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Enlargement of optical Schrödinger's cat states



Superpositions of macroscopically distinct quantum states, introduced in Schrödinger's famous Gedankenexperiment, are an epitome of quantum ‘strangeness’ and a natural tool for determining the validity limits of quantum physics. The optical incarnation of Schrödinger's cat (SC)—the superposition of two opposite-amplitude coherent states—is also the backbone of continuous-variable quantum information processing. However, the existing preparation methods limit the amplitudes of the component coherent states, which curtails the state's usefulness for fundamental and practical applications. Here, we convert a pair of negative squeezed SC states of amplitude 1.15 to a single positive SC state of amplitude 1.85 with a success probability of 0.2. The protocol consists in bringing the initial states into interference on a beamsplitter and a subsequent heralding quadrature measurement in one of the output channels. Our technique can be realized iteratively, so arbitrarily high amplitudes can, in principle, be reached.

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Figure 1: Scheme of the experiment.
Figure 2: Wigner functions of the initial and amplified SC states.


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

    Article  ADS  Google Scholar 

  2. Haroche, S. Nobel lecture: controlling photons in a box and exploring the quantum to classical boundary. Rev. Mod. Phys. 85, 1083–1102 (2013).

    Article  ADS  Google Scholar 

  3. Wineland, D. J. Nobel lecture: superposition, entanglement, and raising Schrödinger's cat. Rev. Mod. Phys. 85, 1103–1114 (2013).

    Article  ADS  Google Scholar 

  4. Markus, A. & Hornberger, K. Testing the limits of quantum mechanical superpositions. Nat. Phys. 10, 271–277 (2014).

    Article  Google Scholar 

  5. Leonhardt, U. Measuring Quantum States of Light (Cambridge Univ. Press, 1997).

    MATH  Google Scholar 

  6. Leggett, A. J. Testing the limits of quantum mechanics: motivation, state of play, prospects. J. Phys. Condens. Matter 14, R415–R451 (2002).

    Article  ADS  Google Scholar 

  7. Lvovsky, A. I., Ghobadi, R., Chandra, A., Prasad, A. S. & Simon, C. Observation of micro–macro entanglement of light. Nat. Phys. 9, 541–544 (2013).

    Article  Google Scholar 

  8. Ralph, T. C., Gilchrist, A., Milburn, G. J., Munro, W. J. & Glancy, S. Quantum computation with optical coherent states. Phys. Rev. A 68, 042319 (2003).

    Article  ADS  Google Scholar 

  9. Lund, A. P., Ralph, T. C. & Haselgrove, H. L. Fault-tolerant linear optical quantum computing with small-amplitude coherent states. Phys. Rev. Lett. 100, 030503 (2007).

    Article  Google Scholar 

  10. Joo, J., Munro, W. J. & Spiller, T. P. Quantum metrology with entangled coherent states. Phys. Rev. Lett. 107, 083601 (2011).

    Article  ADS  Google Scholar 

  11. Facon, A. et al. A sensitive electrometer based on a Rydberg atom in a Schrödinger-cat state. Nature 535, 262–265 (2016).

    Article  ADS  Google Scholar 

  12. Lee, S.-W. & Jeong, H. Near-deterministic quantum teleportation and resource-efficient quantum computation using linear optics and hybrid qubits. Phys. Rev. Lett. 87, 022326 (2012).

    Google Scholar 

  13. Sangouard, N. et al. Quantum repeaters with entangled coherent states. J. Opt. Soc. Am. B 27, A137–A145 (2010).

    Article  Google Scholar 

  14. Brask, J. B., Rigas, I., Polzik, E. S., Andersen, U. L. & Sørensen, A. S. Hybrid long-distance entanglement distribution protocol. Phys. Rev. Lett. 105, 160501 (2010).

    Article  ADS  Google Scholar 

  15. Huang, K. et al. Optical synthesis of large-amplitude squeezed coherent-state superpositions with minimal resource. Phys. Rev. Lett. 115, 023602 (2015).

    Article  ADS  Google Scholar 

  16. Ulanov, A. E., Fedorov, I. A., Sychev, D., Grangier, P. & Lvovsky, A. I. Loss-tolerant state engineering for quantum-enhanced metrology via the reverse Hong–Ou–Mandel effect. Nat. Commun. 7, 11925 (2016).

    Article  ADS  Google Scholar 

  17. Bimbard, E., Jain, N., MacRae, A. & Lvovsky, A. I. Quantum-optical state engineering up to the two-photon level. Nat. Photon. 4, 243–247 (2010).

    Article  ADS  Google Scholar 

  18. Yukawa, M. et al. Generating superposition of up-to three photons for continuous variable quantum information processing. Opt. Express 21, 5529–5535 (2013).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  20. Neergaard-Nielsen, J. S., Melholt Nielsen, B., 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).

    Article  ADS  Google Scholar 

  21. Wakui, K., Takahashi, H., Furusawa, A. & Sasaki, M. Photon subtracted squeezed states generated with periodically poled KTiOPO4 . Opt. Express 15, 3568–3574 (2007).

    Article  ADS  Google Scholar 

  22. Ourjoumtsev, A., Ferreyrol, F., Tualle-Brouri, R. & Grangier, P. Preparation of non-local superpositions of quasi-classical light states. Nat. Phys. 5, 189–192 (2009).

    Article  Google Scholar 

  23. Gerrits, T. et al. Generation of optical coherent state superpositions by number-resolved photon subtraction from squeezed vacuum. Phys. Rev. A 82, 031802(R) (2010).

    Article  ADS  Google Scholar 

  24. Takahashi, H. et al. Generation of large-amplitude coherent-state superposition via ancilla-assisted photon subtraction. Phys. Rev. Lett. 101, 233605 (2008).

    Article  ADS  Google Scholar 

  25. Dong, R. et al. Generation of picosecond pulsed coherent state superpositions. J. Opt. Soc. Am. B 31, 1192–1201 (2014).

    Article  ADS  Google Scholar 

  26. Ourjoumtsev, A., Jeong, H., Tualle-Brouri, R. & Grangier, P. Generation of optical Schrödinger cats from photon number states. Nature 448, 1784–1786 (2007).

    Article  Google Scholar 

  27. Etesse, J., Bouillard, M., Kanseri, B. & Tualle-Brouri, R. Experimental generation of squeezed cat states with an operation allowing iterative growth. Phys. Rev. Lett. 114, 193602 (2015).

    Article  ADS  Google Scholar 

  28. Laghaout, A. et al. Amplification of realistic Schrödinger-cat-state-like states by homodyne heralding. Phys. Rev. A 87, 043826 (2013).

    Article  ADS  Google Scholar 

  29. 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 (2004).

    Article  ADS  Google Scholar 

  30. Dakna, M., Anhut, T., Opatrny, T., Knöll, L. & Welsch, D.-G. Generating Schrödinger-cat-like states by means of conditional measurements on a beam splitter. Phys. Rev. A 55, 3184–3194 (1997).

    Article  ADS  Google Scholar 

  31. Lvovsky, A. I. & Raymer, M. G. Continuous-variable optical quantum-state tomography. Rev. Mod. Phys. 81, 299–332 (2009).

    Article  ADS  Google Scholar 

  32. Lvovsky, A. I. Iterative maximum-likelihood reconstruction in quantum homodyne tomography. J. Opt. B 6, S556–S559 (2004).

    Article  ADS  Google Scholar 

  33. Lee, C. W. & Jeong, H. Quantification of macroscopic quantum superpositions within phase space. Phys. Rev. Lett. 106, 220401 (2011).

    Article  ADS  Google Scholar 

  34. Deléglis, S. et al. Reconstruction of non-classical cavity field states with snapshots of their decoherence. Nature 455, 510–515 (2008).

    Article  ADS  Google Scholar 

  35. Vlastakis, B. et al. Deterministically encoding quantum information using 100-photon Schrödinger cat states. Science 342, 607–610 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  36. Ding, X. et al. On-demand single photons with high extraction efficiency and near-unity indistinguishability from a resonantly driven quantum dot in a micropillar. Phys. Rev. Lett. 116, 020401 (2016).

    Article  ADS  Google Scholar 

  37. Somaschi, N. et al. Near-optimal single-photon sources in the solid state. Nat. Photon. 10, 340–345 (2016).

    Article  ADS  Google Scholar 

  38. Lvovsky, A. I., Sanders, B. C. & Tittel, W. Optical quantum memory. Nat. Photon. 3, 706–714 (2009).

    Article  ADS  Google Scholar 

  39. Fedorov, I. A., Ulanov, A. E., Kurochkin, Y. & Lvovsky, A. I. Synthesis of the Einstein–Podolsky–Rosen entanglement in a sequence of two single-mode squeezers. Opt. Lett. 42, 132–134 (2017).

    Article  ADS  Google Scholar 

  40. Berry, D. W. & Lvovsky, A. I. Linear-optical processing cannot increase photon efficiency. Phys. Rev. Lett. 105, 203601 (2010).

    Article  ADS  Google Scholar 

  41. Kumar, R. et al. Versatile wideband balanced detector for quantum optical homodyne tomography. Opt. Commun. 285, 5259–5267 (2012).

    Article  ADS  Google Scholar 

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We thank Y. Kurochkin and A. Turlapov for discussions. We acknowledge financial support from the Ministry of Education and Science of the Russian Federation (Agreement 14.582.21.0009, ID RFMEFI58215X0009). A.I.L. is supported by the Natural Sciences and Engineering Research Council of Canada and is a Canadian Institute for Advanced Research Fellow.

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All the authors participated in the conception and planning of the project, theoretical analysis and writing of the paper. The experiment was performed by D.V.S., A.E.U., A.A.P., I.A.F. and M.W.R. The data were analysed by D.V.S., A.E.U., I.A.F. and A.I.L.

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Correspondence to Alexander I. Lvovsky.

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Sychev, D., Ulanov, A., Pushkina, A. et al. Enlargement of optical Schrödinger's cat states. Nature Photon 11, 379–382 (2017).

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