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Reconstruction of non-classical cavity field states with snapshots of their decoherence

Nature volume 455, pages 510–514 (2008)Cite this article

Abstract

The state of a microscopic system encodes its complete quantum description, from which the probabilities of all measurement outcomes are inferred. Being a statistical concept, the state cannot be obtained from a single system realization, but can instead be reconstructed1 from an ensemble of copies through measurements on different realizations2,3,4. Reconstructing the state of a set of trapped particles shielded from their environment is an important step in the investigation of the quantum–classical boundary5. Although trapped-atom state reconstructions6,7,8 have been achieved, it is challenging to perform similar experiments with trapped photons because cavities that can store light for very long times are required. Here we report the complete reconstruction and pictorial representation of a variety of radiation states trapped in a cavity in which several photons survive long enough to be repeatedly measured. Atoms crossing the cavity one by one are used to extract information about the field. We obtain images of coherent states9, Fock states with a definite photon number and ‘Schrödinger cat’ states (superpositions of coherent states with different phases10). These states are equivalently represented by their density matrices or Wigner functions11. Quasi-classical coherent states have a Gaussian-shaped Wigner function, whereas the Wigner functions of Fock and Schrödinger cat states show oscillations and negativities revealing quantum interferences. Cavity damping induces decoherence that quickly washes out such oscillations5. We observe this process and follow the evolution of decoherence by reconstructing snapshots of Schrödinger cat states at successive times. Our reconstruction procedure is a useful tool for further decoherence and quantum feedback studies of fields trapped in one or two cavities.

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Figure 1: Reconstructing a coherent state.
Figure 2: Reconstructing Fock states.
Figure 3: Reconstructing Schrödinger cat states.
Figure 4: Movie of decoherence.

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Acknowledgements

This work was supported by the Agence Nationale pour la Recherche (ANR), by the Japan Science and Technology Agency (JST) and by the European Union under the Integrated Projects SCALA and CONQUEST. S.D. is funded by the Délégation Générale pour l’Armement (DGA).

Author Contributions S.D., I.D. and C.S. contributed equally to this work.

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Authors and Affiliations

  1. Laboratoire Kastler Brossel, Ecole Normale Supérieure, CNRS, Université Pierre et Marie Curie, 24 rue Lhomond, 75231 Paris Cedex 05, France ,

    Samuel Deléglise, Igor Dotsenko, Clément Sayrin, Julien Bernu, Michel Brune, Jean-Michel Raimond & Serge Haroche

  2. Collège de France, 11 place Marcelin Berthelot, 75231 Paris Cedex 05, France ,

    Igor Dotsenko & Serge Haroche

Authors
  1. Samuel Deléglise
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  5. Michel Brune
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  6. Jean-Michel Raimond
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  7. Serge Haroche
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Corresponding author

Correspondence to Serge Haroche.

Supplementary information

Supplementary Movie 1

Fifty milliseconds in the life of a Schrödinger cat. Movie of the reconstructed WF of the even Schrödinger cat state of Fig.3a. The state is reconstructed with the data recorded in a 4ms sliding time-window. The resulting WFs are averaged over 4ms. The movie exhibits two different phenomena: a fast decay of the quantum interference feature and a much slower evolution of the classical components towards phase-space origin. Fluctuations observed on top of the regular attenuation of the quantum interference term are due to statistical noise. Since successive frames are not independent, this noise has a 4 ms correlation time. (MOV 4123 kb)

Supplementary Movie 2

Schrödinger cats' quantumness vanishes. The even and odd cats have equal classical components and opposite quantum interferences. By subtracting their WFs, we isolate the interference feature displaying their quantumness. Following the same procedure as in Video 1, we present the evolution of this signal over 50 ms which exhibits the fast decay, due to decoherence, of a pure interference pattern. (MOV 3336 kb)

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Deléglise, S., Dotsenko, I., Sayrin, C. et al. Reconstruction of non-classical cavity field states with snapshots of their decoherence. Nature 455, 510–514 (2008). https://doi.org/10.1038/nature07288

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