Skip to main content

Thank you for visiting 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.

Radiative Auger process in the single-photon limit


In a multi-electron atom, an excited electron can decay by emitting a photon. Typically, the leftover electrons are in their ground state. In a radiative Auger process, the leftover electrons are in an excited state and a redshifted photon is created1,2,3,4. In a semiconductor quantum dot, radiative Auger is predicted for charged excitons5. Here we report the observation of radiative Auger on trions in single quantum dots. For a trion, a photon is created on electron–hole recombination, leaving behind a single electron. The radiative Auger process promotes this additional (Auger) electron to a higher shell of the quantum dot. We show that the radiative Auger effect is a powerful probe of this single electron: the energy separations between the resonance fluorescence and the radiative Auger emission directly measure the single-particle splittings of the electronic states in the quantum dot with high precision. In semiconductors, these single-particle splittings are otherwise hard to access by optical means as particles are excited typically in pairs, as excitons. After the radiative Auger emission, the Auger carrier relaxes back to the lowest shell. Going beyond the original theoretical proposals, we show how applying quantum optics techniques to the radiative Auger photons gives access to the single-electron dynamics, notably relaxation and tunnelling. This is also hard to access by optical means: even for quasi-resonant p-shell excitation, electron relaxation takes place in the presence of a hole, complicating the relaxation dynamics. The radiative Auger effect can be exploited in other semiconductor nanostructures and quantum emitters in the solid state to determine the energy levels and the dynamics of a single carrier.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type



Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Observation of a radiative Auger process on a single QD.
Fig. 2: Magnetic field dispersion of the radiative Auger emission.
Fig. 3: Time-resolved correlation measurements.

Data availability

The data that support this work are available from the corresponding author upon reasonable request.

Code availability

The code that has been used for this work is available from the corresponding author upon reasonable request.


  1. Åberg, T. & Utriainen, J. Evidence for a ‘radiative Auger effect’ in X-ray photon emission. Phys. Rev. Lett. 22, 1346–1348 (1969).

    Article  Google Scholar 

  2. Åberg, T. Theory of the radiative Auger effect. Phys. Rev. A 4, 1735–1740 (1971).

    Article  Google Scholar 

  3. Bloch, F. & Ross, P. A. Radiative Auger effect. Phys. Rev. 47, 884–885 (1935).

    Article  CAS  Google Scholar 

  4. Bloch, F. Double electron transitions in X-ray spectra. Phys. Rev. 48, 187 (1935).

    Article  CAS  Google Scholar 

  5. Hawrylak, P. Single Quantum Dots: Fundamentals, Applications and New Concepts Vol. 90 (Springer Science, Business Media, 2003).

  6. Bambynek, W. et al. X-ray fluorescence yields, Auger, and Coster–Kronig transition probabilities. Rev. Mod. Phys. 44, 716–813 (1972).

    Article  CAS  Google Scholar 

  7. Barthés-Labrousse, M.-G. The Auger effect. Microsc. Microanal. Microstruct. 6, 253–262 (1995).

    Article  Google Scholar 

  8. Kurzmann, A., Ludwig, A., Wieck, A. D., Lorke, A. & Geller, M. Auger recombination in self-assembled quantum dots: quenching and broadening of the charged exciton transition. Nano Lett. 16, 3367–3372 (2016).

    Article  CAS  Google Scholar 

  9. Han, B. et al. Exciton states in monolayer MoSe2 and MoTe2 probed by upconversion spectroscopy. Phys. Rev. X 8, 031073 (2018).

    CAS  Google Scholar 

  10. Siyushev, P. et al. Optically controlled switching of the charge state of a single nitrogen-vacancy center in diamond at cryogenic temperatures. Phys. Rev. Lett. 110, 167402 (2013).

    Article  CAS  Google Scholar 

  11. Blood, P. Quantum Confined Laser Devices: Optical Gain and Recombination in Semiconductors Vol. 23 (OUP Oxford, 2015).

  12. Carlson, T. A. Electron shake-off following the beta decay of Ne23. Phys. Rev. 130, 2361–2365 (1963).

    Article  CAS  Google Scholar 

  13. Dean, P. J., Cuthbert, J. D., Thomas, D. G. & Lynch, R. T. Two-electron transitions in the luminescence of excitons bound to neutral donors in gallium phosphide. Phys. Rev. Lett. 18, 122–124 (1967).

    Article  CAS  Google Scholar 

  14. Skolnick, M. S. et al. Fermi sea shake-up in quantum well luminescence spectra. Solid State Electron. 37, 825–829 (1994).

    Article  CAS  Google Scholar 

  15. Manfra, M. J., Goldberg, B. B., Pfeiffer, L. & West, K. Anderson–Fano resonance and shake-up processes in the magnetophotoluminescence of a two-dimensional electron system. Phys. Rev. B 57, R9467–R9470 (1998).

    Article  CAS  Google Scholar 

  16. Kleemans, N. A. J. M. et al. Many-body exciton states in self-assembled quantum dots coupled to a Fermi sea. Nat. Phys. 6, 534–538 (2010).

    Article  CAS  Google Scholar 

  17. Huo, Y. H., Rastelli, A. & Schmidt, O. G. Ultra-small excitonic fine structure splitting in highly symmetric quantum dots on GaAs (001) substrate. Appl. Phys. Lett. 102, 152105 (2013).

    Article  Google Scholar 

  18. Warburton, R. J. et al. Optical emission from a charge-tunable quantum ring. Nature 405, 926–929 (2000).

    Article  CAS  Google Scholar 

  19. Hansom, J., Schulte, C. H. H., Matthiesen, C., Stanley, M. J. & Atatüre, M. Frequency stabilization of the zero-phonon line of a quantum dot via phonon-assisted active feedback. Appl. Phys. Lett. 105, 172107 (2014).

    Article  Google Scholar 

  20. Koong, Z. X. et al. Fundamental limits to coherent photon generation with solid-state atom-like transitions. Phys. Rev. Lett. 123, 167402 (2019).

    Article  CAS  Google Scholar 

  21. Brash, A. J. et al. Light scattering from solid-state quantum emitters: beyond the atomic picture. Phys. Rev. Lett. 123, 167403 (2019).

    Article  CAS  Google Scholar 

  22. Kouwenhoven, L. P., Austing, D. G. & Tarucha, S. Few-electron quantum dots. Rep. Prog. Phys. 64, 701–736 (2001).

    Article  CAS  Google Scholar 

  23. Fock, V. Bemerkung zur Quantelung des harmonischen Oszillators im Magnetfeld. Z. Phys. 47, 446–448 (1928).

    Article  Google Scholar 

  24. Darwin, C. G. The diamagnetism of the free electron. Proc. Camb. Phil. Soc. 27, 86 (1930).

    Article  Google Scholar 

  25. Ohnesorge, B., Albrecht, M., Oshinowo, J., Forchel, A. & Arakawa, Y. Rapid carrier relaxation in self-assembled Inx Ga1−x As/GaAs quantum dots. Phys. Rev. B 54, 11532–11538 (1996).

    Article  CAS  Google Scholar 

  26. Kurtze, H. et al. Carrier relaxation dynamics in self-assembled semiconductor quantum dots. Phys. Rev. B 80, 235319 (2009).

    Article  Google Scholar 

  27. Li, X.-Q., Nakayama, H. & Arakawa, Y. Phonon bottleneck in quantum dots: role of lifetime of the confined optical phonons. Phys. Rev. B 59, 5069–5073 (1999).

    Article  CAS  Google Scholar 

  28. Müller, K. et al. Probing ultrafast carrier tunneling dynamics in individual quantum dots and molecules. Ann. Phys. 525, 49–58 (2013).

    Article  Google Scholar 

  29. Slater, J. C. The theory of complex spectra. Phys. Rev. 34, 1293–1322 (1929).

    Article  CAS  Google Scholar 

  30. Bethe, H. A. & Jackiw, R. Intermediate Quantum Mechanics (CRC Press, 2018).

  31. Löbl, M. C. et al. Narrow optical linewidths and spin pumping on charge-tunable close-to-surface self-assembled quantum dots in an ultrathin diode. Phys. Rev. B 96, 165440 (2017).

    Article  Google Scholar 

  32. Vora, P. M. et al. Spin-cavity interactions between a quantum dot molecule and a photonic crystal cavity. Nat. Commun. 6, 7665 (2015).

    Article  CAS  Google Scholar 

  33. Javadi, A. et al. Spin-photon interface and spin-controlled photon switching in a nanobeam waveguide. Nat. Nanotechnol. 13, 398–403 (2018).

    Article  CAS  Google Scholar 

  34. Grim, J. Q. et al. Scalable in operando strain tuning in nanophotonic waveguides enabling three-quantum-dot superradiance. Nat. Mater. 18, 963–969 (2019).

    Article  CAS  Google Scholar 

  35. Wang, Z. M., Liang, B. L., Sablon, K. A. & Salamo, G. J. Nanoholes fabricated by self-assembled gallium nanodrill on GaAs(100). Appl. Phys. Lett. 90, 113120 (2007).

    Article  Google Scholar 

  36. Patel, R. B. et al. Two-photon interference of the emission from electrically tunable remote quantum dots. Nat. Photon. 4, 632–635 (2010).

    Article  CAS  Google Scholar 

  37. Kiršanskė, G. et al. Indistinguishable and efficient single photons from a quantum dot in a planar nanobeam waveguide. Phys. Rev. B 96, 165306 (2017).

    Article  Google Scholar 

  38. Kroutvar, M. et al. Optically programmable electron spin memory using semiconductor quantum dots. Nature 432, 81–84 (2004).

    Article  CAS  Google Scholar 

  39. Dreiser, J. et al. Optical investigations of quantum dot spin dynamics as a function of external electric and magnetic fields. Phys. Rev. B 77, 075317 (2008).

    Article  Google Scholar 

  40. Smith, J. M. et al. Voltage control of the spin dynamics of an exciton in a semiconductor quantum dot. Phys. Rev. Lett. 94, 197402 (2005).

    Article  CAS  Google Scholar 

Download references


We thank P. Treutlein for fruitful discussions. M.C.L., C.S. and R.J.W. acknowledge financial support from NCCR QSIT and from SNF project number 200020_156637. L.Z. received funding from the European Union Horizon 2020 Research and Innovation programme under the Marie Skłodowska-Curie grant agreement number 721394 (4PHOTON). A.J. acknowledges support from the European Unions Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement number 840453 (HiFig). J.R., A.L. and A.D.W. gratefully acknowledge financial support from the grants DFH/UFA CDFA05-06, DFG TRR160, DFG project 383065199, and BMBF Q.Link.X 16KIS0867. L.M. and P.L. gratefully acknowledge financial support from the Danish National Research Foundation (Center of Excellence Hy-Q, grant number DNRF139) and the European Research Council (ERC Advanced Grant SCALE).

Author information

Authors and Affiliations



M.C.L., C.S., L.Z., G.N.N. and A.J. performed the experiments. J.R., A.D.W. and A.L. grew the samples. C.S., M.C.L. and L.M. fabricated the different samples. M.C.L., L.Z., P.L. and A.L. designed the samples. M.C.L., C.S., L.Z. and R.J.W. analysed the data. M.C.L. developed the theory of the radiative Auger process. A.J., M.C.L. and C.S. developed the theory for the time-resolved measurements. M.C.L., R.J.W. and C.S. developed the theory for the magnetic field dispersion. M.C.L. and R.J.W. initiated the project and wrote the manuscript with input from all the authors.

Corresponding author

Correspondence to Matthias C. Löbl.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Nanotechnology thanks Val Zwiller and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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

Supplementary information

Supplementary Information

Supplementary Figs. 1–6, tables 1–3 and refs. 1–19.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Löbl, M.C., Spinnler, C., Javadi, A. et al. Radiative Auger process in the single-photon limit. Nat. Nanotechnol. 15, 558–562 (2020).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


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