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Foundations of Physics

, Volume 49, Issue 8, pp 797–815 | Cite as

Testing a Quantum Inequality with a Meta-analysis of Data for Squeezed Light

  • G. Jordan MaclayEmail author
  • Eric W. Davis
Article
  • 42 Downloads

Abstract

In quantum field theory, coherent states can be created that have negative energy density, meaning it is below that of empty space, the free quantum vacuum. If no restrictions existed regarding the concentration and permanence of negative energy regions, it might, for example, be possible to produce exotic phenomena such as Lorentzian traversable wormholes, warp drives, time machines, violations of the second law of thermodynamics, and naked singularities. Quantum Inequalities (QIs) have been proposed that restrict the size and duration of the regions of negative quantum vacuum energy that can be accessed by observers. However, QIs generally are derived for situations in cosmology and are very difficult to test. Direct measurement of vacuum energy is difficult and to date no QI has been tested experimentally. We test a proposed QI for squeezed light by a meta-analysis of published data obtained from experiments with optical parametric amplifiers and balanced homodyne detection. Over the last three decades, researchers in quantum optics have been trying to maximize the squeezing of the quantum vacuum and have succeeded in reducing the variance in the quantum vacuum fluctuations to \(-\,15\) dB. To apply the QI, a time sampling function is required. In our meta-analysis different time sampling functions for the QI were examined, but in all physically reasonable cases the QI is violated by much or all of the measured data. This brings into question the basis for QI. Possible explanations are given for this surprising result.

Keywords

Squeezed light Quantum inequality Vacuum energy Vacuum fluctuations Negative energy Optical parametric amplifier 

Notes

Acknowledgements

We are very grateful to Peter Milonni and Larry Ford for helpful discussions and comments. We would like to thank the Institute for Advanced Studies At Austin and H. E. Puthoff for supporting this work.

References

  1. 1.
    Bekenstein, J.: If vacuum energy can be negative, why is mass always positive?: Uses of the subdominant trace energy condition. Phys. Rev. D 88, 125005 (2013)ADSCrossRefGoogle Scholar
  2. 2.
    Visser, M.: Lorentzian Wormholes, From Einstein to Hawking. AIP, Springer, New York (1995)Google Scholar
  3. 3.
    Ford, L., Roman, T.: Restrictions on negative energy density in flat spacetime. Phys. Rev. D 55, 2082 (1997)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Davies, P., Ottewill, A.: Detection of negative energy: 4-dimensional examples. Phys. Rev. D 65, 104014 (2002)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    Ford, L.: Negative energy densities in quantum field theory. Int. J. Mod. Phys. A 25, 2355 (2010)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Riek, C., Sulzer, P., Seeger, M., Moskalenko, A.S., Burkard, G., Seletskiy, D.V., Leitenstorfer, A.: Subcycle quantum electrodynamics. Nature 541, 376 (2017)ADSCrossRefGoogle Scholar
  7. 7.
    Ford, L.: Quantum coherence effects and the second law of thermodynamics. Proc. R Soc. Lond. Ser. A 364, 227 (1978)ADSCrossRefGoogle Scholar
  8. 8.
    Ford, L.: Constraints on negative-energy fluxes. Phys. Rev. D 4, 3972 (1991)ADSCrossRefGoogle Scholar
  9. 9.
    Marecki, P.: Application of quantum inequalities to quantum optics. Phys. Rev. A 66, 053801 (2002)ADSCrossRefGoogle Scholar
  10. 10.
    Vahlbruch, H., Mehmet, M., Danzmann, K., Schnabel, R.: Detection of 15 dB squeezed states of light and their application for the absolute calibration of photoelectric quantum efficiency. Phys. Rev. Lett. 117, 110801 (2016)ADSCrossRefGoogle Scholar
  11. 11.
    Marecki, P.: Balanced homodyne detectors in quantum field theory. Phys. Rev. A 77, 012101 (2008)ADSCrossRefGoogle Scholar
  12. 12.
    Marecki, P.: Balanced homodyne detectors and Casimir energy densities. J. Phys. A 41, 164037 (2008)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Pfenning, M.: Quantum inequalities for the electromagnetic field. Phys. Rev. D 65, 024009 (2001)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    Gardiner, C., Savage, C.: A multimode quantum theory of a degenerate parametric amplifier in a cavity. Opt. Commun. 50, 173 (1984)ADSCrossRefGoogle Scholar
  15. 15.
    Collett, M., Walls, D.: Squeezing spectra for nonlinear optical systems. Phys. Rev. A 32, 2887 (1985)ADSCrossRefGoogle Scholar
  16. 16.
    Polzit, E., Carri, J., Kimble, H.: Atomic spectroscopy with squeezed light for sensitivity beyond the vacuum-state limit. Appl. Phys. B 55, 279 (1992)ADSCrossRefGoogle Scholar
  17. 17.
    Suzuki, S., Yonezawa, H., Kannari, F., Sasaki, M., Furusawa, A.: 7dB quadrature squeezing at 860nm with periodically poled KTiOPO\(_4\). Appl. Phys. Lett. 89, 061116 (2006)ADSCrossRefGoogle Scholar
  18. 18.
    Takeno, Y., Takahashi, G., Furusawa, A.: Observation of \(-\,9\) dB quadrature squeezing with improvement of phase stability in homodyne measurement. Opt. Exp. 15, 4321 (2007)ADSCrossRefGoogle Scholar
  19. 19.
    Smithey, D., Beck, M., Raymer, M., Faridani, A.: Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: application to squeezed states and the vacuum. Phys. Rev. Lett. 70, 1244 (1993)ADSCrossRefGoogle Scholar
  20. 20.
    Wu, L., Kimble, H., Hall, J., Wu, H.: Generation of squeezed states by parametric down conversion. Phys. Rev. Lett. 57, 2520 (1986)ADSCrossRefGoogle Scholar
  21. 21.
    Zhang, T., Goh, K., Chou, C., Lodahl, P., Kimble, H.: Quantum teleportation of light beams. Phys. Rev. A 67, 033802 (2003)ADSCrossRefGoogle Scholar
  22. 22.
    Tanimura, T., Akamatsu, D., Yokoi, Y., Furusawa, A., Kozuma, M.: Generation of a squeezed vacuum resonant on a rubidium \(D_{1}\) line with periodically poled KTiOPO\(_4\). Opt. Lett. 31, 2344 (2006)ADSCrossRefGoogle Scholar
  23. 23.
    Breitenbach, G., Illuminati, F., Shiller, S., Mlynek, J.: Broadband detection of squeezed vacuum: a spectrum of quantum states. Europhys. Lett. 44(2), 192 (1998)ADSCrossRefGoogle Scholar
  24. 24.
    Aoki, T., Takahashi, G., Furusawa, A.: Squeezing at 946nm with periodically poled KTiOPO\(_4\). Opt. Exp. 14, 6930 (2006)ADSCrossRefGoogle Scholar
  25. 25.
    Hetet, G., Gloecki, O., Pilynas, K., Harb, C., Buchler, B., Bachor, H., Lam, P.: Squeezed light for bandwidth-limited atom optics experiments at the rubidium D1 line. J. Phys. B 40, 221 (2007)ADSCrossRefGoogle Scholar
  26. 26.
    Hirano, T., Kotani, K., Ishibashi, T., Okude, S., Kuwamoto, T.: 3 dB squeezing by single-pass parametric amplification in a periodically poled KTiOPO\(_4\) crystal. Opt. Lett. 30, 1722 (2005)ADSCrossRefGoogle Scholar
  27. 27.
    Fewster, C.J., Teo, E.: Bounds on negative energy densities in static space-times. Phys. Rev. D 59, 104016 (1999)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Quantum Fields LLCSt. CharlesUSA
  2. 2.Institute for Advanced Studies at AustinAustinUSA
  3. 3.Early Universe, Cosmology and Strings Group, Center for Astrophysics, Space Physics and Engineering ResearchBaylor UniversityWacoUSA

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