Abstract

We present generation of photon-subtracted squeezed states at 860 nm, from nearly pure, continuous-wave squeezed vacua generated with a periodically-poled KTiOPO4 crystal as a nonlinear medium of a subthreshold optical parametric oscillator. We observe various kinds of photon-subtracted squeezed states, including non-Gaussian states similar to the single-photon state and superposition states of coherent states, simply by changing the pump power. Nonclassicality of the generated states clearly shows up as its negative region around the origin of the phase-space distributions, i.e., the Wigner functions. We obtain the value, -0.083 at the origin of the Wigner function, which is largest ever observed without any correction for experimental imperfections.

© 2007 Optical Society of America

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  3. S. L. Braunstein and A. K. Pati, Quantum Information with Continuous Variables (Kluwer Academic Publishers, 2003).
  4. B. Yurke and D. Stoler, "Measurement of amplitude probability distributions for photon-number-operator eigenstates," Phys. Rev. A 36, 1955-1958 (1987).
    [CrossRef] [PubMed]
  5. M. Dakna, T. Anhut, T. Opatrn, L. Kn ll, and D.-G. Welsch, "Generating Schr dinger-cat-like states by means of conditional measurements on a beam splitter," Phys. Rev. A 55, 3184-3194 (1997).
    [CrossRef]
  6. U. Leonhardt, Measuring the quantum state of light (Cambridge University Press, 1997).
  7. A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, "Quantum State Reconstruction of the Single-Photon Fock State," Phys. Rev. Lett. 87, 050402/1-4 (2001).
    [CrossRef] [PubMed]
  8. A. Zavatta, S. Viciani, and M. Bellini, "Tomographic reconstruction of the single-photon Fock state by highfrequency homodyne detection," Phys. Rev. A 70, 053821/1-6 (2004).
    [CrossRef]
  9. A. Ourjoumtsev, R. Tualle-Brouri, Ph. Grangier, "Quantum homodyne tomography of a two-photon Fock state," Phys. Rev. Lett. 96, 213601/1-4 (2006).
    [CrossRef] [PubMed]
  10. A. I. Lvovsky, and S. A. Babichev, "Synthesis and tomographic characterization of the displaced Fock state of light," Phys. Rev. A 66, 011801(R)/1-4 (2002).
    [CrossRef]
  11. A. Zavatta, S. Viciani, and M. Bellini, "Quantum-to-Classical Transition with Single-Photon-Added Coherent States of Light," Science 306, 660-662 (2004).
    [CrossRef] [PubMed]
  12. A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and Ph. Grangier, "Generating Optical Schrodinger Kittens for Quantum Information Processing," Science 312, 83-86 (2006).
    [CrossRef] [PubMed]
  13. J. S. Neergaard-Nielsen, B. Melholt Nielsen, C. Hettich, K. Mølmer, and E. S. Polzik, "Generation of a Superposition of Odd Photon Number States for Quantum Information Networks," Phys. Rev. Lett. 97, 083604/1-4 (2006).
    [CrossRef] [PubMed]
  14. H. Mabuchi, E. S. Polzik, and H. J. Kimble, "Blue-light-induced infrared absorption in KNbO3," J. Opt. Soc. Am. B 11, 2023 (1994).
    [CrossRef]
  15. T. Aoki, G. Takahashi, and A. Furusawa, "Squeezing at 946 nm with periodically poled KTiOPO4," Opt. Express 14, 6930-6935 (2006).
    [CrossRef] [PubMed]
  16. S. Suzuki, H. Yonezawa, F. Kannari, M. Sasaki, and A. Furusawa, "7 dB quadrature squeezing at 860 nm with periodically poled KTiOPO4," Appl. Phys. Lett. 89, 061116/1-3 (2006).
    [CrossRef]
  17. E. S. Polzik, J. Carri, and H. J. Kimble, "Atomic spectroscopy with squeezed light for sensitivity beyond the vacuum-state limit," Appl. Phys. B: Photophys. Laser Chem. 55, 279-290 (1992).
    [CrossRef]
  18. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser Phase and Frequency Stabilization Using an Optical Resonator," Appl. Phys. B 31, 97-105 (1983).
    [CrossRef]
  19. A. I. Lvovsky, "Iterative maximum-likelihood reconstruction in quantum homodyne tomography," J. Opt. B: Quantum Semiclass. Opt. 6, S556-S559 (2004).
    [CrossRef]
  20. M. Sasaki and S. Suzuki, "Multimode theory of measurement-induced non-Gaussian operation on wideband squeezed light: Analytical formula," Phys. Rev. A 73, 043807/1-18 (2006).
    [CrossRef]
  21. K. Mølmer, "Non-Gaussian states from continuous-wave Gaussian light sources," Phys. Rev. A 73, 063804/1-7 (2006).
    [CrossRef]
  22. S. L. Braunstein and H. J. Kimble, "Teleportation of Continuous Quantum Variables," Phys. Rev. Lett. 80, 869-872 (1998).
    [CrossRef]
  23. N. Takei, N. Lee, D. Moriyama, J. S. Neergaard-Nielsen, and A. Furusawa, "Time-gated Einstein-Podolsky-Rosen correlation," Phys. Rev. A 74, 060101(R)/1-4 (2006).
    [CrossRef]
  24. T. C. Ralph, A. Gilchrist, G. J. Milburn,W. J. Munro and S. Glancy, "Quantum computation with optical coherent states," Phys. Rev. A 68, 042319/1-11 (2003).
    [CrossRef]
  25. E. Waks, E. Diamanti, B. C. Sanders, S. D. Bartlett, and Y. Yamamoto, "Direct Observation of Nonclassical Photon Statistics in Parametric Down-Conversion," Phys. Rev. Lett. 92, 113602/1-4 (2004).
    [CrossRef] [PubMed]
  26. D. Rosenberg, A. E. Lita, A. J. Miller, and S. W. Nam, "Noise-free high-efficiency photon-number-resolving detectors," Phys. Rev. A 71, 061803(R)/1-4 (2005).
    [CrossRef]
  27. M. Fujiwara and M. Sasaki, "Photon-number-resolving detection at a telecommunications wavelength with a charge-integration photon detector," Opt. Lett. 31, 691-693 (2006).
    [CrossRef] [PubMed]
  28. A. P. Lund, H. Jeong, T. C. Ralph and M. S. Kim, "Conditional production of superpositions of coherent states with inefficient photon detection," Phys. Rev. A 70, 020101(R)/1-4 (2004).
    [CrossRef]
  29. Note that the squeezing levels shown in this paper are for the quadrature observables defined by ˆX= ∫ ∞ -∞ dtΨ0(t) ˆX (t). They can be directly evaluated with the initial squeezed vacua right after the OPO, using following expression; 2(ˆX)2=1-2 γT/ζ0 z(z+3) (z+1)(z+2)2. Here, z =pP/Pth is normalized pump power where P is pump power and Pth is an oscillation threshold of the OPO.

2006 (9)

A. Ourjoumtsev, R. Tualle-Brouri, Ph. Grangier, "Quantum homodyne tomography of a two-photon Fock state," Phys. Rev. Lett. 96, 213601/1-4 (2006).
[CrossRef] [PubMed]

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and Ph. Grangier, "Generating Optical Schrodinger Kittens for Quantum Information Processing," Science 312, 83-86 (2006).
[CrossRef] [PubMed]

J. S. Neergaard-Nielsen, B. Melholt Nielsen, C. Hettich, K. Mølmer, and E. S. Polzik, "Generation of a Superposition of Odd Photon Number States for Quantum Information Networks," Phys. Rev. Lett. 97, 083604/1-4 (2006).
[CrossRef] [PubMed]

T. Aoki, G. Takahashi, and A. Furusawa, "Squeezing at 946 nm with periodically poled KTiOPO4," Opt. Express 14, 6930-6935 (2006).
[CrossRef] [PubMed]

S. Suzuki, H. Yonezawa, F. Kannari, M. Sasaki, and A. Furusawa, "7 dB quadrature squeezing at 860 nm with periodically poled KTiOPO4," Appl. Phys. Lett. 89, 061116/1-3 (2006).
[CrossRef]

M. Sasaki and S. Suzuki, "Multimode theory of measurement-induced non-Gaussian operation on wideband squeezed light: Analytical formula," Phys. Rev. A 73, 043807/1-18 (2006).
[CrossRef]

K. Mølmer, "Non-Gaussian states from continuous-wave Gaussian light sources," Phys. Rev. A 73, 063804/1-7 (2006).
[CrossRef]

N. Takei, N. Lee, D. Moriyama, J. S. Neergaard-Nielsen, and A. Furusawa, "Time-gated Einstein-Podolsky-Rosen correlation," Phys. Rev. A 74, 060101(R)/1-4 (2006).
[CrossRef]

M. Fujiwara and M. Sasaki, "Photon-number-resolving detection at a telecommunications wavelength with a charge-integration photon detector," Opt. Lett. 31, 691-693 (2006).
[CrossRef] [PubMed]

2005 (1)

D. Rosenberg, A. E. Lita, A. J. Miller, and S. W. Nam, "Noise-free high-efficiency photon-number-resolving detectors," Phys. Rev. A 71, 061803(R)/1-4 (2005).
[CrossRef]

2004 (5)

E. Waks, E. Diamanti, B. C. Sanders, S. D. Bartlett, and Y. Yamamoto, "Direct Observation of Nonclassical Photon Statistics in Parametric Down-Conversion," Phys. Rev. Lett. 92, 113602/1-4 (2004).
[CrossRef] [PubMed]

A. P. Lund, H. Jeong, T. C. Ralph and M. S. Kim, "Conditional production of superpositions of coherent states with inefficient photon detection," Phys. Rev. A 70, 020101(R)/1-4 (2004).
[CrossRef]

A. Zavatta, S. Viciani, and M. Bellini, "Quantum-to-Classical Transition with Single-Photon-Added Coherent States of Light," Science 306, 660-662 (2004).
[CrossRef] [PubMed]

A. I. Lvovsky, "Iterative maximum-likelihood reconstruction in quantum homodyne tomography," J. Opt. B: Quantum Semiclass. Opt. 6, S556-S559 (2004).
[CrossRef]

A. Zavatta, S. Viciani, and M. Bellini, "Tomographic reconstruction of the single-photon Fock state by highfrequency homodyne detection," Phys. Rev. A 70, 053821/1-6 (2004).
[CrossRef]

2003 (1)

T. C. Ralph, A. Gilchrist, G. J. Milburn,W. J. Munro and S. Glancy, "Quantum computation with optical coherent states," Phys. Rev. A 68, 042319/1-11 (2003).
[CrossRef]

2002 (1)

A. I. Lvovsky, and S. A. Babichev, "Synthesis and tomographic characterization of the displaced Fock state of light," Phys. Rev. A 66, 011801(R)/1-4 (2002).
[CrossRef]

2001 (1)

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, "Quantum State Reconstruction of the Single-Photon Fock State," Phys. Rev. Lett. 87, 050402/1-4 (2001).
[CrossRef] [PubMed]

1998 (1)

S. L. Braunstein and H. J. Kimble, "Teleportation of Continuous Quantum Variables," Phys. Rev. Lett. 80, 869-872 (1998).
[CrossRef]

1997 (1)

M. Dakna, T. Anhut, T. Opatrn, L. Kn ll, and D.-G. Welsch, "Generating Schr dinger-cat-like states by means of conditional measurements on a beam splitter," Phys. Rev. A 55, 3184-3194 (1997).
[CrossRef]

1994 (1)

1992 (1)

E. S. Polzik, J. Carri, and H. J. Kimble, "Atomic spectroscopy with squeezed light for sensitivity beyond the vacuum-state limit," Appl. Phys. B: Photophys. Laser Chem. 55, 279-290 (1992).
[CrossRef]

1987 (1)

B. Yurke and D. Stoler, "Measurement of amplitude probability distributions for photon-number-operator eigenstates," Phys. Rev. A 36, 1955-1958 (1987).
[CrossRef] [PubMed]

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser Phase and Frequency Stabilization Using an Optical Resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Aichele, T.

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, "Quantum State Reconstruction of the Single-Photon Fock State," Phys. Rev. Lett. 87, 050402/1-4 (2001).
[CrossRef] [PubMed]

Anhut, T.

M. Dakna, T. Anhut, T. Opatrn, L. Kn ll, and D.-G. Welsch, "Generating Schr dinger-cat-like states by means of conditional measurements on a beam splitter," Phys. Rev. A 55, 3184-3194 (1997).
[CrossRef]

Aoki, T.

Babichev, S. A.

A. I. Lvovsky, and S. A. Babichev, "Synthesis and tomographic characterization of the displaced Fock state of light," Phys. Rev. A 66, 011801(R)/1-4 (2002).
[CrossRef]

Bartlett, S. D.

E. Waks, E. Diamanti, B. C. Sanders, S. D. Bartlett, and Y. Yamamoto, "Direct Observation of Nonclassical Photon Statistics in Parametric Down-Conversion," Phys. Rev. Lett. 92, 113602/1-4 (2004).
[CrossRef] [PubMed]

Bellini, M.

A. Zavatta, S. Viciani, and M. Bellini, "Quantum-to-Classical Transition with Single-Photon-Added Coherent States of Light," Science 306, 660-662 (2004).
[CrossRef] [PubMed]

A. Zavatta, S. Viciani, and M. Bellini, "Tomographic reconstruction of the single-photon Fock state by highfrequency homodyne detection," Phys. Rev. A 70, 053821/1-6 (2004).
[CrossRef]

Benson, O.

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, "Quantum State Reconstruction of the Single-Photon Fock State," Phys. Rev. Lett. 87, 050402/1-4 (2001).
[CrossRef] [PubMed]

Braunstein, S. L.

S. L. Braunstein and H. J. Kimble, "Teleportation of Continuous Quantum Variables," Phys. Rev. Lett. 80, 869-872 (1998).
[CrossRef]

Carri, J.

E. S. Polzik, J. Carri, and H. J. Kimble, "Atomic spectroscopy with squeezed light for sensitivity beyond the vacuum-state limit," Appl. Phys. B: Photophys. Laser Chem. 55, 279-290 (1992).
[CrossRef]

Dakna, M.

M. Dakna, T. Anhut, T. Opatrn, L. Kn ll, and D.-G. Welsch, "Generating Schr dinger-cat-like states by means of conditional measurements on a beam splitter," Phys. Rev. A 55, 3184-3194 (1997).
[CrossRef]

Diamanti, E.

E. Waks, E. Diamanti, B. C. Sanders, S. D. Bartlett, and Y. Yamamoto, "Direct Observation of Nonclassical Photon Statistics in Parametric Down-Conversion," Phys. Rev. Lett. 92, 113602/1-4 (2004).
[CrossRef] [PubMed]

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser Phase and Frequency Stabilization Using an Optical Resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser Phase and Frequency Stabilization Using an Optical Resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Fujiwara, M.

Furusawa, A.

S. Suzuki, H. Yonezawa, F. Kannari, M. Sasaki, and A. Furusawa, "7 dB quadrature squeezing at 860 nm with periodically poled KTiOPO4," Appl. Phys. Lett. 89, 061116/1-3 (2006).
[CrossRef]

T. Aoki, G. Takahashi, and A. Furusawa, "Squeezing at 946 nm with periodically poled KTiOPO4," Opt. Express 14, 6930-6935 (2006).
[CrossRef] [PubMed]

N. Takei, N. Lee, D. Moriyama, J. S. Neergaard-Nielsen, and A. Furusawa, "Time-gated Einstein-Podolsky-Rosen correlation," Phys. Rev. A 74, 060101(R)/1-4 (2006).
[CrossRef]

Gilchrist, A.

T. C. Ralph, A. Gilchrist, G. J. Milburn,W. J. Munro and S. Glancy, "Quantum computation with optical coherent states," Phys. Rev. A 68, 042319/1-11 (2003).
[CrossRef]

Glancy, S.

T. C. Ralph, A. Gilchrist, G. J. Milburn,W. J. Munro and S. Glancy, "Quantum computation with optical coherent states," Phys. Rev. A 68, 042319/1-11 (2003).
[CrossRef]

Grangier, Ph.

A. Ourjoumtsev, R. Tualle-Brouri, Ph. Grangier, "Quantum homodyne tomography of a two-photon Fock state," Phys. Rev. Lett. 96, 213601/1-4 (2006).
[CrossRef] [PubMed]

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and Ph. Grangier, "Generating Optical Schrodinger Kittens for Quantum Information Processing," Science 312, 83-86 (2006).
[CrossRef] [PubMed]

Hall, J. L.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser Phase and Frequency Stabilization Using an Optical Resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Hansen, H.

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, "Quantum State Reconstruction of the Single-Photon Fock State," Phys. Rev. Lett. 87, 050402/1-4 (2001).
[CrossRef] [PubMed]

Hettich, C.

J. S. Neergaard-Nielsen, B. Melholt Nielsen, C. Hettich, K. Mølmer, and E. S. Polzik, "Generation of a Superposition of Odd Photon Number States for Quantum Information Networks," Phys. Rev. Lett. 97, 083604/1-4 (2006).
[CrossRef] [PubMed]

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser Phase and Frequency Stabilization Using an Optical Resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Jeong, H.

A. P. Lund, H. Jeong, T. C. Ralph and M. S. Kim, "Conditional production of superpositions of coherent states with inefficient photon detection," Phys. Rev. A 70, 020101(R)/1-4 (2004).
[CrossRef]

Kannari, F.

S. Suzuki, H. Yonezawa, F. Kannari, M. Sasaki, and A. Furusawa, "7 dB quadrature squeezing at 860 nm with periodically poled KTiOPO4," Appl. Phys. Lett. 89, 061116/1-3 (2006).
[CrossRef]

Kim, M. S.

A. P. Lund, H. Jeong, T. C. Ralph and M. S. Kim, "Conditional production of superpositions of coherent states with inefficient photon detection," Phys. Rev. A 70, 020101(R)/1-4 (2004).
[CrossRef]

Kimble, H. J.

S. L. Braunstein and H. J. Kimble, "Teleportation of Continuous Quantum Variables," Phys. Rev. Lett. 80, 869-872 (1998).
[CrossRef]

H. Mabuchi, E. S. Polzik, and H. J. Kimble, "Blue-light-induced infrared absorption in KNbO3," J. Opt. Soc. Am. B 11, 2023 (1994).
[CrossRef]

E. S. Polzik, J. Carri, and H. J. Kimble, "Atomic spectroscopy with squeezed light for sensitivity beyond the vacuum-state limit," Appl. Phys. B: Photophys. Laser Chem. 55, 279-290 (1992).
[CrossRef]

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser Phase and Frequency Stabilization Using an Optical Resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Laurat, J.

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and Ph. Grangier, "Generating Optical Schrodinger Kittens for Quantum Information Processing," Science 312, 83-86 (2006).
[CrossRef] [PubMed]

Lee, N.

N. Takei, N. Lee, D. Moriyama, J. S. Neergaard-Nielsen, and A. Furusawa, "Time-gated Einstein-Podolsky-Rosen correlation," Phys. Rev. A 74, 060101(R)/1-4 (2006).
[CrossRef]

Lita, A. E.

D. Rosenberg, A. E. Lita, A. J. Miller, and S. W. Nam, "Noise-free high-efficiency photon-number-resolving detectors," Phys. Rev. A 71, 061803(R)/1-4 (2005).
[CrossRef]

Lund, A. P.

A. P. Lund, H. Jeong, T. C. Ralph and M. S. Kim, "Conditional production of superpositions of coherent states with inefficient photon detection," Phys. Rev. A 70, 020101(R)/1-4 (2004).
[CrossRef]

Lvovsky, A. I.

A. I. Lvovsky, "Iterative maximum-likelihood reconstruction in quantum homodyne tomography," J. Opt. B: Quantum Semiclass. Opt. 6, S556-S559 (2004).
[CrossRef]

A. I. Lvovsky, and S. A. Babichev, "Synthesis and tomographic characterization of the displaced Fock state of light," Phys. Rev. A 66, 011801(R)/1-4 (2002).
[CrossRef]

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, "Quantum State Reconstruction of the Single-Photon Fock State," Phys. Rev. Lett. 87, 050402/1-4 (2001).
[CrossRef] [PubMed]

Mabuchi, H.

Melholt Nielsen, B.

J. S. Neergaard-Nielsen, B. Melholt Nielsen, C. Hettich, K. Mølmer, and E. S. Polzik, "Generation of a Superposition of Odd Photon Number States for Quantum Information Networks," Phys. Rev. Lett. 97, 083604/1-4 (2006).
[CrossRef] [PubMed]

Milburn, G. J.

T. C. Ralph, A. Gilchrist, G. J. Milburn,W. J. Munro and S. Glancy, "Quantum computation with optical coherent states," Phys. Rev. A 68, 042319/1-11 (2003).
[CrossRef]

Miller, A. J.

D. Rosenberg, A. E. Lita, A. J. Miller, and S. W. Nam, "Noise-free high-efficiency photon-number-resolving detectors," Phys. Rev. A 71, 061803(R)/1-4 (2005).
[CrossRef]

Mlynek, J.

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, "Quantum State Reconstruction of the Single-Photon Fock State," Phys. Rev. Lett. 87, 050402/1-4 (2001).
[CrossRef] [PubMed]

Mølmer, K.

J. S. Neergaard-Nielsen, B. Melholt Nielsen, C. Hettich, K. Mølmer, and E. S. Polzik, "Generation of a Superposition of Odd Photon Number States for Quantum Information Networks," Phys. Rev. Lett. 97, 083604/1-4 (2006).
[CrossRef] [PubMed]

K. Mølmer, "Non-Gaussian states from continuous-wave Gaussian light sources," Phys. Rev. A 73, 063804/1-7 (2006).
[CrossRef]

Moriyama, D.

N. Takei, N. Lee, D. Moriyama, J. S. Neergaard-Nielsen, and A. Furusawa, "Time-gated Einstein-Podolsky-Rosen correlation," Phys. Rev. A 74, 060101(R)/1-4 (2006).
[CrossRef]

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser Phase and Frequency Stabilization Using an Optical Resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Munro, W. J.

T. C. Ralph, A. Gilchrist, G. J. Milburn,W. J. Munro and S. Glancy, "Quantum computation with optical coherent states," Phys. Rev. A 68, 042319/1-11 (2003).
[CrossRef]

Nam, S. W.

D. Rosenberg, A. E. Lita, A. J. Miller, and S. W. Nam, "Noise-free high-efficiency photon-number-resolving detectors," Phys. Rev. A 71, 061803(R)/1-4 (2005).
[CrossRef]

Neergaard-Nielsen, J. S.

N. Takei, N. Lee, D. Moriyama, J. S. Neergaard-Nielsen, and A. Furusawa, "Time-gated Einstein-Podolsky-Rosen correlation," Phys. Rev. A 74, 060101(R)/1-4 (2006).
[CrossRef]

J. S. Neergaard-Nielsen, B. Melholt Nielsen, C. Hettich, K. Mølmer, and E. S. Polzik, "Generation of a Superposition of Odd Photon Number States for Quantum Information Networks," Phys. Rev. Lett. 97, 083604/1-4 (2006).
[CrossRef] [PubMed]

Opatrn, T.

M. Dakna, T. Anhut, T. Opatrn, L. Kn ll, and D.-G. Welsch, "Generating Schr dinger-cat-like states by means of conditional measurements on a beam splitter," Phys. Rev. A 55, 3184-3194 (1997).
[CrossRef]

Ourjoumtsev, A.

A. Ourjoumtsev, R. Tualle-Brouri, Ph. Grangier, "Quantum homodyne tomography of a two-photon Fock state," Phys. Rev. Lett. 96, 213601/1-4 (2006).
[CrossRef] [PubMed]

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and Ph. Grangier, "Generating Optical Schrodinger Kittens for Quantum Information Processing," Science 312, 83-86 (2006).
[CrossRef] [PubMed]

Polzik, E. S.

J. S. Neergaard-Nielsen, B. Melholt Nielsen, C. Hettich, K. Mølmer, and E. S. Polzik, "Generation of a Superposition of Odd Photon Number States for Quantum Information Networks," Phys. Rev. Lett. 97, 083604/1-4 (2006).
[CrossRef] [PubMed]

H. Mabuchi, E. S. Polzik, and H. J. Kimble, "Blue-light-induced infrared absorption in KNbO3," J. Opt. Soc. Am. B 11, 2023 (1994).
[CrossRef]

E. S. Polzik, J. Carri, and H. J. Kimble, "Atomic spectroscopy with squeezed light for sensitivity beyond the vacuum-state limit," Appl. Phys. B: Photophys. Laser Chem. 55, 279-290 (1992).
[CrossRef]

Ralph, T. C.

A. P. Lund, H. Jeong, T. C. Ralph and M. S. Kim, "Conditional production of superpositions of coherent states with inefficient photon detection," Phys. Rev. A 70, 020101(R)/1-4 (2004).
[CrossRef]

T. C. Ralph, A. Gilchrist, G. J. Milburn,W. J. Munro and S. Glancy, "Quantum computation with optical coherent states," Phys. Rev. A 68, 042319/1-11 (2003).
[CrossRef]

Rosenberg, D.

D. Rosenberg, A. E. Lita, A. J. Miller, and S. W. Nam, "Noise-free high-efficiency photon-number-resolving detectors," Phys. Rev. A 71, 061803(R)/1-4 (2005).
[CrossRef]

Sanders, B. C.

E. Waks, E. Diamanti, B. C. Sanders, S. D. Bartlett, and Y. Yamamoto, "Direct Observation of Nonclassical Photon Statistics in Parametric Down-Conversion," Phys. Rev. Lett. 92, 113602/1-4 (2004).
[CrossRef] [PubMed]

Sasaki, M.

S. Suzuki, H. Yonezawa, F. Kannari, M. Sasaki, and A. Furusawa, "7 dB quadrature squeezing at 860 nm with periodically poled KTiOPO4," Appl. Phys. Lett. 89, 061116/1-3 (2006).
[CrossRef]

M. Sasaki and S. Suzuki, "Multimode theory of measurement-induced non-Gaussian operation on wideband squeezed light: Analytical formula," Phys. Rev. A 73, 043807/1-18 (2006).
[CrossRef]

M. Fujiwara and M. Sasaki, "Photon-number-resolving detection at a telecommunications wavelength with a charge-integration photon detector," Opt. Lett. 31, 691-693 (2006).
[CrossRef] [PubMed]

Schiller, S.

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, "Quantum State Reconstruction of the Single-Photon Fock State," Phys. Rev. Lett. 87, 050402/1-4 (2001).
[CrossRef] [PubMed]

Stoler, D.

B. Yurke and D. Stoler, "Measurement of amplitude probability distributions for photon-number-operator eigenstates," Phys. Rev. A 36, 1955-1958 (1987).
[CrossRef] [PubMed]

Suzuki, S.

M. Sasaki and S. Suzuki, "Multimode theory of measurement-induced non-Gaussian operation on wideband squeezed light: Analytical formula," Phys. Rev. A 73, 043807/1-18 (2006).
[CrossRef]

S. Suzuki, H. Yonezawa, F. Kannari, M. Sasaki, and A. Furusawa, "7 dB quadrature squeezing at 860 nm with periodically poled KTiOPO4," Appl. Phys. Lett. 89, 061116/1-3 (2006).
[CrossRef]

Takahashi, G.

Takei, N.

N. Takei, N. Lee, D. Moriyama, J. S. Neergaard-Nielsen, and A. Furusawa, "Time-gated Einstein-Podolsky-Rosen correlation," Phys. Rev. A 74, 060101(R)/1-4 (2006).
[CrossRef]

Tualle-Brouri, R.

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and Ph. Grangier, "Generating Optical Schrodinger Kittens for Quantum Information Processing," Science 312, 83-86 (2006).
[CrossRef] [PubMed]

A. Ourjoumtsev, R. Tualle-Brouri, Ph. Grangier, "Quantum homodyne tomography of a two-photon Fock state," Phys. Rev. Lett. 96, 213601/1-4 (2006).
[CrossRef] [PubMed]

Viciani, S.

A. Zavatta, S. Viciani, and M. Bellini, "Tomographic reconstruction of the single-photon Fock state by highfrequency homodyne detection," Phys. Rev. A 70, 053821/1-6 (2004).
[CrossRef]

A. Zavatta, S. Viciani, and M. Bellini, "Quantum-to-Classical Transition with Single-Photon-Added Coherent States of Light," Science 306, 660-662 (2004).
[CrossRef] [PubMed]

Waks, E.

E. Waks, E. Diamanti, B. C. Sanders, S. D. Bartlett, and Y. Yamamoto, "Direct Observation of Nonclassical Photon Statistics in Parametric Down-Conversion," Phys. Rev. Lett. 92, 113602/1-4 (2004).
[CrossRef] [PubMed]

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser Phase and Frequency Stabilization Using an Optical Resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Yamamoto, Y.

E. Waks, E. Diamanti, B. C. Sanders, S. D. Bartlett, and Y. Yamamoto, "Direct Observation of Nonclassical Photon Statistics in Parametric Down-Conversion," Phys. Rev. Lett. 92, 113602/1-4 (2004).
[CrossRef] [PubMed]

Yonezawa, H.

S. Suzuki, H. Yonezawa, F. Kannari, M. Sasaki, and A. Furusawa, "7 dB quadrature squeezing at 860 nm with periodically poled KTiOPO4," Appl. Phys. Lett. 89, 061116/1-3 (2006).
[CrossRef]

Yurke, B.

B. Yurke and D. Stoler, "Measurement of amplitude probability distributions for photon-number-operator eigenstates," Phys. Rev. A 36, 1955-1958 (1987).
[CrossRef] [PubMed]

Zavatta, A.

A. Zavatta, S. Viciani, and M. Bellini, "Tomographic reconstruction of the single-photon Fock state by highfrequency homodyne detection," Phys. Rev. A 70, 053821/1-6 (2004).
[CrossRef]

A. Zavatta, S. Viciani, and M. Bellini, "Quantum-to-Classical Transition with Single-Photon-Added Coherent States of Light," Science 306, 660-662 (2004).
[CrossRef] [PubMed]

Appl. Phys. B (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser Phase and Frequency Stabilization Using an Optical Resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Appl. Phys. B: Photophys. Laser Chem. (1)

E. S. Polzik, J. Carri, and H. J. Kimble, "Atomic spectroscopy with squeezed light for sensitivity beyond the vacuum-state limit," Appl. Phys. B: Photophys. Laser Chem. 55, 279-290 (1992).
[CrossRef]

Appl. Phys. Lett. (1)

S. Suzuki, H. Yonezawa, F. Kannari, M. Sasaki, and A. Furusawa, "7 dB quadrature squeezing at 860 nm with periodically poled KTiOPO4," Appl. Phys. Lett. 89, 061116/1-3 (2006).
[CrossRef]

J. Opt. B: Quantum Semiclass. Opt. (1)

A. I. Lvovsky, "Iterative maximum-likelihood reconstruction in quantum homodyne tomography," J. Opt. B: Quantum Semiclass. Opt. 6, S556-S559 (2004).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (10)

A. P. Lund, H. Jeong, T. C. Ralph and M. S. Kim, "Conditional production of superpositions of coherent states with inefficient photon detection," Phys. Rev. A 70, 020101(R)/1-4 (2004).
[CrossRef]

D. Rosenberg, A. E. Lita, A. J. Miller, and S. W. Nam, "Noise-free high-efficiency photon-number-resolving detectors," Phys. Rev. A 71, 061803(R)/1-4 (2005).
[CrossRef]

N. Takei, N. Lee, D. Moriyama, J. S. Neergaard-Nielsen, and A. Furusawa, "Time-gated Einstein-Podolsky-Rosen correlation," Phys. Rev. A 74, 060101(R)/1-4 (2006).
[CrossRef]

T. C. Ralph, A. Gilchrist, G. J. Milburn,W. J. Munro and S. Glancy, "Quantum computation with optical coherent states," Phys. Rev. A 68, 042319/1-11 (2003).
[CrossRef]

M. Sasaki and S. Suzuki, "Multimode theory of measurement-induced non-Gaussian operation on wideband squeezed light: Analytical formula," Phys. Rev. A 73, 043807/1-18 (2006).
[CrossRef]

K. Mølmer, "Non-Gaussian states from continuous-wave Gaussian light sources," Phys. Rev. A 73, 063804/1-7 (2006).
[CrossRef]

B. Yurke and D. Stoler, "Measurement of amplitude probability distributions for photon-number-operator eigenstates," Phys. Rev. A 36, 1955-1958 (1987).
[CrossRef] [PubMed]

M. Dakna, T. Anhut, T. Opatrn, L. Kn ll, and D.-G. Welsch, "Generating Schr dinger-cat-like states by means of conditional measurements on a beam splitter," Phys. Rev. A 55, 3184-3194 (1997).
[CrossRef]

A. Zavatta, S. Viciani, and M. Bellini, "Tomographic reconstruction of the single-photon Fock state by highfrequency homodyne detection," Phys. Rev. A 70, 053821/1-6 (2004).
[CrossRef]

A. I. Lvovsky, and S. A. Babichev, "Synthesis and tomographic characterization of the displaced Fock state of light," Phys. Rev. A 66, 011801(R)/1-4 (2002).
[CrossRef]

Phys. Rev. Lett. (5)

A. Ourjoumtsev, R. Tualle-Brouri, Ph. Grangier, "Quantum homodyne tomography of a two-photon Fock state," Phys. Rev. Lett. 96, 213601/1-4 (2006).
[CrossRef] [PubMed]

S. L. Braunstein and H. J. Kimble, "Teleportation of Continuous Quantum Variables," Phys. Rev. Lett. 80, 869-872 (1998).
[CrossRef]

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, "Quantum State Reconstruction of the Single-Photon Fock State," Phys. Rev. Lett. 87, 050402/1-4 (2001).
[CrossRef] [PubMed]

J. S. Neergaard-Nielsen, B. Melholt Nielsen, C. Hettich, K. Mølmer, and E. S. Polzik, "Generation of a Superposition of Odd Photon Number States for Quantum Information Networks," Phys. Rev. Lett. 97, 083604/1-4 (2006).
[CrossRef] [PubMed]

E. Waks, E. Diamanti, B. C. Sanders, S. D. Bartlett, and Y. Yamamoto, "Direct Observation of Nonclassical Photon Statistics in Parametric Down-Conversion," Phys. Rev. Lett. 92, 113602/1-4 (2004).
[CrossRef] [PubMed]

Science (2)

A. Zavatta, S. Viciani, and M. Bellini, "Quantum-to-Classical Transition with Single-Photon-Added Coherent States of Light," Science 306, 660-662 (2004).
[CrossRef] [PubMed]

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and Ph. Grangier, "Generating Optical Schrodinger Kittens for Quantum Information Processing," Science 312, 83-86 (2006).
[CrossRef] [PubMed]

Other (5)

U. Leonhardt, Measuring the quantum state of light (Cambridge University Press, 1997).

H.-A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics (WILEY-VCH Verlag GmbH & Co. KGaA, 2004).
[CrossRef]

C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge University Press, 2005).

S. L. Braunstein and A. K. Pati, Quantum Information with Continuous Variables (Kluwer Academic Publishers, 2003).

Note that the squeezing levels shown in this paper are for the quadrature observables defined by ˆX= ∫ ∞ -∞ dtΨ0(t) ˆX (t). They can be directly evaluated with the initial squeezed vacua right after the OPO, using following expression; 2(ˆX)2=1-2 γT/ζ0 z(z+3) (z+1)(z+2)2. Here, z =pP/Pth is normalized pump power where P is pump power and Pth is an oscillation threshold of the OPO.

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Figures (2)

Fig. 1.
Fig. 1.

Schematic of experimental setup. OC : output coupler, HWP : half-wave plate, PBS : polarizing beam splitter, BS : beam splitter (consisting of HWP and PBS, variable splitting ratio), Triangle : triangle cavity, QWP : quarter-wave plate, FP1 & FP2 : Fabry-Perot cavities, HBS : 50:50 beam-splitter. All the beams including the squeezed vacuum have S-polarization. The sets of PBS+QWP just before FP1 & FP2 are used as optical isolators and also as pick-offs of the reflected beams. Each reflection from the filtering cavities is used for FM-sideband locking when the locking beam passes through at the optical chopper.

Fig. 2.
Fig. 2.

Experimental Wigner functions (top panels) constructed from raw data without any correction of measurement imperfections, in the case of 5% splitting ratio. a : The single-photon state generated by -0.7dB initial squeezed vacuum. b and c : Schrödinger kittens generated by -2.6dB and -3.7dB initial squeezed vacua, respectively. The values of the Wigner function at the origin are a : W(0,0) = -0.049, b : W(0,0) = -0.083, and c : W(0,0) = -0.048. The insets in top panels are the contours of the Wigner functions. The middle panels are quadrature distributions obtained by homodyne detection. The bottom panels are photon-number distributions obtained by the iterative maximum-likelihood estimation.

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