OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry M. Van Driel
  • Vol. 25, Iss. 5 — May. 1, 2008
  • pp: 712–733

Methods for producing optical coherent state superpositions

Scott Glancy and Hilma Macedo de Vasconcelos  »View Author Affiliations


JOSA B, Vol. 25, Issue 5, pp. 712-733 (2008)
http://dx.doi.org/10.1364/JOSAB.25.000712


View Full Text Article

Enhanced HTML    Acrobat PDF (469 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We discuss several methods to produce superpositions of optical coherent states (also known as “cat states”). Cat states have remarkable properties that could allow them to be powerful tools for quantum information processing and metrology. A number of proposals for how one can produce cat states have appeared in the literature in recent years. We describe these proposals and present a new simulation and analysis of them incorporating practical issues such as photon loss, detector inefficiency, and limited strength of nonlinear interactions. We also examine how each would perform in a realistic experiment.

© 2008 Optical Society of America

OCIS Codes
(190.3270) Nonlinear optics : Kerr effect
(270.0270) Quantum optics : Quantum optics
(270.6570) Quantum optics : Squeezed states
(270.5585) Quantum optics : Quantum information and processing

ToC Category:
Quantum Optics

History
Original Manuscript: October 3, 2007
Revised Manuscript: January 11, 2008
Manuscript Accepted: February 20, 2008
Published: April 16, 2008

Citation
Scott Glancy and Hilma Macedo de Vasconcelos, "Methods for producing optical coherent state superpositions," J. Opt. Soc. Am. B 25, 712-733 (2008)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-25-5-712


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. H.-A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics (Wiley-VCH, 2004). [CrossRef]
  2. 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]
  3. 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]
  4. T. C. Ralph, “Coherent superposition states as quantum rulers,” Phys. Rev. A 65, 042313 (2002). [CrossRef]
  5. M. Brune, E. Hagley, J. Dreyer, X. Maître, A. Maali, C. Wunderlich, J. M. Raimond, and S. Haroche, “Observing the progressive decoherence of the meter in a quantum measurement,” Phys. Rev. Lett. 77, 4887-4890 (1996). [CrossRef] [PubMed]
  6. A. Auffeves, P. Maioli, T. Meunier, S. Gleyzes, G. Nogues, M. Brune, J.-M. Raimond, and S. Haroche, “Entanglement of a mesoscopic field with an atom induced by photon graininess in a cavity,” Phys. Rev. Lett. 91, 230405 (2003). [CrossRef] [PubMed]
  7. B. Yurke and D. Stoler, “Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion,” Phys. Rev. Lett. 57, 13-16 (1986). [CrossRef] [PubMed]
  8. M. Wolinsky and H. J. Carmichael, “Quantum noise in the parametric oscillator: from squeezed states to coherent-state superpositions,” Phys. Rev. Lett. 60, 1836-1839 (1988). [CrossRef] [PubMed]
  9. S. Song, C. M. Caves, and B. Yurke, “Generation of superpositions of classically distinguishable quantum states from optical back-action evasion,” Phys. Rev. A 41, 5261-5264 (1990). [CrossRef] [PubMed]
  10. 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]
  11. 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]
  12. H. Jeong, M. S. Kim, T. C. Ralph, and B. S. Ham, “Generation of macroscopic superposition states with small nonlinearity,” Phys. Rev. A 70, 061801 (2004). [CrossRef]
  13. C. C. Gerry, “Generation of optical macroscopic quantum superposition states via state reduction with a Mach-Zender interferometer containing a Kerr medium,” Phys. Rev. A 59, 4095-4098 (1999). [CrossRef]
  14. J. Wenger, R. Tualle-Brouri, and P. Grangier, “Non-Gaussian statistics from individual pulses of squeezed light,” Phys. Rev. Lett. 92, 153601 (2004). [CrossRef] [PubMed]
  15. J. S. Neergaard-Nielsen, B. M. 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] [PubMed]
  16. A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83-86 (2006). [CrossRef] [PubMed]
  17. K. Wakui, H. Takahashi, A. Furusawa, and M. Sasaki, “Controllable generation of highly nonclassical states from nearly pure squeezed vacua,” arXiv.org e-Print archive, quant-ph/0609153v1, 20 September 2006, IL http://arxiv.org/abs/quant-pb/0609153vl.
  18. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  19. U. Leonhardt, Measuring the Quantum State of Light (Cambridge U. Press, 1997).
  20. S. Takeuchi, J. Kim, Y. Yamamoto, and H. Hogue, “Development of a high-quantum-efficiency single-photon counting system,” Appl. Phys. Lett. 74, 1063-1065 (1999). [CrossRef]
  21. J. Kim, S. Takeuchi, and Y. Yamamoto, “Multiphoton detection using visible light photon counter,” Appl. Phys. Lett. 74, 902-904 (1999). [CrossRef]
  22. E. Waks, E. Diamanti, B. C. Sanders, S. D. Bartlett, and Y. Yamamoto, “Direct observation of non-classical photon statistics in parametric downconversion,” Phys. Rev. Lett. 92, 113602 (2004). [CrossRef] [PubMed]
  23. E. Waks, K. Inoue, W. D. Oliver, E. Diamanti, and Y. Yamamoto, “High efficiency photon number detection for quantum information processing,” IEEE J. Quantum Electron. 9, 1502-1511 (2003). [CrossRef]
  24. E. Waks, E. Diamanti, and Y. Yamamoto, “Generation of photon number states,” New J. Phys. 8, 4 (2006). [CrossRef]
  25. 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 (2005). [CrossRef]
  26. P. T. Cochrane, G. J. Milburn, and W. J. Munro, “Macroscopically distinct quantum-superposition states as a bosonic code for amplitude damping,” Phys. Rev. A 59, 2631-2634 (1999). [CrossRef]
  27. S. Glancy, H. M. Vasconcelos, and T. C. Ralph, “Transmission of optical coherent state qubits,” Phys. Rev. A 70, 022317 (2004). [CrossRef]
  28. A. I. Lvovsky and M. G. Raymer, “Continuous-variable optical quantum state tomography,” arXiv.org e-Print archive, quant-ph/0511044v1, 5 November 2005, http://arxiv.org.abs/quant-ph/0511044v1.
  29. E. S. Polzik, J. Carri, and H. J. Kimble, “Spectroscopy with squeezed light,” Phys. Rev. Lett. 68, 3020-3023 (1992). [CrossRef] [PubMed]
  30. M.G. A.Paris and J.Rehàcek, eds., Quantum State Estimation, Vol. 649 of Lecture Notes in Physics (Springer, 2004).
  31. R. Blume-Kohout, “Optimal, reliable estimation of quantum states,” arXiv.org e-Print archive, quant-ph/0611080v1, 7 November 2006, http://arxiv.org/abs/quant-ph/0611080v1.
  32. R. D. Somma, J. Chiaverini, and D. J. Berkeland, “Lower bounds for the fidelity of entangled state preparation,” Phys. Rev. A 74, 052302 (2006). [CrossRef]
  33. G. J. Milburn and C. A. Holmes, “Dissipative quantum and classical Liouville mechanics of the anharmonic oscillator,” Phys. Rev. Lett. 56, 2237-2240 (1986). [CrossRef] [PubMed]
  34. H. J. Carmichael, Statistical Methods in Quantum Optics 1: Master Equations and Fokker-Planck Equations (Springer-Verlag, 1999).
  35. M. Kitagawa and Y. Yamamoto, “Number-phase minimum-uncertainty state with reduced number uncertainty in a kerr nonlinear interferometer,” Phys. Rev. A 34, 3974-3988 (1986). [CrossRef] [PubMed]
  36. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).
  37. R. L. Sutherland, Handbook of Nonlinear Optics, 2nd ed. (Dekker, 2003). [CrossRef]
  38. A. Mecozzi and P. Tombesi, “Distinguishable quantum states generated via nonlinear birefringence,” Phys. Rev. Lett. 58, 1055-1058 (1987). [CrossRef] [PubMed]
  39. B. Yurke and D. Stoler, “Quantum behavior of a four-wave mixer operated in a nonlinear regime,” Phys. Rev. A 35, 4846-4849 (1987). [CrossRef] [PubMed]
  40. P. Tombesi and A. Mecozzi, “Generation of macroscopically distinguishable quantum states and detection by the squeezed-vacuum technique,” J. Opt. Soc. Am. B 4, 1700-1709 (1987). [CrossRef]
  41. D. Vitali, P. Tombesi, and P. Grangier, “Conditional Schrödinger cats generation and detection by quantum non-demolition measurements,” Appl. Phys. B 64, 249-257 (1997). [CrossRef]
  42. M. Soljacic and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3, 211-219 (2004). [CrossRef] [PubMed]
  43. I. Fushman and J. Vuckovic, “Analysis of a quantum nondemolition measurement scheme based on Kerr nonlinearity in photonic crystal waveguides,” arXiv.org e-Print archive, quant-ph/0603150v1, 16 March 2006, http://arxiv.org/abs/quant-ph/0603150v1.
  44. Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65-69 (2005). [CrossRef] [PubMed]
  45. E. Dulkeith, S. J. McNab, and Y. A. Vlasov, “Mapping the optical properties of slap-type two-dimensional photonic crystal waveguides,” Phys. Rev. B 72, 115102 (2005). [CrossRef]
  46. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633-673 (2005). [CrossRef]
  47. H. Schmidt and A. Imamoglu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936-1938 (1996). [CrossRef] [PubMed]
  48. M. D. Lukin and A. Imamoglu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419-1422 (2000). [CrossRef] [PubMed]
  49. M. D. Reid and B. Yurke, “Effect of bistability and superpositions on quantum statistics in degenerate parametric oscillation,” Phys. Rev. A 46, 4131-4137 (1992). [CrossRef] [PubMed]
  50. L. Krippner, W. J. Munro, and M. D. Reid, “Transient macroscopic quantum superposition states in degenerate parametric oscillation: calculations in the large-quantum-noise limit using the positive p representation,” Phys. Rev. A 50, 4330-4338 (1994). [CrossRef] [PubMed]
  51. B. Yurke, “Optical back-action-evading amplifiers,” J. Opt. Soc. Am. B 2, 732-738 (1985). [CrossRef]
  52. B. Yurke, W. Schleich, and D. F. Walls, “Quantum superpositions generated by quantum nondemolition measurements,” Phys. Rev. A 42, 1703-1711 (1990). [CrossRef] [PubMed]
  53. S. L. Braunstein, “Squeezing as an irreducible resource,” Phys. Rev. A 71, 055801 (2006). [CrossRef]
  54. 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] [PubMed]
  55. H. Vahlbruch, M. Mehmet, N. Lastzka, B. Hage, S. Chelkowski, A. Franzen, S. Gossler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10 dB quantum noise reduction,” Phys. Rev. Lett. 100, 033602 (2008). [CrossRef] [PubMed]
  56. 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] [PubMed]
  57. P. Tombesi and D. Vitali, “All-optical model for the generation and the detection of macroscopic quantum coherence,” Phys. Rev. Lett. 77, 411-415 (1996). [CrossRef] [PubMed]
  58. D. Vitali and P. Tombesi, “Generation and detection of linear superpositions of classically distinguishable states of a radiation mode,” Int. J. Mod. Phys. B 11, 2119-2140 (1997). [CrossRef]
  59. M. S. Kim, E. Park, P. L. Knight, and H. Jeong, “Nonclassicality of a photon-subtracted Gaussian field,” Phys. Rev. A 71, 043805 (2005). [CrossRef]
  60. S. Olivares and M. G. A. Paris, “Squeezed Fock state by inconclusive photon subtraction,” J. Opt. B: Quantum Semiclassical Opt. 7, S616-S621 (2005). [CrossRef]
  61. A. LaPorta and R. E. Slusher, “Squeezing limits at high parametric gains,” Phys. Rev. A 44, 2013-2022 (1991). [CrossRef]
  62. W. Wasilewski, A. I. Lvovsky, K. Banaszek, and C. Radzewicz, “Pulsed squeezed light: simultaneous squeezing of multiple modes,” Phys. Rev. A 73, 063819 (2006). [CrossRef]
  63. A. I. Lvovsky, W. Wasilewski, and K. Banaszek, “Decomposing a pulsed optical parametric amplifier into independent squeezers,” J. Mod. Opt. 54, 721-733 (2007). [CrossRef]
  64. P. P. Rohde, W. Mauerer, and C. Silberhorn, “Spectral structure and decompositions of optical states, and their applications,” New J. Phys. 9, 91 (2007). [CrossRef]
  65. W. P. Grice, A. B. U'Ren, and I. A. Walmsley, “Eliminating frequency and space-time correlations in multiphoton states,” Phys. Rev. A 64, 063815 (2001). [CrossRef]
  66. A. B. U'Ren, C. Silberhorn, R. Erdmann, K. Banaszek, W. P. Grice, I. A. Walmsley, and M. G. Raymer, “Generation of pure-state single-photon wavepackets by conditional preparation based on spontaneous parametric downconversion,” Laser Phys. 15, 146-161 (2005).
  67. M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down conversion in a distributed microcavity,” Phys. Rev. A 72, 023825 (2005). [CrossRef]
  68. Figure appears in , but Figs. are new in this paper.
  69. P. Grangier, B. Sanders, and J. Vuckovic, “Focus on single photons on demand,” New J. Phys. 6, 85-100 (2004). [CrossRef]
  70. H. Jeong, A. P. Lund, and T. C. Ralph, “Production of superpositions of coherent states in traveling optical fields with inefficient photon detection,” Phys. Rev. A 72, 013801 (2005). [CrossRef]
  71. P. P. Rhode and A. P. Lund, “Practical effects in cat state breeding,” arXiv.org e-Print archive, quant-ph/0702064vl, 7 February 2007, http://arxiv.org/abs/quant-ph/0702064vl.
  72. U. Titulaer and R. Glauber, “Density operators for coherent fields,” Phys. Rev. 145, 1041-1050 (1965). [CrossRef]
  73. Z. Bialynicka-Birula, “Properties of the generalized coherent state,” Phys. Rev. 173, 1207-1209 (1968). [CrossRef]
  74. K. S. Lee, M. S. Kim, S. D. Lee, and V. Buzek, “Squeezing properties of multicomponent superposition states of light,” J. Korean Phys. Soc. 26, 197-204 (1993).
  75. T. Gantsog and R. Tanas, “Discrete superpositions of coherent states and phase properties of elliptically polarized light propagating in a Kerr medium,” Quantum Opt. 3, 33-48 (1991). [CrossRef]
  76. Although Eq. appears in , they discussed neither the relationship between fidelity and cat amplitude nor the cat's phase's dependence on the homodyne measurement result.
  77. H. Jeong, “Using weak nonlinearity under decoherence for macroscopic entanglement generation and quantum computation,” Phys. Rev. A 72, 034305 (2005). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited