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Experimental observation of electron–hole recollisions


An intense laser field can remove an electron from an atom or molecule and pull the electron into a large-amplitude oscillation in which it repeatedly collides with the charged core it left behind1,2,3,4. Such recollisions result in the emission of very energetic photons by means of high-order-harmonic generation, which has been observed in atomic and molecular gases5,6,7 as well as in a bulk crystal8. An exciton is an atom-like excitation of a solid in which an electron that is excited from the valence band is bound by the Coulomb interaction to the hole it left behind9,10. It has been predicted that recollisions between electrons and holes in excitons will result in a new phenomenon: high-order-sideband generation11,12. In this process, excitons are created by a weak near-infrared laser of frequency fNIR. An intense laser field at a much lower frequency, fTHz, then removes the electron from the exciton and causes it to recollide with the resulting hole. New emission is predicted to occur as sidebands of frequency fNIR + 2nfTHz, where n is an integer that can be much greater than one. Here we report the observation of high-order-sideband generation in semiconductor quantum wells. Sidebands are observed up to eighteenth order (+18fTHz, or n = 9). The intensity of the high-order sidebands decays only weakly with increasing sideband order, confirming the non-perturbative nature of the effect. Sidebands are strongest for linearly polarized terahertz radiation and vanish when the terahertz radiation is circularly polarized. Beyond their fundamental scientific significance, our results suggest a new mechanism for the ultrafast modulation of light, which has potential applications in terabit-rate optical communications.

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Figure 1: Terahertz-sideband generation in a quantum well.
Figure 2: Dependence of sideband strength on terahertz laser intensity.
Figure 3: Dependence of the sideband intensity on the ellipticity of the FEL polarization.


  1. 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)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  3. 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)

    Article  ADS  CAS  Google Scholar 

  4. Corkum, P. B. Recollision physics. Phys. Today 64, 36–41 (2011)

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  6. Liang, Y., Augst, S., Chin, S. L., Beaudoin, Y. & Chaker, M. High harmonic generation in atomic and diatomic molecular gases using intense picosecond laser pulses-a comparison. J. Phys. B 27, 5119–5130 (1994)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  9. Wannier, G. H. The structure of electronic excitation levels in insulating crystals. Phys. Rev. 52, 191–197 (1937)

    Article  ADS  CAS  Google Scholar 

  10. Dingle, R., Wiegmann, W. & Henry, C. H. Quantum states of confined carriers in very thin AlxGa1-xAs-GaAs-AlxGa1-xAs heterostructures. Phys. Rev. Lett. 33, 827–830 (1974)

    Article  ADS  CAS  Google Scholar 

  11. Liu, R.-B. & Zhu, B.-F. High-order THz-sideband generation in semiconductors. AIP Conf. Proc. 893, 1455–1456 (2007)

    Article  ADS  CAS  Google Scholar 

  12. Yan, J.-Y. Theory of excitonic high-order sideband generation in semiconductors under a strong terahertz field. Phys. Rev. B 78, 075204 (2008)

    Article  ADS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Google Scholar 

  15. Uiberacker, M. et al. Attosecond real-time observation of electron tunnelling in atoms. Nature 446, 627–632 (2007)

    Article  ADS  CAS  Google Scholar 

  16. Wagner, M. et al. Resonant enhancement of second order sideband generation for intraexcitonic transitions in GaAs/AlGaAs multiple quantum wells. Appl. Phys. Lett. 94, 241105 (2009)

    Article  ADS  Google Scholar 

  17. Wagner, M. et al. Terahertz nonlinear optics using intra-excitonic quantum well transitions: sideband generation and AC Stark splitting. Phys. Status Solidi 248, 859–862 (2011)

    Article  CAS  Google Scholar 

  18. Nordstrom, K. B. et al. Excitonic dynamical Franz-Keldysh effect. Phys. Rev. Lett. 81, 457–460 (1998)

    Article  ADS  CAS  Google Scholar 

  19. Carter, S. G. et al. Quantum coherence in an optical modulator. Science 310, 651–653 (2005)

    Article  ADS  CAS  Google Scholar 

  20. Danielson, J. R. et al. Interaction of strong single-cycle terahertz pulses with semiconductor quantum wells. Phys. Rev. Lett. 99, 237401 (2007)

    Article  ADS  CAS  Google Scholar 

  21. Leinß, S. et al. Terahertz coherent control of optically dark paraexcitons in Cu2O. Phys. Rev. Lett. 101, 246401 (2008)

    Article  ADS  Google Scholar 

  22. Wagner, M. et al. Observation of the intraexciton Autler-Townes effect in GaAs/AlGaAs semiconductor quantum wells. Phys. Rev. Lett. 105, 167401 (2010)

    Article  ADS  Google Scholar 

  23. Zaks, B. et al. THz-driven quantum wells: Coulomb interactions and Stark shifts in the ultrastrong coupling regime. N. J. Phys. 13, 083009 (2011)

    Article  Google Scholar 

  24. Nordstrom, K. B. et al. Observation of dynamical Franz-Keldysh effect. Phys. Status Solidi 204, 52–54 (1997)

    Article  CAS  Google Scholar 

  25. Kono, J. et al. Resonant terahertz optical sideband generation from confined magnetoexcitons. Phys. Rev. Lett. 79, 1758–1761 (1997)

    Article  ADS  CAS  Google Scholar 

  26. Černe, J. et al. Near-infrared sideband generation induced by intense far-infrared radiation in GaAs quantum wells. Appl. Phys. Lett. 70, 3543–3545 (1997)

    Article  ADS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  29. Vozzi, C. et al. Generalized molecular orbital tomography. Nature Phys. 7, 822–826 (2011)

    Article  ADS  Google Scholar 

  30. Eisele, H. State of the art and future of electronic sources at terahertz frequencies. Electron. Lett. 46, S8–S11 (2010)

    Article  Google Scholar 

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Samples are from the wafers grown at UCSB by C. Wang in the group of L. C. Coldren (15-nm quantum well) and by T. Truong in the group of P. M. Petroff (18- and 22-nm quantum wells; see Supplementary Information) for experiments described in refs 19 and 23, respectively. We would like to thank D. Enyeart for his help in running the UCSB FELs and N. H. Kwong for running simulations helpful to our understanding of these effects. This work was supported by NSF grant DMR-1006603 and Hong Kong RGC/GRF 401011.

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B.Z. was responsible for conducting experiments and analysing the data presented, and for writing the paper. R.B.L. introduced M.S.S. to the predictions of HSG, and provided theoretical support. M.S.S. designed and supervised the study and edited the paper. All authors discussed the results and commented on the paper.

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Correspondence to M. S. Sherwin.

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The authors declare no competing financial interests.

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Supplementary Information

This file contains Supplementary Methods, a Supplementary Discussion, Supplementary Data, Supplementary Equations, Supplementary Figures 1-5 and additional references. (PDF 858 kb)

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

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