Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Size-controlled quantum dots reveal the impact of intraband transitions on high-order harmonic generation in solids

Abstract

Since the discovery of high-order harmonic generation (HHG) in solids1,2,3, much effort has been devoted to understand its generation mechanism and both inter- and intraband transitions are known to be essential1,2,3,4,5,6,7,8,9,10. However, intraband transitions are affected by the electronic structure of a solid, and how they contribute to nonlinear carrier generation and HHG remains an open question. Here we use mid-infrared laser pulses to study HHG in CdSe and CdS quantum dots, where quantum confinement can be used to control the intraband transitions. We find that both HHG intensity per excited volume and generated carrier density increase when the average quantum dot size is increased from about 2 to 3 nm. We show that the reduction in sub-bandgap energy in larger quantum dots enhances intraband transitions, and this—in turn—increases the rate of photocarrier injection by coupling with interband transitions, resulting in enhanced HHG.

Your institute does not have access to this article

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: HHG in CdSe and CdS QD films.
Fig. 2: QD size dependence of HHG.
Fig. 3: TA measurements.
Fig. 4: Calculation results.

Data availability

Source data are provided with this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

References

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

    ADS  Article  Google Scholar 

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

    Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  4. 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 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  9. Garg, M. et al. Multi-petahertz electronic metrology. Nature 538, 359–363 (2016).

    ADS  Article  Google Scholar 

  10. Aversa, C. & Sipe, J. E. Nonlinear optical susceptibilities of semiconductors: results with a length-gauge analysis. Phys. Rev. B 52, 14636–14645 (1995).

    ADS  Article  Google Scholar 

  11. Haug, H. & Koch, S. W. Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, 2004).

  12. Boyd, R. W. Nonlinear Optics 3rd edn (Academic Press, 2008).

    Google Scholar 

  13. Cundiff, S. T. et al. Rabi flopping in semiconductors. Phys. Rev. Lett. 73, 1178–1181 (1994).

    ADS  Article  Google Scholar 

  14. Mücke, O. D., Tritschler, T., Wegener, M., Morgner, U. & Kärtner, F. X. Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics. Phys. Rev. Lett. 89, 127401 (2002).

    ADS  Article  Google Scholar 

  15. Schlaepfer, F. et al. Attosecond optical-field-enhanced carrier injection into the GaAs conduction band. Nat. Phys. 14, 560–564 (2018).

    Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  18. Sommer, A. et al. Attosecond nonlinear polarization and light–matter energy transfer in solids. Nature 534, 86–90 (2016).

    ADS  Article  Google Scholar 

  19. Higuchi, T., Heide, C., Ullmann, K., Weber, H. B. & Hommelhoff, P. Light-field-driven currents in graphene. Nature 550, 224–228 (2017).

    ADS  Article  Google Scholar 

  20. Wang, F. et al. Exciton polarizability in semiconductor nanocrystals. Nat. Mater. 5, 861–864 (2006).

    ADS  Article  Google Scholar 

  21. McDonald, C. R., Amin, K. S., Aalmalki, S. & Brabec, T. Enhancing high harmonic output in solids through quantum confinement. Phys. Rev. Lett. 119, 183902 (2017).

    ADS  Article  Google Scholar 

  22. Efros, Al. L. & Efros, A. L. Interband absorption of light in a semiconductor sphere. Sov. Phys. Semicond. 16, 772–775 (1982).

    Google Scholar 

  23. Brus, L. E. A simple model for the ionization potential, electron affinity, and aqueous redox potentials of small semiconductor crystallites. J. Chem. Phys. 79, 5566–5571 (1983).

    ADS  Article  Google Scholar 

  24. Ekimov, A. I. et al. Absorption and intensity-dependent photoluminescence measurements on CdSe quantum dots: assignment of the first electronic transitions. J. Opt. Soc. Am. B 10, 100–107 (1993).

    ADS  Article  Google Scholar 

  25. Murray, C. B., Norris, D. J. & Bawendi, M. G. Synthesis and characterization of nearly monodisperse CdE (E = sulfur, selenium, tellurium) semiconductor nanocrystallites. J. Am. Chem. Soc. 115, 8706–8715 (1993).

    Article  Google Scholar 

  26. Alivisatos, A. P. Semiconductor clusters, nanocrystals, and quantum dots. Science 271, 933–937 (1996).

    ADS  Article  Google Scholar 

  27. Pietryga, J. I. et al. Spectroscopic and device aspects of nanocrystal quantum dots. Chem. Rev. 116, 10513–10622 (2016).

    Article  Google Scholar 

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

    Article  Google Scholar 

  29. Sivis, M. et al. Tailored semiconductors for high-harmonic optoelectronics. Science 357, 303–306 (2017).

    ADS  Article  Google Scholar 

  30. Ludwig, M. et al. Sub-femtosecond electron transport in a nanoscale gap. Nat. Phys. 16, 341–345 (2020).

    Article  Google Scholar 

  31. Lenzner, M. et al. Femtosecond optical breakdown in dielectrics. Phys. Rev. Lett. 80, 4076–4079 (1998).

    ADS  Article  Google Scholar 

  32. Jürgens, P. et al. Origin of strong-field-induced low-order harmonic generation in amorphous quartz. Nat. Phys. 16, 1035–1039 (2020).

    Article  Google Scholar 

  33. Sanari, Y., Otobe, T., Kanemitsu, Y. & Hirori, H. Modifying angular and polarization selection rules of high-order harmonics by controlling electron trajectories in k-space. Nat. Commun. 11, 3069 (2020).

    ADS  Article  Google Scholar 

Download references

Acknowledgements

Y.K. acknowledges support from the Japan Society for the Promotion of Science (JSPS KAKENHI grant no. JP19H05465).

Author information

Authors and Affiliations

Authors

Contributions

K.N. and H.H. carried out the experiments. K.N., H.H., S.A.S., H.T., F.S., G.Y. and Y.K. analysed the data. S.A.S. performed the simulations. M.S., R.S. and T.T. synthesized the QDs. H.H. and Y.K. conceived and supervised the project. All the authors discussed the results and contributed to the writing of the paper.

Corresponding authors

Correspondence to Hideki Hirori or Yoshihiko Kanemitsu.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Additional calculation results.

a, Bandgap energy Eg (blue squares) and subband gap, Δsub (red circles), as a function of the QD diameter (chain length). b, Diameter dependence of I7 obtained by assuming a size-independent Eg (green squares) and that obtained by the full model with a size-dependent Eg (red circles). c, Dependence of I7 on Δsub for different reduced masses.

Source data

Extended Data Fig. 2 Schematics of multiple excitation paths.

In addition to the contribution of the pure interband transition terms (left), the efficient intraband transition in larger QDs (or bulk) opens multiple excitation paths due to the nonlinear coupling between the intra- and interband transitions (right). These additional excitation channels due to the coupling promote nonlinear carrier injection and enhance HHG in larger QDs.

Extended Data Fig. 3 Yield ratio.

Diameter dependence of the yield ratio of the 7th order for CdSe, I7/nd. The data is normalized to the value at d = 6.4 nm. Vertical and horizontal error bars represent the standard deviation of yield ratio and that of diameter. The solid curve is a guide to the eye.

Source data

Supplementary information

Supplementary Information

Supplementary Sections I–VI and Figs. 1–11.

Source data

Source Data Fig. 1

Source data for Fig. 1b.

Source Data Fig. 2

Source data for Fig. 2.

Source Data Fig. 3

Source data for Fig. 3b,c.

Source Data Fig. 4

Source data for Figs. 4a–c.

Source Data Extended Data Fig. 1

Source data for Extended Data Fig. 1.

Source Data Extended Data Fig. 3

Source data for Extended Data Fig. 3.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Nakagawa, K., Hirori, H., Sato, S.A. et al. Size-controlled quantum dots reveal the impact of intraband transitions on high-order harmonic generation in solids. Nat. Phys. 18, 874–878 (2022). https://doi.org/10.1038/s41567-022-01639-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-022-01639-3

Further reading

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing