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Generation of optical ‘Schrödinger cats’ from photon number states


Schrödinger’s cat1 is a Gedankenexperiment in quantum physics, in which an atomic decay triggers the death of the cat. Because quantum physics allow atoms to remain in superpositions of states, the classical cat would then be simultaneously dead and alive. By analogy, a ‘cat’ state of freely propagating light can be defined as a quantum superposition of well separated quasi-classical states2,3—it is a classical light wave that simultaneously possesses two opposite phases. Such states play an important role in fundamental tests of quantum theory4,5,6,7 and in many quantum information processing tasks, including quantum computation8, quantum teleportation9,10 and precision measurements11. Recently, optical Schrödinger ‘kittens’ were prepared12,13,14; however, they are too small for most of the aforementioned applications and increasing their size is experimentally challenging. Here we demonstrate, theoretically and experimentally, a protocol that allows the generation of arbitrarily large squeezed Schrödinger cat states, using homodyne detection and photon number states as resources. We implemented this protocol with light pulses containing two photons, producing a squeezed Schrödinger cat state with a negative Wigner function. This state clearly exhibits several quantum phase-space interference fringes between the ‘dead’ and ‘alive’ components, and is large enough to become useful for quantum information processing and experimental tests of quantum theory.

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Figure 1: Preparing squeezed ‘Schrödinger cat’ states from Fock states using a single homodyne detection.
Figure 2: Theoretical performance.
Figure 3: Experimental set-up.
Figure 4: Experimental results.
Figure 5: Influence of experimental imperfections.


  1. Schrödinger, E. Die gegenwärtige Situation in der Quantenmechanik. Naturwissenschaften 23, 807–812 (1935)

    ADS  Article  Google Scholar 

  2. Yurke, B. & Stoler, D. Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion. Phys. Rev. Lett. 57, 13–16 (1986)

    ADS  CAS  Article  Google Scholar 

  3. Schleich, W., Pernigo, M. & Kien, F. L. Nonclassical state from two pseudoclassical states. Phys. Rev. A 44, 2172–2187 (1991)

    ADS  CAS  Article  Google Scholar 

  4. Sanders, B. C. Entangled coherent states. Phys. Rev. A 45, 6811–6815 (1992)

    ADS  CAS  Article  Google Scholar 

  5. Wenger, J., Hafezi, M., Grosshans, F., Tualle-Brouri, R. & Grangier, P. Maximal violation of Bell inequalities using continuous-variable measurements. Phys. Rev. A 67, 012105 (2003)

    ADS  Article  Google Scholar 

  6. Jeong, H., Son, W., Kim, M. S., Ahn, D. & Brukner, Č. Quantum nonlocality test for continuous-variable states with dichotomic observables. Phys. Rev. A 67, 012106 (2003)

    ADS  Article  Google Scholar 

  7. Stobińska, M., Jeong, H. & Ralph, T. C. Violation of Bell’s inequality using classical measurements and nonlinear local operations. Phys. Rev. A 75, 052105 (2007)

    ADS  MathSciNet  Article  Google Scholar 

  8. Ralph, T. C. et al. Quantum computation with optical coherent states. Phys. Rev. A 68, 042319 (2003)

    ADS  Article  Google Scholar 

  9. Van Enk, S. J. & Hirota, O. Entangled coherent states: Teleportation and decoherence. Phys. Rev. A 64, 022313 (2001)

    ADS  Article  Google Scholar 

  10. Jeong, H., Kim, M. S. & Lee, J. Quantum-information processing for a coherent superposition state via a mixed entangled coherent channel. Phys. Rev. A 64, 052308 (2001)

    ADS  Article  Google Scholar 

  11. Munro, W. J., Nemoto, K., Milburn, G. J. & Braunstein, S. L. Weak-force detection with superposed coherent states. Phys. Rev. A 66, 023819 (2002)

    ADS  Article  Google Scholar 

  12. Ourjoumtsev, A., Tualle-Brouri, R., Laurat, J. & Grangier, P. Generating optical Schrödinger kittens for quantum information processing. Science 312, 83–86 (2006)

    ADS  CAS  Article  Google Scholar 

  13. Neergaard-Nielsen, J. S., Nielsen, B. M., Hettich, C., Mølmer, K. & Polzik, E. S. Generation of a superposition of odd photon number states for quantum information networks. Phys. Rev. Lett. 97, 083604 (2006)

    ADS  CAS  Article  Google Scholar 

  14. Wakui, K., Takahashi, H., Furusawa, A. & Sasaki, M. Controllable generation of highly nonclassical states from nearly pure squeezed vacua. Opt. Express 15, 3568–3574 (2007)

    ADS  CAS  Article  Google Scholar 

  15. Schrödinger, E. Der stetige Uebergang von der Mikro- zur Makromechanik. Naturwissenschaften 14, 664–666 (1926)

    ADS  Article  Google Scholar 

  16. Zurek, W. H., Habib, S. & Paz, J. P. Coherent states via decoherence. Phys. Rev. Lett. 70, 1187–1190 (1993)

    ADS  CAS  Article  Google Scholar 

  17. Walls, D. F. & Milburn, G. J. Quantum Optics (Springer, Berlin, 1994)

    Book  Google Scholar 

  18. Wigner, E. P. On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40, 749–759 (1932)

    ADS  CAS  Article  Google Scholar 

  19. Brune, M. et al. Observing the progressive decoherence of the “meter” in a quantum measurement. Phys. Rev. Lett. 77, 4887–4890 (1996)

    ADS  CAS  Article  Google Scholar 

  20. Monroe, C., Meekhof, D. M., King, B. E. & Wineland, D. J. A. “Schrödinger cat” superposition state of an atom. Science 272, 1131–1135 (1996)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  21. Lund, A. P., Jeong, H., Ralph, T. C. & Kim, M. S. Conditional production of superpositions of coherent states with inefficient photon detection. Phys. Rev. A 70, 020101(R) (2004)

    ADS  Article  Google Scholar 

  22. Suzuki, S., Takeoka, M., Sasaki, M., Andersen, U. & Kannari, F. Practical purification scheme for decohered coherent-state superpositions via partial homodyne detection. Phys. Rev. A 73, 042304 (2006)

    ADS  Article  Google Scholar 

  23. Serafini, A., De Siena, S., Illuminati, F. & Paris, M. G. A. Minimum decoherence cat-like states in Gaussian noisy channels. J. Opt. B 6, S591–S596 (2004)

    ADS  Article  Google Scholar 

  24. Jeong, H. et al. Quantum-state engineering with continuous-variable postselection. Phys. Rev. A 74, 033813 (2006)

    ADS  Article  Google Scholar 

  25. Yoshikawa, J. et al. Demonstration of a high-fidelity, deterministic and universal squeezing transformation. Preprint at 〈〉 (2007)

  26. Ourjoumtsev, A., Tualle-Brouri, R. & Grangier, P. Quantum homodyne tomography of a two-photon number state. Phys. Rev. Lett. 96, 213601 (2006)

    ADS  Article  Google Scholar 

  27. Waks, E., Diamanti, E. & Yamamoto, Y. Generation of photon number states. N. J. Phys. 8, 4 (2006)

    Article  Google Scholar 

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This work was supported (in France) by the EU IST/FET project COVAQIAL and the ANR/PNANO project IRCOQ, and (in Australia) by the US Army Research Office and the DTO, the Australian Research Council and Queensland State Government. H.J. thanks T. C. Ralph and M. S. Kim for discussions.

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Correspondence to Alexei Ourjoumtsev.

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Supplementary information

Supplementary Methods

This file contains Supplementary Methods which present a detailed theoretical analysis of the proposed protocol. After giving the general proof of principle, authors discuss the influence of its intrinsic limitations. Finally, an analytic model is presented which accounts for all the imperfections of the actual experiment. (PDF 240 kb)

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Ourjoumtsev, A., Jeong, H., Tualle-Brouri, R. et al. Generation of optical ‘Schrödinger cats’ from photon number states. Nature 448, 784–786 (2007).

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