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.
Figures at a glance
Figure 1: Terahertz-sideband generation in a quantum well. 
a, Linearly polarized NIR light creates excitons when incident upon the quantum well sample. b, Intense, linearly polarized terahertz radiation can accelerate an electron away from and back to the exciton core, resulting in a recollision that emits light. HSG predominantly occurs during a short time near the peak of the electric field, such that sidebands are generated in short bursts separated by half the period of the terahertz radiation. Modulations of the NIR beam in the figure are representative of the intensity profile and are not shown to scale. c, Sideband spectra from a 15-nm-wide quantum well driven at various terahertz frequencies. The signal from the NIR laser, of frequency fNIR, is reduced by a factor of 500. Sidebands are observed at even multiples of the terahertz frequency, fsideband = fNIR + 2nfTHz, up to 18th order (2n = 18). At the two lower terahertz frequencies (fTHz = 0.58 and 0.46 THz), we observe a plateau in the sideband intensity for the high-order sidebands that indicates the non-perturbative nature of the generation process. At the highest terahertz frequency (fTHz = 1.56 THz) and lower electric fields, the ponderomotive energy is smaller and many fewer sidebands are observed. a.u., arbitrary units. Error bars, s.e.m.
Figure 2: Dependence of sideband strength on terahertz laser intensity. 
a, Dependence on FEL intensity of the second-order sideband (n = 1) produced in a 15-nm quantum well with fTHz = 0.58 THz. At low powers, the signal increases quadratically with FEL power (red line in inset), indicating a perturbative generation process. At high FEL intensities, the sideband saturates and the sideband signal is constant—behaviour that is non-perturbative. b, Dependence on FEL intensity of the fourth-, sixth- and eighth-order sidebands (n = 2, 3 and 4). A fit to the appropriate perturbative scaling law (∝I2n; black dashed lines) is plotted for each sideband. Our data systematically deviate from the I2n fits, indicating that these sidebands are not generated perturbatively. Error bars, s.e.m.
Figure 3: Dependence of the sideband intensity on the ellipticity of the FEL polarization. 
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