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Probing Planck-scale physics with quantum optics

Nature Physics volume 8, pages 393–397 (2012)Cite this article

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Abstract

One of the main challenges in physics today is to merge quantum theory and the theory of general relativity into a unified framework. Researchers are developing various approaches towards such a theory of quantum gravity, but a major hindrance is the lack of experimental evidence of quantum gravitational effects. Yet, the quantization of spacetime itself can have experimental implications: the existence of a minimal length scale is widely expected to result in a modification of the Heisenberg uncertainty relation. Here we introduce a scheme to experimentally test this conjecture by probing directly the canonical commutation relation of the centre-of-mass mode of a mechanical oscillator with a mass close to the Planck mass. Our protocol uses quantum optical control and readout of the mechanical system to probe possible deviations from the quantum commutation relation even at the Planck scale. We show that the scheme is within reach of current technology. It thus opens a feasible route for table-top experiments to explore possible quantum gravitational phenomena.

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Figure 1: The quantum uncertainty relation and a quantum gravitational modification.
Figure 2: Changes to the optical field following the pulsed optomechanical interactions.
Figure 3: Proposed experimental set-up to probe deformations of the canonical commutator of a macroscopic mechanical resonator.

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Change history

  • 26 March 2012

    In the version of this Article originally published online, ref. 5 was incorrect. This has been corrected in all versions of the Article.

  • 10 April 2012

    In the version of this Article originally published online, the experimental parameters for testing equations (1) and (3) given in Table 2 and subsequently used in the text on the same page were incorrect. These errors have been corrected in all versions of the Article.

References

  1. Heisenberg, W. Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Z. Phys. 43, 172–198 (1927).

    Article  ADS  Google Scholar 

  2. Garay, L. G. Quantum gravity and minimum length. Int. J. Mod. Phys. A10, 145–165 (1995).

    Article  ADS  Google Scholar 

  3. Amati, D., Ciafaloni, M. & Veneziano, G. Superstring collisions at planckian energies. Phys. Lett. B 197, 81–88 (1987).

    Article  ADS  Google Scholar 

  4. Gross, D. J. & Mende, P. F. String theory beyond the Planck scale. Nucl. Phys. B 303, 407–454 (1988).

    Article  ADS  MathSciNet  Google Scholar 

  5. Amelino-Camelia, G. Doubly special relativity: First results and key open problems. Int. J. Mod. Phys. D 11, 1643–1669 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  6. Magueijo, J. & Smolin, L. Generalized Lorentz invariance with an invariant energy scale. Phys. Rev. D 67, 044017 (2003).

    Article  ADS  MathSciNet  Google Scholar 

  7. Amelino-Camelia, G., Freidel, L., Kowalski-Glikman, J. & Smolin, L. Principle of relative locality. Phys. Rev. D 84, 084010 (2011).

    Article  ADS  Google Scholar 

  8. Maggiore, M. A generalized uncertainty principle in quantum gravity. Phys. Lett. B 304, 65–69 (1993).

    Article  ADS  MathSciNet  Google Scholar 

  9. Scardigli, F. Generalized uncertainty principle in quantum gravity from micro-black hole gedanken experiment. Phys. Lett. B 452, 39–44 (1999).

    Article  ADS  Google Scholar 

  10. Jizba, P., Kleinert, H. & Scardigli, F. Uncertainty relation on a world crystal and its applications to micro black holes. Phys. Rev. D 81, 084030 (2010).

    Article  ADS  Google Scholar 

  11. Maggiore, M. The algebraic structure of the generalized uncertainty principle. Phys. Lett. B 319, 83–86 (1993).

    Article  ADS  MathSciNet  Google Scholar 

  12. Kempf, A., Mangano, G. & Mann, R. B. Hilbert space representation of the minimal length uncertainty relation. Phys. Rev. D 52, 1108–1118 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  13. Das, S. & Vagenas, E. C. Universality of quantum gravity corrections. Phys. Rev. Lett. 101, 221301 (2008).

    Article  ADS  Google Scholar 

  14. Ali, A. F., Das, S. & Vagenas, E. C. Discreteness of space from the generalized uncertainty principle. Phys. Lett. B 678, 497–499 (2009).

    Article  ADS  MathSciNet  Google Scholar 

  15. Ali, A. F., Das, S. & Vagenas, E. C. A proposal for testing quantum gravity in the lab. Phys. Rev. D 84, 044013 (2011).

    Article  ADS  Google Scholar 

  16. Amelino-Camelia, G., Ellis, J., Mavromatos, N. E., Nanopoulos, D. V. & Sarkar, S. Tests of quantum gravity from observations of gamma-ray bursts. Nature 393, 763–765 (1998).

    Article  ADS  Google Scholar 

  17. Jacob, U. & Piran, T. Neutrinos from gamma-ray bursts as a tool to explore quantum-gravity-induced Lorentz violation. Nature Phys. 7, 87–90 (2007).

    Article  ADS  Google Scholar 

  18. Abdo, A. A. et al. A limit on the variation of the speed of light arising from quantum gravity effects. Nature 462, 331–334 (2009).

    Article  ADS  Google Scholar 

  19. Tamburini, F., Cuofano, C., Della Valle, M. & Gilmozzi, R. No quantum gravity signature from the farthest quasars. Astron. Astrophys. 533, A71 (2011).

    Article  ADS  Google Scholar 

  20. Grote, H. & the LIGO Scientific Collaboration. The status of GEO 600. Class. Quantum Grav. 25, 114043 (2008).

  21. Abbott, B. P. et al. LIGO: The Laser Interferometer Gravitational-wave Observatory. Rep. Prog. Phys. 72, 076901 (2009).

    Article  ADS  Google Scholar 

  22. Kippenberg, T. J. & Vahala, K. J. Cavity optomechanics: Back-action at the mesoscale. Science 321, 1172–1176 (2008).

    Article  ADS  Google Scholar 

  23. Aspelmeyer, M., Groeblacher, S., Hammerer, K. & Kiesel, N. Quantum optomechanics—throwing a glance. J. Opt. Soc. Am. B 27, A189–A197 (2010).

    Article  ADS  Google Scholar 

  24. Milburn, G. J. Lorentz invariant intrinsic decoherence. New J. Phys. 8, 96 (2006).

    Article  ADS  Google Scholar 

  25. Kempf, A. Information-theoretic natural ultraviolet cutoff for spacetime. Phys. Rev. Lett. 103, 231301 (2009).

    Article  ADS  Google Scholar 

  26. Barnett, S. M. & Radmore, P. M. Methods in Theoretical Quantum Optics (Oxford Univ. Press, 2002).

    Book  Google Scholar 

  27. Milburn, G. J., Schneider, S. & James, D. F. V. Ion trap quantum computing with warm ions. Fortschr. Phys. 48, 801–810 (2000).

    Article  Google Scholar 

  28. Sørensen, A. & Mølmer, K. Entanglement and quantum computation with ions in thermal motion. Phys. Rev. A 62, 022311 (2000).

    Article  ADS  Google Scholar 

  29. Leibfried, D. et al. Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate. Nature 422, 412–415 (2003).

    Article  ADS  Google Scholar 

  30. Wilcox, R. M. Exponential operators and parameter differentiation in quantum physics. J. Math. Phys. 8, 962–982 (1967).

    Article  ADS  MathSciNet  Google Scholar 

  31. Nozari, K. Some aspects of Planck scale quantum optics. Phys. Lett. B. 629, 41–52 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  32. Ghosh, S. & Roy, P. “Stringy” coherent states inspired by generalized uncertainty principle. Preprint at http://arxiv.org/hep-ph/11105136 (2011).

  33. Parigi, V., Zavatta, A., Kim, M. S. & Bellini, M. Probing quantum commutation rules by addition and subtraction of single photons to/from a light field. Science 317, 1890–1893 (2007).

    Article  ADS  Google Scholar 

  34. Kim, M. S., Jeong, H., Zavatta, A., Parigi, V. & Bellini, M. Scheme for proving the bosonic commutation relation using single-photon interference. Phys. Rev. Lett. 101, 260401 (2008).

    Article  ADS  Google Scholar 

  35. Teufel, J. D. et al. Sideband cooling of micromechanical motion to the quantum ground state. Nature 475, 359–363 (2010).

    Article  ADS  Google Scholar 

  36. Chan, J. et al. Laser cooling of a nanomechanical oscillator into its quantum ground state. Nature 478, 89–92 (2011).

    Article  ADS  Google Scholar 

  37. Gröblacher, S., Hammerer, K., Vanner, M. R. & Aspelmeyer, M. Observation of strong coupling between a micromechanical resonator and an optical cavity field. Nature 460, 724–727 (2009).

    Article  ADS  Google Scholar 

  38. Teufel, J. D. et al. Circuit cavity electromechanics in the strong-coupling regime. Nature 471, 204–208 (2011).

    Article  ADS  Google Scholar 

  39. O’Connell, A. D. et al. Quantum ground state and single-phonon control of a mechanical resonator. Nature 464, 697–703 (2010).

    Article  ADS  Google Scholar 

  40. Verhagen, E., Deléglise, S., Weis, S., Schliesser, A. & Kippenberg, T. J. Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode. Nature 482, 63–67 (2012).

    Article  ADS  Google Scholar 

  41. Marshall, W., Simon, C., Penrose, R. & Bouwmeester, D. Towards quantum superpositions of a mirror. Phys. Rev. Lett. 91, 130401 (2003).

    Article  ADS  MathSciNet  Google Scholar 

  42. Romero-Isart, O. et al. Large quantum superpositions and interference of massive nanometer-sized objects. Phys. Rev. Lett. 107, 020405 (2011).

    Article  ADS  Google Scholar 

  43. Vanner, M. R. et al. Pulsed quantum optomechanics. Proc. Natl Acad. Sci. USA 108, 16182–16187 (2011).

    Article  ADS  Google Scholar 

  44. Law, C. K. Interaction between a moving mirror and radiation pressure: A Hamiltonian formulation. Phys. Rev. A 51, 2537–2541 (1995).

    Article  ADS  Google Scholar 

  45. Karrai, K., Favero, I. & Metzger, C. Doppler optomechanics of a photonic crystal. Phys. Rev. Lett. 100, 240801 (2008).

    Article  ADS  Google Scholar 

  46. Boixo, S. et al. Quantum-limited metrology and Bose–Einstein condensates. Phys. Rev. A 80, 032103 (2009).

    Article  ADS  Google Scholar 

  47. Corbitt, T. et al. Optical dilution and feedback cooling of a gram-scale oscillator to 6.9 mK. Phys. Rev. Lett. 99, 160801 (2007).

    Article  ADS  Google Scholar 

  48. Thompson, J. D. et al. Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane. Nature 452, 72–76 (2008).

    Article  ADS  Google Scholar 

  49. Verlot, P., Tavernarakis, A., Briant, T., Cohadon, P-F. & Heidmann, A. Scheme to probe optomechanical correlations between two optical beams down to the quantum level. Phys. Rev. Lett. 102, 103601 (2008).

    Article  ADS  Google Scholar 

  50. Kleckner, D. et al. Optomechanical trampoline resonators. Opt. Express 19, 19708–19716 (2011).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by the Royal Society, by the Engineering and Physical Sciences Research Council, by the European Comission (Quantum InterfacES, SENsors, and Communication based on Entanglement (Q-ESSENCE)), by the European Research Council Quantum optomechanics: quantum foundations and quantum information on the micro- and nanoscale (QOM), by the Austrian Science Fund (FWF) (Complex Quantum Systems (CoQuS), START program, Special Research Programs (SFB) Foundations and Applications of Quantum Science (FoQuS)), by the Foundational Questions Institute and by the John Templeton Foundation. M.R.V. is a recipient of a DOC fellowship of the Austrian Academy of Sciences. I.P. and M.R.V are members of the FWF Doctoral Programme CoQuS and they are grateful for the kind hospitality provided by Imperial College London. The authors thank S. Das, S. Gielen, H. Grosse, A. Kempf, W. T. Kim and J. Lee for discussions.

Author information

Authors and Affiliations

  1. Vienna Center for Quantum Science and Technology (VCQ), Boltzmanngasse 5, A-1090 Vienna, Austria

    Igor Pikovski, Michael R. Vanner & Markus Aspelmeyer

  2. Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria

    Igor Pikovski, Michael R. Vanner, Markus Aspelmeyer & Časlav Brukner

  3. Quantum Optics and Laser Science (QOLS) group, Blackett Laboratory, Imperial College London, SW7 2BW, UK

    M. S. Kim

  4. Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria

    Časlav Brukner

Authors
  1. Igor Pikovski
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Contributions

I.P. and M.S.K. conceived the research, which was further developed by Č.B. and all co-authors. M.R.V. conceived the experimental scheme. M.A. analysed the feasibility of the scheme with input from all co-authors. All authors performed the research under the supervision of Č.B. and all authors wrote the manuscript.

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Correspondence to Igor Pikovski or M. S. Kim.

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Pikovski, I., Vanner, M., Aspelmeyer, M. et al. Probing Planck-scale physics with quantum optics. Nature Phys 8, 393–397 (2012). https://doi.org/10.1038/nphys2262

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