Minimal-excitation states for electron quantum optics using levitons

Abstract

The on-demand generation of pure quantum excitations is important for the operation of quantum systems, but it is particularly difficult for a system of fermions. This is because any perturbation affects all states below the Fermi energy, resulting in a complex superposition of particle and hole excitations. However, it was predicted nearly 20 years ago1,2,3 that a Lorentzian time-dependent potential with quantized flux generates a minimal excitation with only one particle and no hole. Here we report that such quasiparticles (hereafter termed levitons) can be generated on demand in a conductor by applying voltage pulses to a contact. Partitioning the excitations with an electronic beam splitter generates a current noise that we use to measure their number. Minimal-excitation states are observed for Lorentzian pulses, whereas for other pulse shapes there are significant contributions from holes. Further identification of levitons is provided in the energy domain with shot-noise spectroscopy, and in the time domain with electronic Hong–Ou–Mandel noise correlations4,5,6,7,8. The latter, obtained by colliding synchronized levitons on a beam splitter, exemplifies the potential use of levitons for quantum information: using linear electron quantum optics9 in ballistic conductors, it is possible to imagine flying-qubit10,11 operation in which the Fermi statistics are exploited12,13,14 to entangle synchronized electrons emitted by distinct sources15,16,17,18. Compared with electron sources based on quantum dots19,20,21, the generation of levitons does not require delicate nanolithography, considerably simplifying the circuitry for scalability. Levitons are not limited to carrying a single charge, and so in a broader context n-particle levitons could find application in the study of full electron counting statistics22,23,24,25. But they can also carry a fraction of charge if they are implemented in Luttinger liquids3 or in fractional quantum Hall edge channels26; this allows the study of Abelian and non-Abelian quasiparticles in the time domain. Finally, the generation technique could be applied to cold atomic gases27,28, leading to the possibility of atomic levitons.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Levitons and the principle of their experimental detection.
Figure 2: Electron–hole excitation content of charge pulses and the dynamical orthogonality catastrophe.
Figure 3: energy distribution of electron–hole excitations: shot-noise spectroscopy.
Figure 4: Leviton wavefunction in the time domain.

References

  1. 1

    Levitov, L. S., Lee, H. & Lesovik, G. Electron counting statistics and coherent states of electric current. J. Math. Phys. 37, 4845–4856 (1996)

    ADS  MathSciNet  Article  Google Scholar 

  2. 2

    Ivanov, D. A. Lee, H. W. & Levitov, L. S. Coherent states of alternating current. Phys. Rev. B 56, 6839–6850 (1997)

    ADS  CAS  Article  Google Scholar 

  3. 3

    Keeling, J., Klich, I. & Levitov, L. Minimal excitation states of electrons in one-dimensional wires. Phys. Rev. Lett. 97, 116403 (2006)

    ADS  CAS  Article  Google Scholar 

  4. 4

    Hong, C. K., Ou, Z. Y. & Mandel, L. Measurement of subpicosecond time intervals between two photons by interference. Phys. Rev. Lett. 59, 2044–2046 (1987)

    ADS  CAS  Article  Google Scholar 

  5. 5

    Henny, M. et al. The fermionic Hanbury Brown and Twiss experiment. Science 284, 296–298 (1999)

    ADS  CAS  Article  Google Scholar 

  6. 6

    Oliver, W. D., Kim, J., Liu, R. C. & Yamamoto, Y. Hanbury Brown and Twiss-type experiment with electrons. Science 284, 299–301 (1999)

    ADS  CAS  Article  Google Scholar 

  7. 7

    Liu, R. C., Odom, B., Yamamoto, Y. & Tarucha, S. Quantum interference in electron collision. Nature 391, 263–265 (1998)

    ADS  CAS  Article  Google Scholar 

  8. 8

    Bocquillon, E. et al. Coherence and indistinguishability of single electrons emitted by independent sources. Science 339, 1054–1057 (2013)

    ADS  CAS  Article  Google Scholar 

  9. 9

    Ji, Y. et al. An electronic Mach–Zehnder interferometer. Nature 422, 415–418 (2003)

    ADS  CAS  Article  Google Scholar 

  10. 10

    Bertoni, A., Bordone, P., Brunetti, R., Jacoboni, C. & Reggiani, S. Quantum logic gates based on coherent electron transport in quantum wires. Phys. Rev. Lett. 84, 5912–5915 (2000)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Yamamoto, M. et al. Electrical control of a solid-state flying qubit. Nature Nanotechnol. 7, 247–251 (2012)

    ADS  CAS  Article  Google Scholar 

  12. 12

    Burkard, G., Loss, D. & Sukhorukov, E. V. Noise of entangled electrons: bunching and antibunching. Phys. Rev. B 61, R16303–R16306 (2000)

    ADS  CAS  Article  Google Scholar 

  13. 13

    Beenakker, C. W. J. Emary, C. Kindermann, M. & van Velsen, J. L. Proposal for production and detection of entangled electron-hole pairs in a degenerate electron gas. Phys. Rev. Lett. 91, 147901 (2003)

    ADS  CAS  Article  Google Scholar 

  14. 14

    Samuelsson, P., Sukhorukov, E. V. & Büttiker, M. Two-particle Aharonov-Bohm effect and entanglement in the electronic Hanbury Brown–Twiss setup. Phys. Rev. Lett. 92, 026805 (2004)

    ADS  CAS  Article  Google Scholar 

  15. 15

    Ol’khovskaya, S., Splettstoesser, J., Moskalets, M. & Büttiker, M. Shot noise of a mesoscopic two-particle collider. Phys. Rev. Lett. 101, 166802 (2008)

    ADS  Article  Google Scholar 

  16. 16

    Splettstoesser, J., Moskalets, M. & Büttiker, M. Two-particle nonlocal Aharonov-Bohm effect from two single-particle emitters. Phys. Rev. Lett. 103, 076804 (2009)

    ADS  Article  Google Scholar 

  17. 17

    Haack, G., Moskalets, M., Splettstoesser, J. & Büttiker, M. Coherence of single-electron sources from Mach-Zehnder interferometry. Phys. Rev. B 84, 081303 (2011)

    ADS  Article  Google Scholar 

  18. 18

    Sherkunov, Y. B., d’Ambrumenil, N., Samuelsson, P. & Büttiker, M. Optimal pumping of orbital entanglement with single-particle emitters. Phys. Rev. B 85, 081108 (2012)

    ADS  Article  Google Scholar 

  19. 19

    Fève, G. et al. An on-demand coherent single-electron source. Science 316, 1169–1172 (2007)

    ADS  Article  Google Scholar 

  20. 20

    Hermelin, S. et al. Electrons surfing on a sound wave as a platform for quantum optics with flying electrons. Nature 477, 435–438 (2011)

    ADS  CAS  Article  Google Scholar 

  21. 21

    McNeil, R. P. G. et al. On-demand single-electron transfer between distant quantum dots. Nature 477, 439–442 (2011)

    ADS  CAS  Article  Google Scholar 

  22. 22

    Levitov, L. S. & Lesovik, G. B. Charge distribution in quantum shot noise. . Pis’ma Z. Eksp. Teor. Fiz. 58, 225–230 (1993) JETP Lett. 58, 230–235 (1993)

    CAS  Google Scholar 

  23. 23

    Hassler, F., Lesovik, G. B. & Blatter, G. Effects of exchange symmetry on full counting statistics. Phys. Rev. Lett. 99, 076804 (2007)

    ADS  CAS  Article  Google Scholar 

  24. 24

    Vanević, M., Nazarov, Y. V. & Belzig, W. Elementary events of electron transfer in a voltage-driven quantum point contact. Phys. Rev. Lett. 99, 076601 (2007)

    ADS  Article  Google Scholar 

  25. 25

    Sherkunov, Y. B., Pratap, A., Muzykantskii, B. & d’Ambrumenil, N. Full counting statistics as the geometry of two planes. Phys. Rev. Lett. 100, 196601 (2008)

    ADS  CAS  Article  Google Scholar 

  26. 26

    Jonckheere, T., Creux, M. & Martin, T. Time-controlled charge injection in a quantum Hall fluid. Phys. Rev. B 72, 205321 (2005)

    ADS  Article  Google Scholar 

  27. 27

    Brantut, J. P. et al. Conduction of ultracold fermions through a mesoscopic channel. Science 337, 1069–1071 (2012)

    ADS  CAS  Article  Google Scholar 

  28. 28

    Thywissen, J. H., Westervelt, R. M. & Prentiss, M. Quantum point contacts for neutral atoms. Phys. Rev. Lett. 83, 3762–3765 (1999)

    ADS  CAS  Article  Google Scholar 

  29. 29

    Anderson, P. W. Infrared catastrophe in Fermi gases with local scattering potential. Phys. Rev. Lett. 18, 1049–1051 (1967)

    ADS  CAS  Article  Google Scholar 

  30. 30

    Lee, H. W. & Levitov, L. Orthogonality catastrophe in a mesoscopic conductor due to a time-dependent flux. Preprint at http://arxiv.org/abs/cond-mat/9312013 (1993)

  31. 31

    Dubois, J. et al. Integer and fractional charge Lorentzian voltage pulses analyzed in the framework of photon-assisted shot noise. Phys. Rev. B 88, 085301 (2013)

    ADS  Article  Google Scholar 

Download references

Acknowledgements

The ERC Advanced Grant 228273 MeQuaNo is acknowledged. We thank P. Jacques for technical help and P. Pari and P. Forget for support with cryogenics.

Author information

Affiliations

Authors

Contributions

D.C.G. designed the project. J.D. fabricated sample A on wafer provided by W.W., set up the radio-frequency and cryogenic systems with T.J., and, together with P. Roulleau, did the measurement and data analysis. The cryogenic amplifiers were made by P. Roulleau and T.J. F.P. helped in the early stages of the experiment and, together with P. Roulleau, T.J., P. Roche and D.C.G., wrote the paper. Sample B was provided by Y.J. on wafer from A.C.

Corresponding author

Correspondence to D. C. Glattli.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Methods, Supplementary Discussion, Supplementary Data, Supplementary Figures 1-7 and Supplementary References. (PDF 966 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Dubois, J., Jullien, T., Portier, F. et al. Minimal-excitation states for electron quantum optics using levitons. Nature 502, 659–663 (2013). https://doi.org/10.1038/nature12713

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

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