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.

Observation of the dynamical Casimir effect in a superconducting circuit

Nature volume 479, pages 376–379 (2011)Cite this article

Subjects

Abstract

One of the most surprising predictions of modern quantum theory is that the vacuum of space is not empty. In fact, quantum theory predicts that it teems with virtual particles flitting in and out of existence. Although initially a curiosity, it was quickly realized that these vacuum fluctuations had measurable consequences—for instance, producing the Lamb shift1 of atomic spectra and modifying the magnetic moment of the electron2. This type of renormalization due to vacuum fluctuations is now central to our understanding of nature. However, these effects provide indirect evidence for the existence of vacuum fluctuations. From early on, it was discussed whether it might be possible to more directly observe the virtual particles that compose the quantum vacuum. Forty years ago, it was suggested3 that a mirror undergoing relativistic motion could convert virtual photons into directly observable real photons. The phenomenon, later termed the dynamical Casimir effect4,5, has not been demonstrated previously. Here we observe the dynamical Casimir effect in a superconducting circuit consisting of a coplanar transmission line with a tunable electrical length. The rate of change of the electrical length can be made very fast (a substantial fraction of the speed of light) by modulating the inductance of a superconducting quantum interference device at high frequencies (>10 gigahertz). In addition to observing the creation of real photons, we detect two-mode squeezing in the emitted radiation, which is a signature of the quantum character of the generation process.

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

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Learn more

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

Figure 1: Experimental overview.
Figure 2: Photons generated by the dynamical Casimir effect.
Figure 3: Two-mode squeezing of the DCE field.

References

  1. Scully, M. O. & Zubairy, M. S. Quantum Optics (Cambridge Univ. Press, 1997)

    Book  Google Scholar 

  2. Greiner, W. & Schramm, S. Resource letter QEDV-1: the QED vacuum. Am. J. Phys. 76, 509–518 (2008)

    Article  ADS  Google Scholar 

  3. Moore, G. Quantum theory of the electromagnetic field in a variable-length one-dimensional cavity. J. Math. Phys. 11, 2679–2691 (1970)

    Article  ADS  Google Scholar 

  4. Dodonov, V. Current status of the dynamical Casimir effect. Phys. Scripta 82, 038105 (2010)

    Article  ADS  Google Scholar 

  5. Dalvit, D. A. R., Neto, P. A. M. & Mazzitelli, F. D. Fluctuations, dissipation and the dynamical Casimir effect. Preprint at 〈http://arXiv.org/abs/1006.4790v2〉 (2010)

  6. Casimir, H. B. G. On the attraction between two perfectly conducting plates. Proc. K. Ned. Akad. Wet. B 51, 793 (1948)

    MATH  Google Scholar 

  7. Lamoreaux, S. K. Casimir forces: still surprising after 60 years. Phys. Today 60, 40–45 (2007)

    Article  CAS  Google Scholar 

  8. Braggio, C. et al. A novel experimental approach for the detection of the dynamical Casimir effect. Europhys. Lett. 70, 754–760 (2005)

    Article  CAS  ADS  Google Scholar 

  9. Yablonovitch, E. Accelerating reference frame for electromagnetic waves in a rapidly growing plasma: Unruh-Davies-Fulling-Dewitt radiation and the nonadiabatic Casimir effect. Phys. Rev. Lett. 62, 1742–1745 (1989)

    Article  CAS  ADS  Google Scholar 

  10. Lozovik, Y., Tsvetus, V. & Vinogradov, E. Femtosecond parametric excitation of electromagnetic field in a cavity. JETP Lett. 61, 723–729 (1995)

    ADS  Google Scholar 

  11. Dodonov, V., Klimov, A. & Nikonov, D. Quantum phenomena in nonstationary media. Phys. Rev. A 47, 4422–4429 (1993)

    Article  CAS  ADS  Google Scholar 

  12. Schützhold, R., Plunien, G. & Soff, G. Quantum radiation in external background fields. Phys. Rev. A 58, 1783–1793 (1998)

    Article  ADS  Google Scholar 

  13. Kim, W., Brownell, J. & Onofrio, R. Detectability of dissipative motion in quantum vacuum via superradiance. Phys. Rev. Lett. 96, 200402 (2006)

    Article  ADS  Google Scholar 

  14. De Liberato, S., Ciuti, C. & Carusotto, I. Quantum vacuum radiation spectra from a semiconductor microcavity with a time-modulated vacuum Rabi frequency. Phys. Rev. Lett. 98, 103602 (2007)

    Article  ADS  Google Scholar 

  15. Günter, G. et al. Sub-cycle switch-on of ultrastrong light–matter interaction. Nature 458, 178–181 (2009)

    Article  ADS  Google Scholar 

  16. Johansson, J. R., Johansson, G., Wilson, C. M. & Nori, F. Dynamical Casimir effect in a superconducting coplanar waveguide. Phys. Rev. Lett. 103, 147003 (2009)

    Article  CAS  ADS  Google Scholar 

  17. Johansson, J. R., Johansson, G., Wilson, C. M. & Nori, F. Dynamical Casimir effect in superconducting microwave circuits. Phys. Rev. A 82, 052509 (2010)

    Article  ADS  Google Scholar 

  18. Wilson, C. M. et al. Photon generation in an electromagnetic cavity with a time-dependent boundary. Phys. Rev. Lett. 105, 233907 (2010)

    Article  CAS  ADS  Google Scholar 

  19. Dezael, F. & Lambrecht, A. Analogue Casimir radiation using an optical parametric oscillator. Europhys. Lett. 89, 14001 (2010)

    Article  ADS  Google Scholar 

  20. Nation, P. D., Johansson, J. R., Blencowe, M. P. & Nori, F. Stimulating uncertainty: amplifying the quantum vacuum with superconducting circuits. Rev. Mod. Phys. . (in the press); preprint at 〈http://arXiv.org/abs/1103.0835v1〉 (2011)

  21. Sandberg, M. et al. Tuning the field in a microwave resonator faster than the photon lifetime. Appl. Phys. Lett. 92, 203501 (2008)

    Article  ADS  Google Scholar 

  22. Fulling, S. A. & Davies, P. C. W. Radiation from a moving mirror in two dimensional space-time: conformal anomaly. Proc. R. Soc. Lond. A 348, 393–414 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  23. Lambrecht, A., Jaekel, M. & Reynaud, S. Motion induced radiation from a vibrating cavity. Phys. Rev. Lett. 77, 615–618 (1996)

    Article  CAS  ADS  Google Scholar 

  24. Dodonov, V., Klimov, A. & Man’ko, V. Generation of squeezed states in a resonator with a moving wall. Phys. Lett. A 149, 225–228 (1990)

    Article  ADS  Google Scholar 

  25. Caves, C. M. & Schumaker, B. L. New formalism for 2-photon quantum optics. 1. Quadrature phases and squeezed states. Phys. Rev. A 31, 3068–3092 (1985)

    Article  CAS  ADS  MathSciNet  Google Scholar 

  26. Yurke, B. & Denker, J. S. Quantum network theory. Phys. Rev. A 29, 1419–1437 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  27. Hoi, I.-C. et al. Demonstration of a single-photon router in the microwave regime. Phys. Rev. Lett. 107, 073601 (2011)

    Article  ADS  Google Scholar 

  28. Spietz, L., Lehnert, K., Siddiqi, I. & Schoelkopf, R. Primary electronic thermometry using the shot noise of a tunnel junction. Science 300, 1929–1932 (2003)

    Article  CAS  ADS  Google Scholar 

Download references

Acknowledgements

We thank G. Milburn and V. Shumeiko for discussions, and J. Aumentado and L. Spietz for providing the shot-noise thermometer. C.M.W., P.D., G.J., A.P. and M.S. were supported by the Swedish Research Council, the Wallenberg Foundation, STINT and the European Research Council. F.N. and J.R.J. acknowledge partial support from the LPS, NSA, ARO, DARPA, AFOSR, NSF grant no. 0726909, Grant-in-Aid for Scientific Research (S), MEXT Kakenhi on Quantum Cybernetics, and the JSPS-FIRST programme. T.D. acknowledges support from STINT and the Australian Research Council (grants DP0986932 and FT100100025).

Author information

Authors and Affiliations

  1. Department of Microtechnology and Nanoscience, Chalmers University of Technology, Göteborg 412 96+, Sweden,

    C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen & P. Delsing

  2. Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198, Japan ,

    J. R. Johansson & F. Nori

  3. University of New South Wales, Sydney, New South Wales 2052, Australia ,

    T. Duty

  4. University of Michigan, Ann Arbor, 48109, Michigan, USA

    F. Nori

Authors
  1. C. M. Wilson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Johansson
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Pourkabirian
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Simoen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. J. R. Johansson
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. T. Duty
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. F. Nori
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. P. Delsing
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

The experimental work was carried out by C.M.W., A.P., M.S., T.D. and P.D. The theoretical work was performed by J.R.J., F.N., C.M.W. and G.J.

Corresponding author

Correspondence to C. M. Wilson.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

The file contains Supplementary Figures 1-4 with legends, a Supplementary Discussion and Supplementary Methods. (PDF 340 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Wilson, C., Johansson, G., Pourkabirian, A. et al. Observation of the dynamical Casimir effect in a superconducting circuit. Nature 479, 376–379 (2011). https://doi.org/10.1038/nature10561

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature10561

This article is cited by

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

Advanced 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