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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Grover Swartzlander
  • Vol. 31, Iss. 5 — May. 1, 2014
  • pp: 1192–1201

Generation of picosecond pulsed coherent state superpositions

Ruifang Dong, Anders Tipsmark, Amine Laghaout, Leonid A. Krivitsky, Miroslav Ježek, and Ulrik Lund Andersen  »View Author Affiliations

JOSA B, Vol. 31, Issue 5, pp. 1192-1201 (2014)

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We present the generation of approximated coherent state superpositions—referred to as Schrödinger cat states—by the process of subtracting single photons from picosecond pulsed squeezed states of light. The squeezed vacuum states are produced by spontaneous parametric down-conversion (SPDC) in a periodically poled KTiOPO4 crystal while the single photons are probabilistically subtracted using a beamsplitter and a single photon detector. The resulting states are fully characterized with time-resolved homodyne quantum state tomography. Varying the pump power of the SPDC, we generated different states which exhibit non-Gaussian behavior.

© 2014 Optical Society of America

OCIS Codes
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes
(270.0270) Quantum optics : Quantum optics
(270.6570) Quantum optics : Squeezed states
(320.5390) Ultrafast optics : Picosecond phenomena
(270.5585) Quantum optics : Quantum information and processing

ToC Category:
Quantum Optics

Original Manuscript: January 7, 2014
Revised Manuscript: March 1, 2014
Manuscript Accepted: March 28, 2014
Published: April 28, 2014

Ruifang Dong, Anders Tipsmark, Amine Laghaout, Leonid A. Krivitsky, Miroslav Ježek, and Ulrik Lund Andersen, "Generation of picosecond pulsed coherent state superpositions," J. Opt. Soc. Am. B 31, 1192-1201 (2014)

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  1. L. A. Wu, H. J. Kimble, J. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520–2523 (1986). [CrossRef]
  2. H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Gossler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10-dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008). [CrossRef]
  3. Y. Takeno, M. Yukawa, H. Yonezawa, and A. Furusawa, “Observation of −9  dB quadrature squeezing with improvement of phase stability in homodyne measurement,” Opt. Express 15, 4321–4327 (2007). [CrossRef]
  4. R. Dong, J. Heersink, J. F. Corney, P. D. Drummond, U. L. Andersen, and G. Leuchs, “Experimental evidence for Raman-induced limits to efficient squeezing in optical fibers,” Opt. Lett. 33, 116–118 (2008). [CrossRef]
  5. M. G. A. Paris, “Displacement operator by beam splitter,” Phys. Lett. 217, 78–80 (1996). [CrossRef]
  6. S. Lloyd, “Coherent quantum feedback,” Phys. Rev. A 62, 022108 (2000). [CrossRef]
  7. S. Scheel, W. Munro, J. Eisert, K. Nemoto, and P. Kok, “Feed-forward and its role in conditional linear optical quantum dynamics,” Phys. Rev. A 73, 034301 (2006). [CrossRef]
  8. H. M. Wiseman and G. J. Milburn, “Quantum theory of optical feedback via homodyne detection,” Phys. Rev. Lett. 70, 548–551 (1993). [CrossRef]
  9. A. Furusawa, S. L. Braunstein, J. L. Sørensen, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998). [CrossRef]
  10. F. Grosshans, G. V. Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature (London) 421, 238–241 (2003). [CrossRef]
  11. U. L. Andersen, V. Josse, and G. Leuchs, “Unconditional quantum cloning of coherent states with linear optics,” Phys. Rev. Lett. 94, 240503 (2005). [CrossRef]
  12. A. M. Lance, T. Symul, W. P. Bowen, B. Sanders, T. Tyc, T. C. Ralph, and P. K. Lam, “Continuous-variable quantum-state sharing via quantum disentanglement,” Phys. Rev. Lett. 71, 033814 (2005).
  13. R. Ukai, N. Iwata, Y. Shimokawa, S. Armstrong, A. Politi, J. Yoshikawa, P. V. Loock, and A. Furusawa, “Demonstration of unconditional one-way quantum computations for continuous variables,” Phys. Rev. Lett. 106, 240504 (2011). [CrossRef]
  14. C. Weedbrook, S. Pirandola, R. Garca-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621 (2012). [CrossRef]
  15. J. Eisert, S. Scheel, and M. Plenio, “Distilling Gaussian states with Gaussian operations is impossible,” Phys. Rev. Lett. 89, 137903 (2002). [CrossRef]
  16. J. Fiurášek, “Gaussian transformations and distillation of entangled Gaussian states,” Phys. Rev. Lett. 89, 137904 (2002). [CrossRef]
  17. G. Giedke and J. I. Cirac, “Characterization of Gaussian operations and distillation of Gaussian states,” Phys. Rev. A 66, 032316 (2002). [CrossRef]
  18. J. Niset, J. Fiurášek, and N. J. Cerf, “No-go theorem for Gaussian quantum error correction,” Phys. Rev. Lett. 102, 120501 (2009). [CrossRef]
  19. S. Lloyd and S. L. Braunstein, “Quantum computation over continuous variables,” Phys. Rev. Lett. 82, 1784–1787 (1999). [CrossRef]
  20. M. Ohliger, K. Kieling, and J. Eisert, “Limitations of quantum computing with Gaussian cluster states,” Phys. Rev. A 82, 042336 (2010). [CrossRef]
  21. L. Magnin, F. Magniez, A. Leverrier, and N. J. Cerf, “Strong no-go theorem for Gaussian quantum bit commitment,” Phys. Rev. A 81, 010302 (2010). [CrossRef]
  22. J. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University, 1987).
  23. N. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, “Universal quantum computation with continuous-variable cluster states,” Phys. Rev. Lett. 97, 110501 (2006). [CrossRef]
  24. A. Ourjoumtsev, R. Tualle-Brouri, P. Grangier, and A. Dantan, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007). [CrossRef]
  25. H. Takahashi, J. S. Neergaard-Nielsen, M. Takeuchi, M. Takeoka, K. Hayasaka, A. Furusawa, and M. Sasaki, “Entanglement distillation from Gaussian input states,” Nat. Photonics 4, 178–181 (2010). [CrossRef]
  26. M. Lassen, M. Sabuncu, A. Huck, J. Niset, G. Leuchs, N. J. Cerf, and U. L. Andersen, “Quantum optical coherence can survive photon losses using a continuous-variable quantum erasure-correcting code,” Nat. Photonics 4, 700–705 (2010). [CrossRef]
  27. 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 (2003). [CrossRef]
  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 (2004). [CrossRef]
  29. A. Gilchrist, K. Nemoto, W. Munro, T. C. Ralph, S. Glancy, S. L. Braunstein, and G. J. Milburn, “Schrödinger cats and their power for quantum information processing,” J. Opt. B 6, 828–833 (2004).
  30. T. C. Ralph, “Quantum error correction of continuous-variable states against Gaussian noise,” Phys. Rev. A 84, 022309 (2011). [CrossRef]
  31. R. Garca-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and P. Grangier, “Proposal for a loophole-free bell test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004). [CrossRef]
  32. A. Mandilara and N. J. Cerf, “Quantum bit commitment under Gaussian constraints,” Phys. Rev. A 85, 062310 (2012). [CrossRef]
  33. 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 (2001). [CrossRef]
  34. T. Aichele, A. I. Lvovsky, and S. Schiller, “Optical mode characterization of single photons prepared by means of conditional measurements on a biphoton state,” Eur. Phys. J. D 18, 237–245 (2002).
  35. A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier, “Quantum homodyne tomography of a two-photon Fock state,” Phys. Rev. Lett. 96, 213601 (2006). [CrossRef]
  36. S. R. Huisman, N. Jain, S. A. Babichev, F. Vewinger, A. N. Zhang, S. H. Youn, and A. I. Lvovsky, “Instant single-photon Fock state tomography,” Opt. Lett. 34, 2739–2741 (2009). [CrossRef]
  37. J. Wenger, R. Tualle-Brouri, and P. Grangier, “Non-Gaussian statistics from individual pulses of squeezed light,” Phys. Rev. Lett. 92, 153601 (2004). [CrossRef]
  38. M. Cooper, L. J. Wright, C. Söller, and B. J. Smith, “Experimental generation of multi-photon Fock states,” Opt. Express 21, 5309–5317 (2013). [CrossRef]
  39. K. Laiho, K. N. Cassemiro, D. Gross, and C. Silberhorn, “Probing the negative Wigner function of a pulsed single photon point by point,” Phys. Rev. Lett. 105, 253603 (2010). [CrossRef]
  40. Y. Miwa, J. Yoshikawa, N. Iwata, M. Endo, P. Marek, R. Filip, P. van Loock, and A. Furusawa, “Unconditional conversion between a single-photon state and a coherent-state superposition via squeezing operation,” Quantum Electronics and Laser Science Conference, San Jose, California, United States, May6–11, 2012.
  41. H. Jeong, M. S. Kim, and J. Lee, “Quantum-information processing for a coherent superposition state via a mixed entangled coherent channel,” Phys. Rev. A 64, 052308 (2001). [CrossRef]
  42. P. Marek and M. S. Kim, “Suitability of the approximate superposition of squeezed coherent states for various quantum protocols,” Phys. Rev. A 78, 022309 (2008). [CrossRef]
  43. H. Jeong and M. S. Kim, “Efficient quantum computation using coherent states,” Phys. Rev. A 65, 042305 (2002). [CrossRef]
  44. P. Marek and J. Fiurášek, “Elementary gates for quantum information with superposed coherent states,” Phys. Rev. A 82, 014304 (2010). [CrossRef]
  45. A. Tipsmark, R. Dong, A. Laghaout, P. Marek, M. Ježek, and U. L. Andersen, “Experimental demonstration of a Hadamard gate for coherent state qubits,” Phys. Rev. A 84, 050301 (2011). [CrossRef]
  46. R. Blandino, F. Ferreyrol, M. Barbieri, P. Grangier, and R. Tualle-Brouri, “Characterization of a π-phase shift quantum gate for coherent-state qubits,” New J. Phys. 14, 013017 (2012). [CrossRef]
  47. D. Wilson, H. Jeong, and M. S. Kim, “Quantum nonlocality for a mixed entangled coherent state,” J. Mod. Opt. 49, 851–864 (2002), Special Issue for QEP 15. [CrossRef]
  48. H. Jeong, W. Son, M. S. Kim, D. Ahn, and C. Brukner, “Quantum nonlocality test continuous-variable states with dichotomic observable,” Phys. Rev. A 67, 012106 (2003). [CrossRef]
  49. H. Jeong, “Testing Bell inequalities with photon-subtracted Gaussian states,” Phys. Rev. A 78, 042101 (2008). [CrossRef]
  50. M. Dakna, T. Anhut, T. Opatrný, L. Knöll, and D. G. Welsch, “Generating Schrödinger-cat-like states by means of conditional measurements on a beam splitter,” Phys. Rev. A 55, 3184–3194 (1997). [CrossRef]
  51. P. Marek, H. Jeong, and M. S. Kim, “Generating “squeezed” superpositions of coherent states using photon addition and subtraction,” Phys. Rev. A 78, 063811 (2008). [CrossRef]
  52. H. Takahashi, K. Wakui, S. Suzuki, M. Takeoka, K. Hayasaka, A. Furusawa, and M. Sasaki, “Generation of large-amplitude coherent-state superposition via ancilla-assisted photon subtraction,” Phys. Rev. Lett. 101, 233605 (2008). [CrossRef]
  53. J. B. Brask, R. Chaves, and N. Brunner, “Testing nonlocality of a single photon without a shared reference frame,” Phys. Rev. A 88, 012111 (2013). [CrossRef]
  54. A. Laghaout, J. S. Neergaard-Nielsen, I. Rigas, C. Kragh, A. Tipsmark, and U. L. Andersen, “Amplification of realistic Schrödinger-cat-state-like states by homodyne heralding,” Phys. Rev. A 87, 043826 (2013). [CrossRef]
  55. A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006). [CrossRef]
  56. A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical “Schrödinger cats” from photon number stataes,” Nature 448, 784–786 (2007). [CrossRef]
  57. 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 (2006). [CrossRef]
  58. K. Wakui, H. Takahashi, A. Furusawa, and M. Sasaki, “Photon subtracted squeezed states generated with periodically poled KTiOPO4,” Opt. Express 15, 3568–3574 (2007). [CrossRef]
  59. T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent state superpositions by number-resolved photon subtraction from squeezed vacuum,” Phys. Rev. A 82, 031802 (2010). [CrossRef]
  60. N. Namekata, Y. Takahashi, G. Fujii, D. Fukuda, S. Kurimura, and S. Inoue, “Non-Gaussian operation based on photon subtraction using a photon-number-resolving detector at a telecommunications wavelength,” Nat. Photonics 4, 655–660 (2010). [CrossRef]
  61. J. S. Neergaard-Nielsen, M. Takeuchi, K. Wakui, H. Takahashi, K. Hayasaka, M. Takeoka, and M. Sasaki, “Optical continuous-variable qubit,” Phys. Rev. Lett. 105, 053602 (2010). [CrossRef]
  62. N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–333 (2011). [CrossRef]
  63. C. Kim, R. D. Li, and P. Kumar, “Deamplification response of a traveling-wave phase-sensitive optical parametric amplifier,” Opt. Lett. 19, 132–134 (1994). [CrossRef]
  64. G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968). [CrossRef]
  65. J. Wenger, R. Tualle-Brouri, and P. Grangier, “Pulsed homodyne measurements of femtosecond squeezed pulses generated by single-pass parametric deamplification,” Opt. Lett. 29, 1267–1269 (2004). [CrossRef]
  66. A. La Porta and R. Slusher, “Squeezing limits at high parametric gains,” Phys. Rev. A 44, 2013–2022 (1991). [CrossRef]
  67. A. I. Lvovsky, “Continuous-variable optical quantum-state tomography,” Rev. Mod. Phys. 81, 299–332 (2009). [CrossRef]
  68. H. Hansen, T. Aichele, C. Hettich, P. Lodahl, A. I. Lvovsky, J. Mlynek, and S. Schiller, “Ultrasensitive pulsed, balanced homodyne detector: application to time-domain quantum measurements,” Opt. Lett. 26, 1714–1716 (2001). [CrossRef]
  69. J. P. Gordon, W. Louisel, and L. Walker, “Quantum fluctuations and noise in parametric processes. II,” Phys. Rev. Lett. 129, 481–485 (1963).
  70. W. Wagner and R. Hellwarth, “Quantum noise in a parametric amplifier with lossy modes,” Phys. Rev. A 133, A915–A920 (1964). [CrossRef]
  71. R. Byer and S. Harris, “Power and bandwidth of spontaneous parametric emission,” Phys. Rev. 168, 1064–1068 (1968). [CrossRef]
  72. T. Hirano, K. Kotani, T. Ishibashi, S. Okude, and T. Kuwamoto, “3  dB squeezing by single-pass parametric amplification in a periodically poled KTiOPO4 crystal,” Opt. Lett. 30, 1722–1724 (2005). [CrossRef]
  73. J. Appel, D. Hoffman, E. Figueroa, and A. I. Lvovsky, “Electronic noise in optical homodyne tomography,” Phys. Rev. A 75, 035802 (2007). [CrossRef]
  74. R. Tualle-Brouri, A. Ourjoumtsev, A. Dantan, P. Grangier, M. Wubs, and A. Sørensen, “Multimode model for projective photon-counting measurements,” Phys. Rev. A 80, 013806 (2009). [CrossRef]
  75. S. Suzuki, K. Tsujino, F. Kannari, and M. Sasaki, “Analysis on generation schemes of Schrödinger cat-like states under experimental imperfections,” Opt. Commun. 259, 758–764 (2006). [CrossRef]
  76. R. Demkowicz-Dobrzanski, U. Dorner, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Quantum phase estimation with lossy interferometers,” Phys. Rev. A 80, 013825 (2009). [CrossRef]
  77. M. Ježek, A. Tipsmark, R. Dong, J. Fiurášek, L. Mišta, R. Filip, and U. L. Andersen, “Experimental test of the strongly nonclassical character of a noisy squeezed single-photon state,” Phys. Rev. A 86, 043813 (2012). [CrossRef]
  78. Z. Hradil, “Quantum-state estimation,” Phys. Rev. A 55, R1561–R1564 (1997). [CrossRef]
  79. M. Ježek, J. Fiurášek, and Z. Hradil, “Quantum inference of states and processes,” Phys. Rev. A 68, 012305 (2003). [CrossRef]
  80. A. I. Lvovsky, “Iterative maximum-likelihood reconstruction in quantum homodyne tomography,” J. Opt. B 6, S556–S559 (2004). [CrossRef]

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