High-harmonic spectroscopy of ultrafast many-body dynamics in strongly correlated systems

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We bring together two topics that, until now, have been the focus of intense but non-overlapping research efforts. The first concerns high-harmonic generation in solids, which occurs when an intense light field excites a highly non-equilibrium electronic response in a semiconductor or a dielectric. The second concerns many-body dynamics in strongly correlated systems such as the Mott insulator. We show that high-harmonic generation can be used to time-resolve ultrafast many-body dynamics associated with an optically driven phase transition, with accuracy far exceeding one cycle of the driving light field. Our work paves the way for time-resolving highly non-equilibrium many-body dynamics in strongly correlated systems, with few femtosecond accuracy.

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  1. 1.

    Krausz, F. & Ivanov, M. Attosecond physics. Rev. Mod. Phys. 81, 163–234 (2009).

  2. 2.

    Baker, S. et al. Probing proton dynamics in molecules on an attosecond time scale. Science 312, 424–427 (2006).

  3. 3.

    Lein, M. Molecular imaging using recolliding electrons. J. Phys. B 40, R135–R173 (2007).

  4. 4.

    Smirnova, O. et al. High harmonic interferometry of multi-electron dynamics in molecules. Nature 460, 972–977 (2009).

  5. 5.

    Haessler, S. et al. Attosecond imaging of molecular electronic wavepackets. Nat. Phys. 6, 200–206 (2010).

  6. 6.

    Shafir, D. et al. Resolving the time when an electron exits a tunnelling barrier. Nature 485, 343–346 (2012).

  7. 7.

    Pedatzur, O. et al. Attosecond tunnelling interferometry. Nat. Phys. 11, 815–819 (2015).

  8. 8.

    Bruner, B. D. et al. Multidimensional high harmonic spectroscopy of polyatomic molecules: detecting sub-cycle laser-driven hole dynamics upon ionization in strong mid-IR laser fields. Faraday Discuss. 194, 369–405 (2016).

  9. 9.

    Kraus, P. M. et al. Measurement and laser control of attosecond charge migration in ionized iodoacetylene. Science 350, 790–795 (2015).

  10. 10.

    Shiner, A. et al. Probing collective multi-electron dynamics in xenon with high-harmonic spectroscopy. Nat. Phys. 7, 464–467 (2011).

  11. 11.

    Pabst, S. & Santra, R. Strong-field many-body physics and the giant enhancement in the high-harmonic spectrum of xenon. Phys. Rev. Lett. 111, 233005 (2013).

  12. 12.

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

  13. 13.

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

  14. 14.

    Hohenleutner, M. et al. Real-time observation of interfering crystal electrons in high-harmonic generation. Nature 523, 572–575 (2015).

  15. 15.

    Langer, F. et al. Lightwave-driven quasiparticle collisions on a subcycle timescale. Nature 533, 225–229 (2016).

  16. 16.

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

  17. 17.

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

  18. 18.

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

  19. 19.

    Hawkins, P. G., Ivanov, M. Y. & Yakovlev, V. S. Effect of multiple conduction bands on high-harmonic emission from dielectrics. Phys. Rev. A. 91, 013405 (2015).

  20. 20.

    You, Y. S., Reis, D. A. & Ghimire, S. Anisotropic high-harmonic generation in bulk crystals. Nat. Phys. 13, 345–349 (2017).

  21. 21.

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

  22. 22.

    Higuchi, T., Stockman, M. I. & Hommelhoff, P. Strong-field perspective on high-harmonic radiation from bulk solids. Phys. Rev. Lett. 113, 213901 (2014).

  23. 23.

    Vampa, G. & Brabec, T. Merge of high harmonic generation from gases and solids and its implications for attosecond science. J. Phys. B 50, 083001 (2017).

  24. 24.

    Tancogne-Dejean, N., Mücke, O. D., Kärtner, F. X. & Rubio, A. Impact of the electronic band structure in high-harmonic generation spectra of solids. Phys. Rev. Lett. 118, 087403 (2017).

  25. 25.

    Kemper, A. F., Moritz, B., Freericks, J. K. & Devereaux, T. P. Theoretical description of high-order harmonic generation in solids. New. J. Phys. 15, 023003 (2013).

  26. 26.

    Eisert, J., Friesdorf, M. & Gogolin, C. Quantum many-body systems out of equilibrium. Nat. Phys. 11, 124–130 (2015).

  27. 27.

    Bloch, I., Dalibard, J. & Zwerger, W. Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885–964 (2008).

  28. 28.

    Heyl, M., Polkovnikov, A. & Kehrein, S. Dynamical quantum phase transitions in the transverse-field Ising model. Phys. Rev. Lett. 110, 135704 (2013).

  29. 29.

    Nasu, K. Photo-Induced Phase Transitions (World Scientific, Hackensack, NJ, USA, 2004).

  30. 30.

    Oka, T. & Aoki, H. Photoinduced Tomonaga–Luttinger-like liquid in a Mott insulator. Phys. Rev. B 78, 241104 (2008).

  31. 31.

    Liu, M. et al. Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial. Nature 487, 345–348 (2012).

  32. 32.

    Mayer, B. et al. Tunneling breakdown of a strongly correlated insulating state in VO2 induced by intense multiterahertz excitation. Phys. Rev. B 91, 235113 (2015).

  33. 33.

    Gebhard, F. The Mott Metal–Insulator Transition: Models and Methods (Springer, Berlin, Germany, 1997).

  34. 34.

    Oka, T. Nonlinear doublon production in a Mott insulator: Landau–Dykhne method applied to an integrable model. Phys. Rev. B 86, 075148 (2012).

  35. 35.

    Essler, F. H. L, Frahm, H., Göhmann, F., Klümper, A. & Korepin, V. E. The One-Dimensional Hubbard Model (Cambridge Univ. Press, Cambridge, UK, 2010).

  36. 36.

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

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The authors acknowledge fruitful discussions with T. Oka, B. Amorim and P. Hawkins. M.I. and R.E.F.S. acknowledge support from EPSRC/DSTL MURI grant EP/N018680/1.

Author information


  1. Max-Born-Institut, Berlin, Germany

    • R. E. F. Silva
    • , O. Smirnova
    •  & M. Ivanov
  2. Russian Quantum Center, Skolkovo, Russia

    • Igor V. Blinov
    •  & Alexey N. Rubtsov
  3. Moscow Institute of Physics and Technology, Dolgoprudny, Moscow, Russia

    • Igor V. Blinov
  4. Department of Physics, Moscow State University, Moscow, Russia

    • Alexey N. Rubtsov
  5. Technische Universität Berlin, Ernst-Ruska-Gebäude, Berlin, Germany

    • O. Smirnova
  6. Blackett Laboratory, Imperial College London, South Kensington Campus, London, UK

    • M. Ivanov
  7. Department of Physics, Humboldt University, Berlin, Germany

    • M. Ivanov


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R.E.F.S. developed the numerical code. M.I., R.E.F.S and O.S. developed the idea. All authors contributed to analysis of the results. M.I. and R.E.F.S. wrote the main part of the manuscript, which was discussed by all authors.

Competing interests

The authors declare no competing interests.

Corresponding authors

Correspondence to R. E. F. Silva or M. Ivanov.