Foundations of Physics

, Volume 44, Issue 5, pp 492–511 | Cite as

Quantum Thermometry

  • Robert B. MannEmail author
  • Eduardo Martín-Martínez


We show how Berry phase can be used to construct a precision quantum thermometer. An important advantage of our scheme is that there is no need for the thermometer to acquire thermal equilibrium with the sample. This reduces measurement times and avoids precision limitations. We also discuss how such methods can be used to detect the Unruh effect.


Entanglement Berry phase Unruh effect Temperature 



This work was supported in part by the Natural Sciences and Engineering Research Council of Canada. R.B.M. is grateful to Fabio Scardigli and the organizers of the Horizons of Quantum Physics conference for their invitation to speak at this meeting. E. M-M. gratefully acknowledges the funding of the Banting Postdoctoral Fellowship Programme.


  1. 1.
    Berry, M.V.: Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. Lond. A 392, 45–57 (1984)ADSCrossRefzbMATHGoogle Scholar
  2. 2.
    Martin-Martinez, E., Dragan, A., Mann, R.B., Fuentes, I.: Berry phase quantum thermometer. New J. Phys. 15, 053036 (2013)ADSCrossRefGoogle Scholar
  3. 3.
    Martín-Martínez, E., Fuentes, I., Mann, R.B.: Using Berry’s phase to detect the Unruh effect at lower accelerations. Phys. Rev. Lett. 107, 131301 (2011)ADSCrossRefGoogle Scholar
  4. 4.
    Unruh, W.G.: Notes on black-hole evaporation. Phys. Rev. D 14, 870–892 (1976)ADSCrossRefGoogle Scholar
  5. 5.
    Crispino, L.C.B., Higuchi, A., Matsas, G.E.A.: The Unruh effect and its applications. Rev. Mod. Phys. 80, 787–838 (2008)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Chen, P., Tajima, T.: Testing Unruh radiation with ultraintense lasers. Phys. Rev. Lett. 83, 256–259 (1999)ADSCrossRefGoogle Scholar
  7. 7.
    Rosu, H.C.: Hawking-like effects and Unruh-like effects: toward experiments? Gravit. Cosmol. 7, 1–17 (2001)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Hawking, S.W.: Black hole explosions? Nature 248, 30 (1974)ADSCrossRefGoogle Scholar
  9. 9.
    Turner, M.S.: Could primordial black holes be the source of the cosmic ray antiprotons? Nature 297, 379 (1982)ADSCrossRefGoogle Scholar
  10. 10.
    Davies, P.C.W.: Quantum vacuum noise in physics and cosmology. Chaos 11, 539 (2001)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Gibbons, G.W., Shellard, E.P.S.: Tales of singularities. Science 295, 1476–1477 (2002)CrossRefGoogle Scholar
  12. 12.
    Vanzella, D.A.T., Matsas, G.E.A.: Decay of accelerated protons and the existence of the Fulling–Davies–Unruh effect. Phys. Rev. Lett. 87, 151301 (2001)ADSCrossRefGoogle Scholar
  13. 13.
    Taubes, G.: String theorists find a Rosetta Stone. Science 285, 512–517 (1999)CrossRefGoogle Scholar
  14. 14.
    Fuentes-Schuller, I., Mann, R.B.: Alice falls into a black hole: entanglement in non-inertial frames. Phys. Rev. Lett. 95, 120404 (2005)ADSCrossRefMathSciNetGoogle Scholar
  15. 15.
    Unruh, W.G.: Experimental black-hole evaporation? Phys. Rev. Lett. 46, 1351–1353 (1981)ADSCrossRefGoogle Scholar
  16. 16.
    Weinfurtner, S., Tedford, E.W., Penrice, M.C., Unruh, W.G., Lawrence, G.A.: Measurement of stimulated Hawking emission in an analogue system. Phys. Rev. Lett. 106, 021302 (2011)ADSCrossRefGoogle Scholar
  17. 17.
    Garay, L.J., Anglin, J.R., Cirac, J.I., Zoller, P.: Sonic analog of gravitational black holes in Bose–Einstein condensates. Phys. Rev. Lett. 85, 4643 (2000)ADSCrossRefGoogle Scholar
  18. 18.
    Philbin, T.G., et al.: Fiber-optical analog of the event horizon. Science 319, 1367–1370 (2008)ADSCrossRefGoogle Scholar
  19. 19.
    Leonhardt, U.: A laboratory analogue of the event horizon using slow light in an atomic medium. Nature 415, 406 (2002)ADSCrossRefGoogle Scholar
  20. 20.
    Nation, P.D., Blencowe, M.P., Rimberg, A.J., Buks, E.: Analogue Hawking radiation in a dc-SQUID array transmission line. Phys. Rev. Lett. 103, 087004 (2009)ADSCrossRefGoogle Scholar
  21. 21.
    Horstmann, B., Reznik, B., Fagnocchi, S., Cirac, J.I.: Hawking radiation from an acoustic black hole on an ion ring. Phys. Rev. Lett. 104, 250403 (2010)ADSCrossRefGoogle Scholar
  22. 22.
    Lin, S.-Y., Hu, B.L.: Backreaction and the Unruh effect: new insights from exact solutions of uniformly accelerated detectors. Phys. Rev. D 76, 064008 (2007)ADSCrossRefGoogle Scholar
  23. 23.
    Scully, M.O., Zubairy, M.S.: Quantum Optics. Cambridge University Press, Cambridge (1997)CrossRefGoogle Scholar
  24. 24.
    Benincasa, D.M.T., Borsten, L., Buck, M., Dowker, F.: Quantum information processing and relativistic quantum fields. arXiv:1206.5205 (2012)
  25. 25.
    Jonsson, R.H., Martín-Martínez, E., Kempf, A.: Quantum signaling in cavity qed. Phys. Rev. A 89, 022330 (2014)ADSCrossRefGoogle Scholar
  26. 26.
    Onuma-Kalu, M., Mann, R.B., Martín-Martínez, E.: Mode invisibility and single-photon detection. Phys. Rev. A 88, 063824 (2013)ADSCrossRefGoogle Scholar
  27. 27.
    Brown, E.G., Martín-Martínez, E., Menicucci, N.C., Mann, R.B.: Detectors for probing relativistic quantum physics beyond perturbation theory. Phys. Rev. D 87, 084062 (2013)ADSCrossRefGoogle Scholar
  28. 28.
    Bruschi, D.E., Lee, A.R., Fuentes, I.: Time evolution techniques for detectors in relativistic quantum information. J. Phys. A 46(16), 165303 (2013)ADSCrossRefMathSciNetGoogle Scholar
  29. 29.
    Louko, J., Satz, A.: Transition rate of the Unruh–Dewitt detector in curved spacetime. Class. Quantum Gravity 25, 055012 (2008)ADSCrossRefMathSciNetGoogle Scholar
  30. 30.
    Holstein, B.R.: The adiabatic theorem and Berry’s phase. Am. J. Phys. 57, 1079–1084 (1989)ADSCrossRefMathSciNetGoogle Scholar
  31. 31.
    Sjöqvist, E., et al.: Geometric phases for mixed states in interferometry. Phys. Rev. Lett. 85, 2845–2849 (2000)ADSCrossRefGoogle Scholar
  32. 32.
    Scully, M.O., Kocharovsky, V.V., Belyanin, A., Fry, E., Capasso, F.: Enhancing acceleration radiation from ground-state atoms via cavity quantum electrodynamics. Phys. Rev. Lett. 91, 243004 (2003)ADSCrossRefGoogle Scholar
  33. 33.
    Raimond, J.M., Brune, M., Haroche, S.: Manipulating quantum entanglement with atoms and photons in a cavity. Rev. Mod. Phys. 73, 565–582 (2001)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  34. 34.
    Onuma-Kalu, M., Mann, R.B., Martín-Martínez, E.: Mode invisibility as a quantum non-demolition measurement of coherent light. arXiv:1404.0726 (2014)
  35. 35.
    Sabin, C., White, A., Hackermuller, L., Fuentes, I.: Dynamical phase quantum thermometer for an ultracold Bose–Einstein condensate. arXiv:1303.6208 (2013)

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Physics and Astronomy, Institute for Quantum ComputingUniversity of WaterlooWaterlooCanada
  2. 2.Department of Applied Mathematics, Institute for Quantum ComputingUniversity of WaterlooWaterlooCanada

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