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.

Bose–Einstein condensation of photons in an optical microcavity

Abstract

Bose–Einstein condensation (BEC)—the macroscopic ground-state accumulation of particles with integer spin (bosons) at low temperature and high density—has been observed in several physical systems1,2,3,4,5,6,7,8,9, including cold atomic gases and solid-state quasiparticles. However, the most omnipresent Bose gas, blackbody radiation (radiation in thermal equilibrium with the cavity walls) does not show this phase transition. In such systems photons have a vanishing chemical potential, meaning that their number is not conserved when the temperature of the photon gas is varied10; at low temperatures, photons disappear in the cavity walls instead of occupying the cavity ground state. Theoretical works have considered thermalization processes that conserve photon number (a prerequisite for BEC), involving Compton scattering with a gas of thermal electrons11 or photon–photon scattering in a nonlinear resonator configuration12,13. Number-conserving thermalization was experimentally observed14 for a two-dimensional photon gas in a dye-filled optical microcavity, which acts as a ‘white-wall’ box. Here we report the observation of a Bose–Einstein condensate of photons in this system. The cavity mirrors provide both a confining potential and a non-vanishing effective photon mass, making the system formally equivalent to a two-dimensional gas of trapped, massive bosons. The photons thermalize to the temperature of the dye solution (room temperature) by multiple scattering with the dye molecules. Upon increasing the photon density, we observe the following BEC signatures: the photon energies have a Bose–Einstein distribution with a massively populated ground-state mode on top of a broad thermal wing; the phase transition occurs at the expected photon density and exhibits the predicted dependence on cavity geometry; and the ground-state mode emerges even for a spatially displaced pump spot. The prospects of the observed effects include studies of extremely weakly interacting low-dimensional Bose gases9 and new coherent ultraviolet sources15.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Cavity mode spectrum and set-up.
Figure 2: Spectral and spatial intensity distribution.
Figure 3: Critical power.
Figure 4: Spatial redistribution of photons.

References

  1. Einstein, A. Quantentheorie des einatomigen idealen Gases. Zweite Abhandlung. Sitz. ber. Preuss. Akad. Wiss. 1, 3–14 (1925)

    MATH  Google Scholar 

  2. Anderson, M. H., Ensher, J. R., Matthews, M. R., Wieman, C. E. & Cornell, E. A. Observation of Bose–Einstein condensation in a dilute atomic vapor. Science 269, 198–201 (1995)

    ADS  CAS  Article  Google Scholar 

  3. Davis, K. B. et al. Bose-Einstein condensation in a gas of sodium atoms. Phys. Rev. Lett. 75, 3969–3973 (1995)

    ADS  CAS  Article  Google Scholar 

  4. Bradley, C. C., Sackett, C. A. & Hulet, R. G. Bose-Einstein condensation of lithium: observation of limited condensate number. Phys. Rev. Lett. 78, 985–989 (1997)

    ADS  CAS  Article  Google Scholar 

  5. Deng, H., Weihs, G., Santori, C., Bloch, J. & Yamamoto, Y. Condensation of semiconductor microcavity exciton polaritons. Science 298, 199–202 (2002)

    ADS  CAS  Article  Google Scholar 

  6. Kasprzak, J. et al. Bose–Einstein condensation of exciton polaritons. Nature 443, 409–414 (2006)

    ADS  CAS  Article  Google Scholar 

  7. Balili, R., Hartwell, V., Snoke, D., Pfeiffer, L. & West, K. Bose-Einstein condensation of microcavity polaritons in a trap. Science 316, 1007–1010 (2007)

    ADS  CAS  Article  Google Scholar 

  8. Demokritov, S. O. et al. Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumping. Nature 443, 430–433 (2006)

    ADS  CAS  Article  Google Scholar 

  9. Griffin, A., Snoke, D. W., Stringari, S., eds. Bose-Einstein Condensation (Cambridge University Press, 1995)

    Book  Google Scholar 

  10. Huang, K. Statistical Mechanics 2nd edn 293–294 (Wiley, 1987)

    Google Scholar 

  11. Zel'dovich, Y. B. & Levich, E. V. Bose condensation and shock waves in photon spectra. Sov. Phys. JETP 28, 1287–1290 (1969)

    ADS  Google Scholar 

  12. Chiao, R. Y. Bogoliubov dispersion relation for a ‘photon fluid’: is this a superfluid? Opt. Commun. 179, 157–166 (2000)

    ADS  CAS  Article  Google Scholar 

  13. Bolda, E. L., Chiao, R. Y. & Zurek, W. H. Dissipative optical flow in a nonlinear Fabry-Pérot cavity. Phys. Rev. Lett. 86, 416–419 (2001)

    ADS  CAS  Article  Google Scholar 

  14. Klaers, J., Vewinger, F. & Weitz, M. Thermalization of a two-dimensional photonic gas in a ‘white-wall’ photon box. Nature Phys. 6, 512–515 (2010)

    ADS  CAS  Article  Google Scholar 

  15. Jonkers, J. High power extreme ultra-violet (EUV) light sources for future lithography. Plasma Sources Sci. Technol. 15, S8–S16 (2006)

    ADS  Article  Google Scholar 

  16. Siegman, A. E. Lasers (University Science Books, 1986)

    Google Scholar 

  17. Ketterle, W., Durfee, D. S. & Stamper-Kurn, D. M. in Bose–Einstein Condensation in Atomic Gases (eds Inguscio, M., Stringari, S. & Wieman, C. E., ) CXL, 67–176 (Proceedings of the International School of Physics “Enrico Fermi”, IOS Press, 1999)

    Google Scholar 

  18. De Angelis, E., De Martini, F. & Mataloni, P. Microcavity superradiance. J. Opt. B 2, 149–155 (2000)

    ADS  CAS  Article  Google Scholar 

  19. Yokoyama, H. & Brorson, S. D. Rate equation analysis of microcavity lasers. J. Appl. Phys. 66, 4801–4805 (1989)

    ADS  CAS  Article  Google Scholar 

  20. Bagnato, V. & Kleppner, D. Bose-Einstein condensation in low-dimensional traps. Phys. Rev. A 44, 7439–7441 (1991)

    ADS  CAS  Article  Google Scholar 

  21. Mullin, W. J. Bose-Einstein condensation in a harmonic potential. J. Low-Temp. Phys. 106, 615–641 (1997)

    ADS  CAS  Article  Google Scholar 

  22. Lakowicz, J. R. Principles of Fluorescence Spectroscopy 2nd edn, 6 (Kluwer Academic/Plenum, 1999)

    Book  Google Scholar 

  23. Hadzibabic, Z. & Dalibard, J. Two-dimensional Bose fluids: an atomic physics perspective. Preprint at 〈http://arxiv.org/abs/0912.1490〉 (2009)

  24. Hadzibabic, Z., Krüger, P., Cheneau, M., Battelier, B. & Dalibard, J. Berezinskii–Kosterlitz–Thouless crossover in a trapped atomic gas. Nature 441, 1118–1121 (2006)

    ADS  CAS  Article  Google Scholar 

  25. De Martini, F. & Jacobovitz, G. R. Anomalous spontaneous–stimulated-decay phase transition and zero-threshold laser action in a microscopic cavity. Phys. Rev. Lett. 60, 1711–1714 (1988)

    ADS  CAS  Article  Google Scholar 

  26. Yokoyama, H. et al. Controlling spontaneous emission and threshold-less laser oscillation with optical microcavities. Quantum Electron. 24, S245–S272 (1992)

    CAS  Article  Google Scholar 

  27. Yamamoto, Y., Machida, S. & Björk, G. Micro-cavity semiconductor lasers with controlled spontaneous emission. Opt. Quantum Electron. 24, S215–S243 (1992)

    CAS  Article  Google Scholar 

  28. Kocharovsky, V. V. et al. Fluctuations in ideal and interacting bose–einstein condensates: from the laser phase transition analogy to squeezed states and Bogoliubov quasiparticles. Adv. At. Mol. Opt. Phys. 53, 291–411 (2006)

    ADS  CAS  Article  Google Scholar 

  29. McCumber, D. E. Einstein relations connecting broadband emission and absorption spectra. Phys. Rev. 136, A954–A957 (1964)

    ADS  Article  Google Scholar 

  30. Einstein, A. Zur Quantentheorie der Strahlung. Physik . Zeitschr. 18, 121–128 (1917)

    CAS  Google Scholar 

Download references

Acknowledgements

We thank J. Dalibard and Y. Castin for discussions. Financial support from the Deutsche Forschungsgemeinschaft within the focused research unit FOR557 is acknowledged. M.W. thanks the IFRAF for support of a guest stay at LKB Paris, where part of the discussion on interacting two-dimensional photon gases was developed.

Author information

Authors and Affiliations

Authors

Contributions

J.K. and M.W. contributed to the experimental idea; J.K. carried out the experiments. J.S. contributed to the experimental set-up. All authors analysed the experimental data and discussed the results.

Corresponding author

Correspondence to Martin Weitz.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Klaers, J., Schmitt, J., Vewinger, F. et al. Bose–Einstein condensation of photons in an optical microcavity. Nature 468, 545–548 (2010). https://doi.org/10.1038/nature09567

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature09567

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

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