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Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations


Ultrafast charge transport in strongly biased semiconductors is at the heart of high-speed electronics, electro-optics and fundamental solid-state physics1,2,3,4,5,6,7,8,9,10,11,12,13. Intense light pulses in the terahertz spectral range have opened fascinating vistas14,15,16,17,18,19,20,21. Because terahertz photon energies are far below typical electronic interband resonances, a stable electromagnetic waveform may serve as a precisely adjustable bias5,11,17,19. Novel quantum phenomena have been anticipated for terahertz amplitudes, reaching atomic field strengths8,9,10. We exploit controlled (multi-)terahertz waveforms with peak fields of 72 MV cm−1 to drive coherent interband polarization combined with dynamical Bloch oscillations in semiconducting gallium selenide. These dynamics entail the emission of phase-stable high-harmonic transients, covering the entire terahertz-to-visible spectral domain between 0.1 and 675 THz. Quantum interference of different ionization paths of accelerated charge carriers is controlled via the waveform of the driving field and explained by a quantum theory of inter- and intraband dynamics. Our results pave the way towards all-coherent terahertz-rate electronics.

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Figure 1: Field-sensitive terahertz nonlinear optics.
Figure 2: CEP-stable terahertz HHG in bulk GaSe.
Figure 3: Sub-cycle carrier dynamics driven by CEP-stable terahertz transients.
Figure 4: CEP control of terahertz HHG in GaSe.


  1. Bloch, F. Űber die Quantenmechanik der Elektronen in Kristallgittern. Z. Phys. 52, 555–600 (1929).

    ADS  Article  Google Scholar 

  2. Zener, C. Non-adiabatic crossing of energy levels. Proc. R. Soc. A 137, 696–702 (1932).

    ADS  Article  Google Scholar 

  3. Keldysh, L. V. Ionization in the field of a strong electromagnetic wave. Sov. Phys. JETP 20, 1307–1314 (1965).

    Google Scholar 

  4. Leitenstorfer, A., Hunsche, S., Shah, J., Nuss, M. C. & Knox, W. H. Femtosecond charge transport in polar semiconductors. Phys. Rev. Lett. 82, 5140–5143 (1999).

    ADS  Article  Google Scholar 

  5. Kuehn, W. et al. Coherent ballistic motion of electrons in a periodic potential. Phys. Rev. Lett. 104, 146602 (2010).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  7. Ghimire, S. et al. Generation and propagation of high-order harmonics in crystals. Phys. Rev. A 85, 043836 (2012).

    ADS  Article  Google Scholar 

  8. 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).

    ADS  MathSciNet  Article  Google Scholar 

  9. 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).

    ADS  Article  Google Scholar 

  10. 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).

    ADS  Article  Google Scholar 

  11. Hirori, H. et al. Extraordinary carrier multiplication gated by a picosecond electric field pulse. Nature Commun. 2, 594 (2011).

    ADS  Article  Google Scholar 

  12. Schiffrin, A. et al. Optical-field-induced current in dielectrics. Nature 493, 70–74 (2013).

    ADS  Article  Google Scholar 

  13. Schultze, M. et al. Controlling dielectrics with the electric field of light. Nature 493, 75–78 (2013).

    ADS  Article  Google Scholar 

  14. Hebling, J., Yeh, K.-L., Hoffmann, M. C., Bartal, B. & Nelson, K. A. Generation of high-power terahertz pulses by tilted-pulse-front excitation and their application possibilities. J. Opt. Soc. Am. B 25, B6–B19 (2008).

    Article  Google Scholar 

  15. Sell, A., Leitenstorfer, A. & Huber, R. Phase-locked generation and field-resolved detection of widely tunable terahertz pulses with amplitudes exceeding 100 MV/cm. Opt. Lett. 33, 2767–2769 (2008).

    ADS  Article  Google Scholar 

  16. Hirori, H., Doi, A., Blanchard, F. & Tanaka, K. Single-cycle terahertz pulses with amplitudes exceeding 1 MV/cm generated by optical rectification in LiNbO3 . Appl. Phys. Lett. 98, 091106 (2011).

    ADS  Article  Google Scholar 

  17. Cocker, T. L. et al. An ultrafast terahertz scanning/tunneling microscope. Nature Photon. 7, 620–625 (2013).

    ADS  Article  Google Scholar 

  18. Kampfrath, T. et al. Coherent terahertz control of antiferromagnetic spin waves. Nature Photon. 5, 31–34 (2011).

    ADS  Article  Google Scholar 

  19. Kampfrath, T., Tanaka, K. & Nelson, K. A. Resonant and nonresonant control over matter and light by intense terahertz transients. Nature Photon. 7, 680–690 (2013).

    ADS  Article  Google Scholar 

  20. Chin, A. H., Calderon, O. G. & Kono, J. Extreme midinfrared nonlinear optics in semiconductors. Phys. Rev. Lett. 86, 3292–3295 (2001).

    ADS  Article  Google Scholar 

  21. Zaks, B., Liu, R. B. & Sherwin, M. S. Experimental observation of electron–hole recollisions. Nature 483, 580–583 (2012).

    ADS  Article  Google Scholar 

  22. Feldmann, J. et al. Optical investigation of Bloch oscillations in a semiconductor superlattice. Phys. Rev. B 46, 7252–7255 (1992).

    ADS  Article  Google Scholar 

  23. Waschke, C. et al. Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice. Phys. Rev. Lett. 70, 3319–3322 (1993).

    ADS  Article  Google Scholar 

  24. Unterrainer, K. et al. Inverse Bloch oscillator: strong terahertz-photocurrent resonances at the Bloch frequency. Phys. Rev. Lett. 76, 2973–2976 (1996).

    ADS  Article  Google Scholar 

  25. Delahaye, J. et al. Low-noise current amplifier based on mesoscopic Josephson junction. Science 299, 1045–1048 (2003).

    ADS  Article  Google Scholar 

  26. Christodoulides, D. N., Lederer, F. & Silberberg, Y. Discretizing light behaviour in linear and nonlinear waveguide lattices. Nature 424, 817–823 (2003).

    ADS  Article  Google Scholar 

  27. Bloch, I. Quantum coherence and entanglement with ultracold atoms in optical lattices. Nature 453, 1016–1022 (2008).

    ADS  Article  Google Scholar 

  28. Krauss, G. et al. All-passive phase locking of a compact Er:fiber laser system. Opt. Lett. 36, 540–542 (2011).

    ADS  Article  Google Scholar 

  29. Corkum, P. B. & Krausz, F. Attosecond science. Nature Phys. 3, 381–387 (2007).

    ADS  Article  Google Scholar 

  30. Schlüter, M. et al. Optical properties of GaSe and GaSxSe1−x mixed crystals. Phys. Rev. B 13, 3534–3547 (1976).

    ADS  Article  Google Scholar 

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The authors thank K. Renk and T. Cocker for helpful discussions. This work was supported by the European Research Council (via starting grant QUANTUMsubCYCLE) and the Deutsche Forschungsgemeinschaft (grant no. KI 917/2-1).

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O.S., M.H., F.L. and R.H. conceived the study. O.S., M.H., F.L., B.U., C.L. and R.H. carried out the experiment. U.H., D.G., T.M., M.K. and S.W.K. developed the quantum-mechanical model and carried out the computations. O.S., M.H., F.L., U.H., M.K., S.W.K and R.H. wrote the manuscript. All authors discussed the results.

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Correspondence to R. Huber.

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Schubert, O., Hohenleutner, M., Langer, F. et al. Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations. Nature Photon 8, 119–123 (2014).

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