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Monitoring the Decoherence of Mesoscopic Quantum Superpositions in a Cavity

  • Jean-Michel Raimond
  • Serge Haroche
Part of the Progress in Mathematical Physics book series (PMP, volume 48)

Abstract

Decoherence is an extremely fast and efficient environment-induced process transforming macroscopic quantum superpositions into statistical mixtures. It is an essential step in quantum measurement and a formidable obstacle for a practical use of quantum superpositions (quantum computing for instance). For large objects, decoherence is so fast that its dynamics is unobservable. Mesoscopic fields stored in a high-quality superconducting millimeter-wave cavity, a modern equivalent to Einstein’s ‘photon box’, are ideal tools to reveal the dynamics of the decoherence process. Their interaction with a single circular Rydberg atom prepares them in a quantum superposition of fields, containing a few photons, with different classical phases. The evolution of this ‘Schrödinger cat’ state can be later probed with a ‘quantum mouse’, another atom, assessing its coherence. We describe here the experiments performed along these lines at ENS, and stress the deep links between decoherence and complementarity.

Keywords

Coherent State Master Equation Density Operator Cavity Mode Wigner Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    H. D. Zeh, Found. Phys. 1, 69 (1970).CrossRefADSGoogle Scholar
  2. [2]
    W. H. Zurek, Decoherence and the transition from quantum to classical, Phys. Today 44, 36 (octobre 1991).CrossRefGoogle Scholar
  3. [3]
    W. H. Zurek, Decoherence, einselection, and the quantum origins of the classical, Rev. Mod. Phys. 75, 715 (2003).CrossRefMathSciNetADSGoogle Scholar
  4. [4]
    J.-M. Raimond, M. Brune, and S. Haroche, Manipulating quantum entanglement with atoms and photons in a cavity, Rev. Mod. Phys. 73, 565 (2001).CrossRefMathSciNetADSGoogle Scholar
  5. [5]
    D. Leibfried, R. Blatt, C. Monroe, and D. J. Wineland, Quantum dynamics of single trapped ions, Rev. Mod. Phys. 75, 281 (2003).CrossRefADSGoogle Scholar
  6. [6]
    C. Monroe, D. M. Meekhof, B. E. King, and D. J. Wineland, A “Schrödinger cat” superposition state of an atom, Science 272, 1131 (1996).CrossRefMathSciNetADSGoogle Scholar
  7. [7]
    M. Brune, E. Hagley, J. Dreyer, X. Maître, A. Maali, C. Wunderlich, J.-M. Raimond, and S. Haroche, Observing the progressive decoherence of the meter in a quantum measurement, Phys. Rev. Lett. 77, 4887 (1996).CrossRefADSGoogle Scholar
  8. [8]
    Q. J. Myatt, B. E. King, Q. A. Turchette, C. A. Sackett, D. Kielpinski, W. M. Itano, C. Monroe, and D. J. Wineland, Decoherence of quantum superpositions through coupling to engineered reservoirs, Nature (London) 403, 269 (2000).CrossRefADSGoogle Scholar
  9. [9]
    A. Einstein, B. Podolsky, and N. Rosen, Can quantum mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935).CrossRefMATHADSGoogle Scholar
  10. [10]
    R. J. Glauber, Coherent and incoherent states of the radiation field, Phys. Rev. 131, 2766 (1963).CrossRefMathSciNetADSGoogle Scholar
  11. [11]
    U. M. Titulaer and R. J. Glauber, Density operators for coherent fields, Phys. Rev. 145, 1041 (1966).CrossRefADSGoogle Scholar
  12. [12]
    S. M. Barnett and P. M. Radmore, Methods in Theoretical Quantum Optics, Oxford University Press, Oxford, 1997.Google Scholar
  13. [13]
    V. Buzek, H. Moya-Cessa, P. L. Knight, and S. D. L. Phoenix, Schrödinger-cat states in the resonant Jaynes-Cummings model: Collapse and revival of oscillations of the photon-number distribution, Phys. Rev. A 45, 8190 (1992).CrossRefADSGoogle Scholar
  14. [14]
    M. Brune, S. Haroche, J.-M. Raimond, L. Davidovich, and N. Zagury, Manipulation of photons in a cavity by dispersive atom-field coupling: Quantum non demolition measurements and generation of Schrödinger cat states, Phys. Rev. A 45, 5193 (1992).CrossRefADSGoogle Scholar
  15. [15]
    W. P. Schleich, Quantum Optics in Phase Space, Wiley, Berlin, 2001.MATHCrossRefGoogle Scholar
  16. [16]
    J.-M. Raimond, T. Meunier, P. Bertet, S. Gleyzes, P. Maioli, A. Auffeves, G. Nogues, M. Brune, and S. Haroche, Probing a quantum field in a photon box, J. Phys. B 38, S535 (2005).CrossRefADSGoogle Scholar
  17. [17]
    E. P. Wigner, On the quantum correction for thermodynamic equilibrium, Phys. Rev. 40, 749 (1932).CrossRefMATHADSGoogle Scholar
  18. [18]
    K. E. Cahill and R. J. Glauber, Ordered expansions in boson amplitude operators, Phys. Rev. 177, 1857 (1969).CrossRefADSGoogle Scholar
  19. [19]
    J. Dalibard, Y. Castin, and K. Mölmer, Wave-function approach to dissipative processes in quantum optics, Phys. Rev. Lett. 68, 580 (1992).CrossRefADSGoogle Scholar
  20. [20]
    M. B. Plenio and P. L. Knight, The quantum-jump approach to dissipative dynamics in quantum optics, Rev. Mod. Phys. 70, 101 (1998).CrossRefADSGoogle Scholar
  21. [21]
    T. Sauter, W. Neuhauser, R. Blatt, and P. Toschek, Observation of quantum jumps, Phys. Rev. Lett. 57, 1696 (1986).CrossRefADSGoogle Scholar
  22. [22]
    J. C. Bergquist, R. G. Hulet, W. M. Itano, and D. J. Wineland, Observation of quantum jumps in a single atom, Phys. Rev. Lett. 57, 1699 (1986).CrossRefADSGoogle Scholar
  23. [23]
    C. Cohen-Tannoudji and J. Dalibard, Single-atom laser spectroscopy-looking for dark periods in fluorescence, EuroPhys. Lett. 1, 441 (1986).ADSCrossRefGoogle Scholar
  24. [24]
    E. T. Jaynes and F. W. Cummings, Comparison of quantum and semiclassical radiation theories with application to the beam maser, Proc. IEEE 51, 89 (1963).CrossRefGoogle Scholar
  25. [25]
    S. Haroche and J.-M. Raimond, Manipulation of non-classical field states in a cavity by atom interferometry, In P. Berman, editor, Advances in Atomic and Molecular Physics, supplement 2, page 123. Academic Press, New York, 1994.Google Scholar
  26. [26]
    S. Haroche. Cavity quantum electrodynamics, In J. Dalibard, J.-M. Raimond, and J. Zinn-Justin, editors, Fundamental Systems in Quantum Optics, Les Houches Summer School, Session LIII, page 767. North Holland, Amsterdam, 1992.Google Scholar
  27. [27]
    P. Maioli, T. Meunier, S. Gleyzes, A. Auffeves, G. Nogues, M. Brune, J.-M. Raimond, and S. Haroche, Non-destructive Rydberg atom counting with mesoscopic fields in a cavity, Phys. Rev. Lett. 94, 113601 (2005).CrossRefADSGoogle Scholar
  28. [28]
    M. Brune, P. Nussenzveig, F. Schmidt-Kaler, F. Bernardot, A. Maali, J.-M. Raimond, and S. Haroche, From Lamb shifts to light shifts: Vacuum and subphoton cavity fields measured by atomic phase sensitive detection, Phys. Rev. Lett. 72, 3339 (1994).CrossRefADSGoogle Scholar
  29. [29]
    N. F. Ramsey. Molecular Beams, International series of monographs on physics, Oxford University Press, Oxford, 1985.Google Scholar
  30. [30]
    P. Bertet, S. Osnaghi, A. Rauschenbeutel, G. Nogues, A. Auffeves, M. Brune, J.-M. Raimond, and S. Haroche, A complementarity experiment with an interferometer at the quantum-classical boundary, Nature (London) 411, 166 (2001).CrossRefADSGoogle Scholar
  31. [31]
    L. Davidovich, M. Brune, J.-M. Raimond, and S. Haroche, Mesoscopic quantum coherences in cavity QED: Preparation and decoherence monitoring schemes, Phys. Rev. A 53, 1295 (1996).CrossRefADSGoogle Scholar
  32. [32]
    J.-M. Raimond, M. Brune, and S. Haroche, Reversible decoherence of a mesoscopic superposition of field states, Phys. Rev. Lett. 79, 1964 (1997).CrossRefADSGoogle Scholar
  33. [33]
    P. Bertet, A. Auffeves, P. Maioli, S. Osnaghi, T. Meunier, M. Brune, J.-M. Raimond, and S. Haroche, Direct measurement of the Wigner function of a one-photon Fock state in a cavity, Phys. Rev. Lett. 89, 200402 (2002).CrossRefADSGoogle Scholar
  34. [34]
    M. Fortunato, J.-M. Raimond, P. Tombesi, and D. Vitali, Autofeedback scheme for schrödinger cat preservation in microwave cavities, Phys. Rev. A 60, 1687 (1999).CrossRefADSGoogle Scholar
  35. [35]
    S. Zippilli, D. Vitali, P. Tombesi, and J.-M. Raimond, Scheme for decoherence control in microwave cavities, Phys. Rev. A 67, 052101 (2003).CrossRefADSGoogle Scholar
  36. [36]
    J. D. Jackson, Classical Electrodynamics, Wiley, New York, second edition, 1975.MATHGoogle Scholar
  37. [37]
    A. Faist, E. Geneux, P. Meystre, and A. Quattropani, Coherent radiation in interaction with two-level system, Helv. Phys. Acta 45, 956 (1972).Google Scholar
  38. [38]
    J. H. Eberly, N. B. Narozhny, and J. J. Sanchez-Mondragon, Periodic spontaneous collapse and revival in a simple quantum model, Phys. Rev. Lett. 44, 1323 (1980).CrossRefMathSciNetADSGoogle Scholar
  39. [39]
    P. L. Knight and P. M. Radmore, Quantum origin of dephasing and revivals in the coherent-state Jaynes-Cummings model, Phys. Rev. A 26, 676 (1982).CrossRefADSGoogle Scholar
  40. [40]
    J. Gea-Banacloche, Atom and field evolution in the Jaynes and Cummings model for large initial fields, Phys. Rev. A 44, 5913 (1991).CrossRefADSGoogle Scholar
  41. [41]
    M. Fleischhauer and W. P. Schleich, Revivals made simple: Poisson summation formula as a key to the revivals in the Jaynes-Cummings model, Phys. Rev. A 47, 4258 (1993).CrossRefADSGoogle Scholar
  42. [42]
    V. Buzek and P. L. Knight, Quantum interference, superposition states of light and non-classical effects, In Progress in Optics XXXIV, volume 34, page 1. Elsevier, 1995.CrossRefGoogle Scholar
  43. [43]
    A. Auffeves, P. Maioli, T. Meunier, S. Gleyzes, G. Nogues, M. Brune, J.-M. Raimond, and S. Haroche, Entanglement of a mesoscopic field with an atom induced by photon graininess in a cavity, Phys. Rev. Lett. 91, 230405 (2003).CrossRefADSGoogle Scholar
  44. [44]
    G. Morigi, E. Solano, B.-G. Englert, and H. Walther, Measuring irreversible dynamics of a quantum harmonic oscillator, Phys. Rev. A 65, 040102 (2002).CrossRefADSGoogle Scholar
  45. [45]
    T. Meunier, S. Gleyzes, P. Maioli, A. Auffeves, G. Nogues, M. Brune, J.M. Raimond, and S. Haroche, Rabi oscillations revival induced by time reversal: a test of mesoscopic quantum coherence, Phys. Rev. Lett. 94, 010401 (2005).CrossRefADSGoogle Scholar
  46. [46]
    L. G. Lutterbach and L. Davidovich, Method for direct measurement of the Wigner function in cavity QED and ion traps, Phys. Rev. Lett. 78, 2547 (1997).CrossRefADSGoogle Scholar
  47. [47]
    K. Banaszek and K. Wodkiewicz, Testing quantum nonlocality in phase space, Phys. Rev. Lett. 82, 2009 (1999).CrossRefMathSciNetMATHADSGoogle Scholar
  48. [48]
    A. Aspect, J. Dalibard, and G. Roger, Experimental test of Bell’s inequalities using time-varying analysers, Phys. Rev. Lett. 49, 1804 (1982).CrossRefMathSciNetADSGoogle Scholar
  49. [49]
    A. Zeilinger, Experiment and the foundations of quantum physics, Rev. Mod. Phys. 71, S288 (1999).CrossRefGoogle Scholar
  50. [50]
    P. Milman, A. Auffeves, F. Yamaguchi, M. Brune, J.M. Raimond, and S. Haroche, A proposal to test Bell’s inequalities with mesoscopic non-local states in cavity qed, Eur. Phys. J. D 32, 233 (2005).CrossRefADSGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel 2006

Authors and Affiliations

  • Jean-Michel Raimond
    • 1
  • Serge Haroche
    • 2
  1. 1.Laboratoire Kastler Brossel Département de Physiquel’Ecole Normale SupérieureParis Cedex 05France
  2. 2.Collège de FranceParis Cedex 05France

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