Coupling a single electron to a Bose–Einstein condensate

Abstract

The coupling of electrons to matter lies at the heart of our understanding of material properties such as electrical conductivity. Electron–phonon coupling can lead to the formation of a Cooper pair out of two repelling electrons, which forms the basis for Bardeen–Cooper–Schrieffer superconductivity1. Here we study the interaction of a single localized electron with a Bose–Einstein condensate and show that the electron can excite phonons and eventually trigger a collective oscillation of the whole condensate. We find that the coupling is surprisingly strong compared to that of ionic impurities, owing to the more favourable mass ratio. The electron is held in place by a single charged ionic core, forming a Rydberg bound state. This Rydberg electron is described by a wavefunction extending to a size of up to eight micrometres, comparable to the dimensions of the condensate. In such a state, corresponding to a principal quantum number of n = 202, the Rydberg electron is interacting with several tens of thousands of condensed atoms contained within its orbit. We observe surprisingly long lifetimes and finite size effects caused by the electron exploring the outer regions of the condensate. We anticipate future experiments on electron orbital imaging, the investigation of phonon-mediated coupling of single electrons, and applications in quantum optics.

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: Size comparison in the spatial and energy domains.
Figure 2: Rydberg excitation spectra for different principal quantum numbers and the mechanical effect on the condensate.
Figure 3: Energy shift and lifetime reduction of the Rydberg state in a condensate and Rydberg electron induced loss of BEC atoms.

References

  1. 1

    Bardeen, J., Cooper, L. N. & Schrieffer, J. R. Theory of superconductivity. Phys. Rev. 108, 1175–1204 (1957)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  2. 2

    Reif, F. & Meyer, L. Study of superfluidity in liquid He by ion motion. Phys. Rev. 119, 1164–1173 (1960)

    ADS  CAS  Article  Google Scholar 

  3. 3

    Rayfield, G. W. & Reif, F. Evidence for the creation and motion of quantized vortex rings in superfluid helium. Phys. Rev. Lett. 11, 305–308 (1963)

    ADS  CAS  Article  Google Scholar 

  4. 4

    Fisher, D. S., Halperin, B. I. & Platzman, P. M. Phonon-ripplon coupling and the two-dimensional electron solid on a liquid-helium surface. Phys. Rev. Lett. 42, 798–801 (1979)

    ADS  CAS  Article  Google Scholar 

  5. 5

    Platzman, P. M. & Dykman, M. I. Quantum computing with electrons floating on liquid helium. Science 284, 1967–1969 (1999)

    CAS  Article  Google Scholar 

  6. 6

    Robert, A. et al. A Bose-Einstein condensate of metastable atoms. Science 292, 461–464 (2001)

    ADS  CAS  Article  Google Scholar 

  7. 7

    Ciampini, D. et al. Photoionization of ultracold and Bose-Einstein-condensed Rb atoms. Phys. Rev. A 66, 043409 (2002)

    ADS  Article  Google Scholar 

  8. 8

    Zipkes, C., Palzer, S., Sias, C. & Köhl, M. A trapped single ion inside a Bose-Einstein condensate. Nature 464, 388–391 (2010)

    ADS  CAS  Article  Google Scholar 

  9. 9

    Ratschbacher, L., Zipkes, C., Sias, C. & Köhl, M. Controlling chemical reactions of a single particle. Nature Phys. 8, 649–652 (2012)

    ADS  CAS  Article  Google Scholar 

  10. 10

    Härter, A. et al. Single ion as a three-body reaction center in an ultracold atomic gas. Phys. Rev. Lett. 109, 123201 (2012)

    ADS  Article  Google Scholar 

  11. 11

    Shin, Y., Schunck, C. H., Schirotzek, A. & Ketterle, W. Tomographic rf spectroscopy of a trapped Fermi gas at unitarity. Phys. Rev. Lett. 99, 090403 (2007)

    ADS  CAS  Article  Google Scholar 

  12. 12

    Schirotzek, A., Wu, C.-H., Sommer, A. & Zwierlein, M. W. Observation of Fermi polarons in a tunable Fermi liquid of ultracold atoms. Phys. Rev. Lett. 102, 230402 (2009)

    ADS  Article  Google Scholar 

  13. 13

    Massignan, P., Pethick, C. J. & Smith, H. Static properties of positive ions in atomic Bose-Einstein condensates. Phys. Rev. A 71, 023606 (2005)

    ADS  Article  Google Scholar 

  14. 14

    Amaldi, E. & Segrè, E. Effect of pressure on high terms of alkaline spectra. Nature 133, 141 (1934)

    ADS  CAS  Article  Google Scholar 

  15. 15

    Fermi, E. Sopra lo spostamento per pressione delle righe elevate delle serie spettrali. Nuovo Cim. 11, 157–166 (1934)

    ADS  CAS  Article  Google Scholar 

  16. 16

    Greene, C. H., Dickinson, A. S. & Sadeghpour, H. R. Creation of polar and nonpolar ultralong-range Rydberg molecules. Phys. Rev. Lett. 85, 2458–2461 (2000)

    ADS  CAS  Article  Google Scholar 

  17. 17

    Bendkowsky, V. et al. Observation of ultralong-range Rydberg molecules. Nature 458, 1005–1008 (2009)

    ADS  CAS  Article  Google Scholar 

  18. 18

    Bendkowsky, V. et al. Rydberg trimers and excited dimers bound by internal quantum reflection. Phys. Rev. Lett. 105, 163201 (2010)

    ADS  CAS  Article  Google Scholar 

  19. 19

    Butscher, B. et al. Lifetimes of ultralong-range Rydberg molecules in vibrational ground and excited states. J. Phys. At. Mol. Opt. Phys. 44, 184004 (2011)

    ADS  Article  Google Scholar 

  20. 20

    Saffman, M., Walker, T. G. & Mølmer, K. Quantum information with Rydberg atoms. Rev. Mod. Phys. 82, 2313–2363 (2010)

    ADS  CAS  Article  Google Scholar 

  21. 21

    Bahrim, C., Thumm, U. & Fabrikant, I. I. 3S e and 1S e scattering lengths for e + Rb, Cs and Fr collisions. J. Phys. At. Mol. Opt. Phys. 34, L195–L201 (2001)

    ADS  CAS  Article  Google Scholar 

  22. 22

    Beterov, I. I., Ryabtsev, I. I., Tretyakov, D. B. & Entin, V. M. Quasiclassical calculations of blackbody-radiation-induced depopulation rates and effective lifetimes of Rydberg ns, np, and nd alkali-metal atoms with n ≤ 80. Phys. Rev. A 79, 052504 (2009)

    ADS  Article  Google Scholar 

  23. 23

    Honer, J., Löw, R., Weimer, H., Pfau, T. & Büchler, H. P. Artificial atoms can do more than atoms: deterministic single photon subtraction from arbitrary light fields. Phys. Rev. Lett. 107, 093601 (2011)

    ADS  Article  Google Scholar 

  24. 24

    Reinhard, A. et al. Double-resonance spectroscopy of interacting Rydberg-atom systems. Phys. Rev. Lett. 100, 233201 (2008)

    ADS  CAS  Article  Google Scholar 

  25. 25

    Löw, R. et al. An experimental and theoretical guide to strongly interacting Rydberg gases. J. Phys. At. Mol. Opt. Phys. 45, 113001 (2012)

    ADS  Article  Google Scholar 

Download references

Acknowledgements

We thank K. Rzążewski and J. Hecker Denschlag for discussions and C. Tresp for setting up the Rydberg laser system. This work was funded by the Deutsche Forschungsgemeinschaft (DFG) within SFB/TRR21 and project PF 381/4-2. We also acknowledge support by the ERC under contract number 267100, and A.G. acknowledges support from EU Marie Curie programme ITN-Coherence 265031. S.H. is supported by the DFG through project HO 4787/1-1.

Author information

Affiliations

Authors

Contributions

The experiment was conceived by J.B.B., R.L., S.H. and T.P. and carried out by J.B.B., A.T.K. and A.G.; data analysis was accomplished by J.B.B., A.T.K. and A.G.; perturbation theory was developed by D.P. and H.P.B.; and J.B.B. and D.P. wrote the manuscript with contributions from all authors.

Corresponding author

Correspondence to Tilman Pfau.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data, which includes a Supplementary Discussion, Supplementary Figures 1-2 and additional references. (PDF 214 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Balewski, J., Krupp, A., Gaj, A. et al. Coupling a single electron to a Bose–Einstein condensate. Nature 502, 664–667 (2013). https://doi.org/10.1038/nature12592

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