Enlargement of optical Schrödinger's cat states

Journal name:
Nature Photonics
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Published online


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.

At a glance


  1. Scheme of the experiment.
    Figure 1: Scheme of the experiment.

    A squeezed vacuum state is generated in each input channel via degenerate parametric downconversion (PPKTP). A small portion of the photon flux from each squeezer is directed to a SPCM; preparation of the two initial negative SC states is heralded by simultaneous clicks of SPCMs 1 and 2. The resulting SC states interfere on a 50:50 beamsplitter (BS). Optical homodyne tomography of the state in output mode 1 of the BS is performed, conditioned on the near-zero result of the position quadrature measurement in output mode 2. LO, local oscillator; PZT, piezoelectric transducer.

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

    a, Experimental reconstruction via homodyne tomography corrected for the total quantum efficiency of 62%. Left insets: Wigner functions reconstructed without efficiency corrections. X and P denote the position and momentum quadratures, respectively. Right insets: absolute values of density matrices ρmn in the Fock basis reconstructed with efficiency correction. b, Best fit with the ideal squeezed SC state. Left (right): initial (amplified) SC state. The best-fit state is |SC[1.15]〉 (|SC+[1.85]〉) squeezed by 1.74 dB (3.04 dB). The fidelity between the theoretical and experimental (corrected) states is 84% (77%).


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Author information

  1. These authors contributed equally to the work.

    • Demid V. Sychev,
    • Alexander E. Ulanov &
    • Ilya A. Fedorov


  1. International Center for Quantum Optics and Quantum Technologies (Russian Quantum Center), Skolkovo, Moscow 143025, Russia

    • Demid V. Sychev,
    • Alexander E. Ulanov,
    • Anastasia A. Pushkina,
    • Ilya A. Fedorov &
    • Alexander I. Lvovsky
  2. Moscow State Pedagogical University, Department of Theoretical Physics, M. Pirogovskaya Str. 29, Moscow 119991 Russia

    • Demid V. Sychev
  3. Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia

    • Alexander E. Ulanov
  4. Institute for Quantum Science and Technology, University of Calgary, Calgary, Alberta T2N 1N4, Canada

    • Anastasia A. Pushkina,
    • Matthew W. Richards &
    • Alexander I. Lvovsky
  5. P. N. Lebedev Physics Institute, Leninsky Prospect 53, Moscow 119991, Russia

    • Ilya A. Fedorov &
    • Alexander I. Lvovsky
  6. Canadian Institute for Advanced Research, 661 University Avenue, Toronto, Ontario M5G 1M1, Canada

    • Alexander I. Lvovsky


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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The authors declare no competing financial interests.

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