixing in solids. Phys. Rev. A 108, L051103 (2023).

    ADS  Google Scholar 

  126. Gorlach, A. et al. High-harmonic generation driven by quantum light. Nat. Phys. 19, 1689–1696 (2023).

    Google Scholar 

  127. Finger, M. A., Iskhakov, T. S. H., Joly, N. Y., Chekhova, M. V. & Russell, P. St. J. Raman-free, noble-gas-filled photonic-crystal fiber source for ultrafast, very bright twin-beam squeezed vacuum. Phys. Rev. Lett. 115, 143602 (2015).

    ADS  Google Scholar 

  128. Ko, D. H. & Corkum, P. B. Quantum optics meets attosecond science. Nat. Phys. 19, 1556–1557 (2023).

    Google Scholar 

  129. Kraus, P. M. et al. Measurement and laser control of attosecond charge migration in ionized iodoacetylene. Science 350, 6292 (2015).

    Google Scholar 

  130. Ito, S. et al. Build-up and dephasing of Floquet–Bloch bands on subcycle timescales. Nature 616, 696–701 (2023).

    ADS  Google Scholar 

  131. Yue, L. et al. Signatures of multiband effects in high-harmonic generation in monolayer MoS2. Phys. Rev. Lett. 129, 147401 (2022).

    ADS  Google Scholar 

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Acknowledgements

This work was primarily supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division through the AMOS programme. C.H. acknowledges support from the W. M. Keck Foundation and an Alexander von Humboldt Research Fellowship. S.R.U.H. acknowledges support from the Stanford Institute for Materials and Energy Sciences (SIMES). We thank D. Reis for fruitful discussion and feedback on the paper.

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Authors and Affiliations

  1. Stanford PULSE Institute, SLAC National Accelerator Laboratory, Menlo Park, CA, USA

    Christian Heide, Yuki Kobayashi & Shambhu Ghimire

  2. Department of Applied Physics, Stanford University, Stanford, CA, USA

    Christian Heide & Sheikh Rubaiat Ul Haque

  3. Department of Chemistry, University of Michigan, Ann Arbor, MI, USA

    Yuki Kobayashi

  4. Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, USA

    Sheikh Rubaiat Ul Haque

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  3. Sheikh Rubaiat Ul Haque
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  4. Shambhu Ghimire
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All authors contributed equally to this Review.

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Correspondence to Christian Heide or Shambhu Ghimire.

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Nature Physics thanks Jens Biegert, Tran Trung Luu and Angel Rubio for their contribution to the peer review of this work.

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Heide, C., Kobayashi, Y., Haque, S.R.U. et al. Ultrafast high-harmonic spectroscopy of solids. Nat. Phys. 20, 1546–1557 (2024). https://doi.org/10.1038/s41567-024-02640-8

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