Electric field correlation measurements on the electromagnetic vacuum state

Abstract

Quantum mechanics ascribes to the ground state of the electromagnetic radiation1 zero-point electric field fluctuations that permeate empty space at all frequencies. No energy can be extracted from the ground state of a system, and therefore these fluctuations cannot be measured directly with an intensity detector. The experimental proof of their existence therefore came from more indirect evidence, such as the Lamb shift2,3,4, the Casimir force between close conductors5,6,7 or spontaneous emission1,8. A direct method of determining the spectral characteristics of vacuum field fluctuations has so far been missing. Here we perform a direct measurement of the field correlation on these fluctuations in the terahertz frequency range by using electro-optic detection9 in a nonlinear crystal placed in a cryogenic environment. We investigate their temporal and spatial coherence, which, at zero time delay and spatial distance, has a peak value of 6.2 × 10−2 volts squared per square metre, corresponding to a fluctuating vacuum field10,11 of 0.25 volts per metre. With this measurement, we determine the spectral components of the ground state of electromagnetic radiation within the bandwidth of our electro-optic detection.

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Fig. 1: Experimental setup for the temporal and spatial electro-optic field correlation on vacuum and thermal fields.
Fig. 2: Mean photon occupation number per mode, coherence length and electric field transmission of THz radiation.
Fig. 3: Electro-optic field correlation results at 300 K and 4 K.
Fig. 4: Electro-optic field correlation result of thermal radiation at 45 K.

Data availability

The raw data associated with Figs. 2b, c, 3a–e and 4a, b are provided with the manuscript. Other data that support the findings of this study are available from the corresponding author on reasonable request.

References

  1. 1.

    Loudon, R. The Quantum Theory of Light (Oxford Univ. Press, Oxford, 2000).

  2. 2.

    Lamb, W. E. Jr. & Retherford, R. C. Fine structure of the hydrogen atom by a microwave method. Phys. Rev. 72, 241–243 (1947).

    ADS  CAS  Article  Google Scholar 

  3. 3.

    Bethe, H. A. The electromagnetic shift of energy levels. Phys. Rev. 72, 339–341 (1947).

    ADS  CAS  Article  Google Scholar 

  4. 4.

    Fragner, A. et al. Resolving vacuum fluctuations in an electrical circuit by measuring the Lamb shift. Science 322, 1357–1360 (2008).

    ADS  CAS  Article  Google Scholar 

  5. 5.

    Casimir, H. B. G. On the attraction between two perfectly conducting plates. Indag. Math. 10, 261–263 (1948).

    MATH  Google Scholar 

  6. 6.

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

    ADS  Article  Google Scholar 

  7. 7.

    Wilson, C. M. et al. Observation of the dynamical Casimir effect in a superconducting circuit. Nature 479, 376–379 (2011).

    ADS  CAS  Article  Google Scholar 

  8. 8.

    Walls, D. & Milburn, G. Quantum Optics ch. 10 (Springer, 1994).

  9. 9.

    Wu, Q. & Zhang, X. C. Free-space electro-optic sampling of terahertz beams. Appl. Phys. Lett. 67, 3523–3525 (1995).

    ADS  CAS  Article  Google Scholar 

  10. 10.

    Riek, C. et al. Direct sampling of electric-field vacuum fluctuations. Science 350, 420–423 (2015).

    ADS  MathSciNet  CAS  Article  Google Scholar 

  11. 11.

    Riek, C. et al. Subcycle quantum electrodynamics. Nature 541, 376–379 (2017).

    ADS  CAS  Article  Google Scholar 

  12. 12.

    Purcell, E. M. Spontaneous emission probabilities at radio frequencies. Phys. Rev. 69, 681 (1946).

    Article  Google Scholar 

  13. 13.

    Scalari, G. et al. Ultrastrong coupling of the cyclotron transition of a 2D electron gas to a THz metamaterial. Science 335, 1323–1326 (2012).

    ADS  CAS  Article  Google Scholar 

  14. 14.

    Keller, J. et al. Few-electron ultrastrong light–matter coupling at 300 GHz with nanogap hybrid LC microcavities. Nano Lett. 17, 7410–7415 (2017).

    ADS  CAS  Article  Google Scholar 

  15. 15.

    Bayer, A. et al. Terahertz light–matter interaction beyond unity coupling strength. Nano Lett. 17, 6340–6344 (2017).

    ADS  CAS  Article  Google Scholar 

  16. 16.

    Ciuti, C., Bastard, G. & Carusotto, I. Quantum vacuum properties of the intersubband cavity polariton field. Phys. Rev. B 72, 115303 (2005).

    ADS  Article  Google Scholar 

  17. 17.

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

    ADS  Article  Google Scholar 

  18. 18.

    Benea-Chelmus, I.-C. et al. Subcycle measurement of intensity correlations in the terahertz frequency range. Phys. Rev. A 93, 043812–043819 (2016).

    Article  Google Scholar 

  19. 19.

    Benea-Chelmus, I.-C., Rösch, M., Scalari, G., Beck, M. & Faist, J. Intensity autocorrelation measurements of frequency combs in the terahertz range. Phys. Rev. A 96, 033821–033828 (2017).

    ADS  Article  Google Scholar 

  20. 20.

    Moskalenko, A. S., Riek, C., Seletskiy, D. V., Burkard, G. & Leitenstorfer, A. Paraxial theory of direct electro-optic sampling of the quantum vacuum. Phys. Rev. Lett. 115, 263601–263605 (2015).

    ADS  CAS  Article  Google Scholar 

  21. 21.

    Aspelmeyer, M., Kippenberg, T. J. & Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391–1452 (2014).

    ADS  Article  Google Scholar 

  22. 22.

    Khalili, F. Y. et al. Quantum back-action in measurements of zero-point mechanical oscillations. Phys. Rev. A 86, 033840 (2012).

    ADS  Article  Google Scholar 

  23. 23.

    Kwiat, P. G. et al. New high-intensity source of polarization-entangled photon pairs. Phys. Rev. Lett. 75, 4337–4341 (1995).

    ADS  CAS  Article  Google Scholar 

  24. 24.

    da Silva, M. P., Bozyigit, D., Wallraff, A. & Blais, A. Schemes for the observation of photon correlation functions in circuit QED with linear detectors. Phys. Rev. A 82, 043804 (2010).

    ADS  Article  Google Scholar 

  25. 25.

    Bozyigit, D. et al. Antibunching of microwave-frequency photons observed in correlation measurements using linear detectors. Nat. Phys. 7, 154–158 (2011).

    CAS  Article  Google Scholar 

  26. 26.

    Lähteenmäki, P., Paraoanu, G. S., Hassel, J. & Hakonen, P. J. Coherence and multimode correlations from vacuum fluctuations in a microwave superconducting cavity. Nat. Commun. 7, 12548 (2016).

    ADS  Article  Google Scholar 

  27. 27.

    Kizmann, M. et al. Subcycle squeezing of light from a time flow perspective. Preprint at https://arxiv.org/abs/1807.10519 (2018).

  28. 28.

    Benea-Chelmus, I.-C. et al. Three-dimensional phase modulator at telecom wavelength acting as a terahertz detector with an electro-optic bandwidth of 1.25 terahertz. ACS Photonics 5, 1398–1403 (2018).

    CAS  Article  Google Scholar 

  29. 29.

    Cong, K. et al. Dicke superradiance in solids. J. Opt. Soc. Am. B 33, C80–C101 (2016).

    Article  Google Scholar 

  30. 30.

    Hagenmüller, D., Schachenmayer, J., Schütz, S., Genes, C. & Pupillo, G. Cavity-enhanced transport of charge. Phys. Rev. Lett. 119, 223601 (2017).

    ADS  Article  Google Scholar 

  31. 31.

    Orgiu, E. et al. Conductivity in organic semiconductors hybridized with the vacuum field. Nat. Mater. 14, 1123–1129 (2015).

    ADS  CAS  Article  Google Scholar 

  32. 32.

    Rungsawang, R. et al. Intensity detection of terahertz quantum cascade laser radiation using electro-optic sampling. Appl. Phys. Lett. 93, 191111 (2008).

    ADS  Article  Google Scholar 

  33. 33.

    van Kolck, A. et al. Thermo-optic detection of terahertz radiation from a quantum cascade laser. Appl. Phys. Lett. 97, 251103 (2010).

    ADS  Article  Google Scholar 

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Acknowledgements

This work was funded by the European Research Council (Advanced Grant, Quantum Metamaterials in the Ultra Strong Coupling Regime) and the Swiss National Science Foundation (grant 165639). We acknowledge the mechanical workshop at ETHZ. We acknowledge the contribution of M. Ernzer to the noise analysis tools, E. Mavrona to the design of opto-mechanical components and the extraction of the refractive index of ZnTe, and A. Imamoglu for discussions.

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I.-C.B.-C. and J.F. conceived and designed the experiments. I.-C.B.-C., F.F.S and G.S. built the experimental setup. I.-C.B.-C. developed the data acquisition system and noise suppression protocols. I.-C.B.-C. and F.F.S. performed the measurements. I.-C.B.-C., F.F.S. and J.F. analysed and interpreted the data. I.-C.B.-C., F.F.S. and J.F. derived the theory. J.F. was the scientific supervisor of this work. All authors discussed the results and contributed to the writing of the manuscript.

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Correspondence to Ileana-Cristina Benea-Chelmus or Jérôme Faist.

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Benea-Chelmus, I., Settembrini, F.F., Scalari, G. et al. Electric field correlation measurements on the electromagnetic vacuum state. Nature 568, 202–206 (2019). https://doi.org/10.1038/s41586-019-1083-9

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