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Squeezed states and uncertainty relations since 1991

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Journal of Russian Laser Research Aims and scope

Abstract

A brief review of the history of ten workshops/conferences on “Squeezed States and Uncertainty Relations” and main achievements in the related fields of quantum physics for the period from 1991 to 2007 are presented.

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References

  1. W. Heisenberg, “Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik,” Z. Phys., 43, 172–198 (1927).

    Article  ADS  Google Scholar 

  2. N. Bohr, “The quantum postulate and the recent development of atomic theory,” Nature (Suppl.), 121, 580–590 (1928).

    ADS  MATH  Google Scholar 

  3. E. H. Kennard, “Zur Quantenmechanik einfacher Bewegungstypen,” Z. Phys., 44, 326–352 (1927).

    Article  ADS  Google Scholar 

  4. M. M. Nieto, “The discovery of squeezed states-in 1927,” in: D. Han, J. Janszky, Y. S. Kim, and V. I. Man’ko (eds.), Proceedings of the Fifth International Conference on Squeezed States and Uncertainty Relations (Balatonfüred, Hungary, May 27–31, 1997), NASA, Greenbelt (1998), CP-1998-206855, pp. 175–180.

    Google Scholar 

  5. M. Jammer, The Conceptual Development of Quantum Mechanics, McGraw-Hill, New York (1967).

    Google Scholar 

  6. H. P. Robertson, “The uncertainty principle,” Phys. Rev., 34, 163–164 (1929).

    Article  ADS  Google Scholar 

  7. H. P. Robertson, “A general formulation of the uncertainty principle and its classical interpretation,” Phys. Rev., 35, 667 (1930).

    Google Scholar 

  8. E. Schrödinger, “Zum Heisenbergschen Unschärfeprinzip,” Ber. Kgl. Akad. Wiss. Berlin, 24, 296–303 (1930).

    Google Scholar 

  9. K. Husimi, “Miscellanea in elementary quantum mechanics. I,” Prog. Theor. Phys., 9, 238–244 (1953).

    Article  ADS  MathSciNet  Google Scholar 

  10. H. Takahasi, “Information theory of quantum-mechanical channels,” in: A. V. Balakrishnan (ed.), Advances in Communication Systems. Theory and Applications, Academic, New York (1965), Vol. 1, pp. 227–310.

    Google Scholar 

  11. H. P. Yuen and J. H. Shapiro, “Optical communication with two-photon coherent states-part I: Quantum-state propagation and quantum-noise reduction,” IEEE Trans. Inform. Theory, IT-24, 657–668 (1978).

    Article  ADS  MathSciNet  Google Scholar 

  12. J. N. Hollenhorst, “Quantum limits on resonant-mass gravitational-radiation detectors,” Phys. Rev. D, 19, 1669–1679 (1979).

    Article  ADS  Google Scholar 

  13. C. M. Caves, K. S. Thorne, R. W. P. Drever, V. D. Sandberg, and M. Zimmermann, “On the measurement of a weak classical force coupled to a quantum mechanical oscillator. I. Issue of principle,” Rev. Mod. Phys., 52, 341–392 (1980).

    Article  ADS  Google Scholar 

  14. C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D, 23, 1693–1708 (1981).

    Article  ADS  Google Scholar 

  15. K. O. Friedrichs, Mathematical Aspects of the Quantum Theory of Fields, Interscience, New York (1953).

    MATH  Google Scholar 

  16. L. Infeld and J. Plebański, “On a certain class of unitary transformations,” Acta Phys. Polon., 14, 41–75 (1955).

    MATH  MathSciNet  Google Scholar 

  17. J. Plebański, “Wave functions of a harmonic oscillator,” Phys. Rev., 101, 1825–1826 (1956).

    Article  ADS  Google Scholar 

  18. D. Stoler, “Equivalence classes of minimum uncertainty packets,” Phys. Rev. D, 1, 3217–3219 (1970).

    Article  ADS  Google Scholar 

  19. D. Stoler, “Equivalence classes of minimum uncertainty packets. II,” Phys. Rev. D, 4, 1925–1926 (1971).

    Article  ADS  Google Scholar 

  20. H. P. Yuen, “Two-photon coherent states of the radiation field,” Phys. Rev. A, 13, 2226–2243 (1976).

    Article  ADS  Google Scholar 

  21. D. F. Walls, “Squeezed states of light,” Nature, 306, 141–146 (1983).

    Article  ADS  Google Scholar 

  22. R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett., 55, 2409–2412 (1985).

    Article  ADS  Google Scholar 

  23. R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broad-band parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett., 57, 691–694 (1986).

    Article  ADS  Google Scholar 

  24. L. A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett., 57, 2520–2523 (1986).

    Article  ADS  Google Scholar 

  25. D. Han, Y. S. Kim, and W. W. Zachary, Introduction to the Proceedings of the Workshop on Squeezed States and Uncertainty Relations (College Park, Maryland, March 28–30, 1991), NASA, Greenbelt (1992), NASA Conference Publication 3135, p. 1.

    Google Scholar 

  26. C. Fabre, “Squeezed states of light,” Phys. Rep., 219, 215–225 (1992).

    Article  ADS  Google Scholar 

  27. H. J. Kimble, “Squeezed states of light: an (incomplete) survey of experimental progress and prospects,” Phys. Rep., 219, 227–234 (1992).

    Article  ADS  Google Scholar 

  28. E. S. Polzik, J. Carri, and H. J. Kimble, “Atomic spectroscopy with squeezed light for sensitivity beyond the vacuum-state limit,” Appl. Phys. B, 55, 279–290 (1992).

    Article  ADS  Google Scholar 

  29. Y. Yamamoto, S. Machida, and W. H. Richardson, “Photon number squeezed states in semiconductor lasers,” Science, 255, 1219–1224 (1992).

    Article  ADS  Google Scholar 

  30. D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, “Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: application to squeezed states and the vacuum,” Phys. Rev. Lett., 70, 1244–1247 (1993).

    Article  ADS  Google Scholar 

  31. G. Breitenbach, S. Schiller, and J. Mlynek, “Measurement of the quantum states of squeezed light,” Nature, 387, 471–475 (1997).

    Article  ADS  Google Scholar 

  32. L. G. Lutterbach and L. Davidovich, “Production and detection of highly squeezed states in cavity QED,” Phys. Rev. A, 61, 023813 (2000).

    Google Scholar 

  33. J. I. Cirac, A. S. Parkins, R. Blatt, and P. Zoller, “Dark squeezed states of the motion of a trapped ion,” Phys. Rev. Lett., 70, 556–559 (1993).

    Article  ADS  Google Scholar 

  34. D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, “Quantum dynamics of single trapped ions,” Rev. Mod. Phys., 75, 281–324 (2003).

    Article  ADS  Google Scholar 

  35. C. Orzel, A. K. Tuchman, M. L. Fenselau, M. Yasuda, and M. A. Kasevich, “Squeezed states in a Bose-Einstein condensate,” Science, 291, 2386–2389 (2001).

    Article  ADS  Google Scholar 

  36. E. A. Calzetta and B. L. Hu, “Bose-Einstein condensate collapse and dynamical squeezing of vacuum fluctuations,” Phys. Rev. A, 68, 043625 (2003).

    Google Scholar 

  37. K. Mølmer, “Quantum atom optics with Bose-Einstein condensates,” New J. Phys., 5, 55 (2003).

    Article  Google Scholar 

  38. V. I. Yukalov, E. P. Yukalova, and V. S. Bagnato, “Resonant Bose condensate: Analog of resonant atom,” Laser Phys., 13, 551–561 (2003).

    Google Scholar 

  39. J.-P. Martikainen and H. T. C. Stoof, “Spontaneous squeezing of a vortex in an optical lattice,” Phys. Rev. A, 70, 013604 (2004).

    Google Scholar 

  40. F. Gerbier, S. Fölling, A. Widera, O. Mandel, and I. Bloch, “Probing number squeezing of ultracold atoms across the superfluid-Mott insulator transition,” Phys. Rev. Lett., 96, 090401 (2006).

    Google Scholar 

  41. G.-B. Jo, Y. Shin, S. Will, T. A. Pasquini, M. Saba, W. Ketterle, and D. E. Pritchard, “Long phase coherence time and number squeezing of two Bose-Einstein condensates on an atom chip,” Phys. Rev. Lett., 98, 030407 (2007).

    Google Scholar 

  42. W. Li, A. K. Tuchman, H.-C. Chien, and M. A. Kasevich, “Extended coherence time with atom-number squeezed states,” Phys. Rev. Lett., 98, 040402 (2007).

    Google Scholar 

  43. J. Grochmalicki and M. Lewenstein, “Are squeezed states necessary? A case study of photon detection based on quantum interference,” Phys. Rep., 208, 189–265 (1991).

    Article  ADS  Google Scholar 

  44. J. Mlynek, G. Rempe, S. Schiller, and M. Wilkens (eds.), Quantum Nondemolition Measurements, Appl. Phys. B, 64, special issue No. 2 (1997).

  45. N. B. An, “Squeezed excitons in semiconductors,” Mod. Phys. Lett. B, 5, 587–591 (1991).

    Article  ADS  Google Scholar 

  46. M. Artoni and J. L. Birman, “Quantum-optical properties of polariton waves,” Phys. Rev. B, 44, 3736–3756 (1991).

    Article  ADS  Google Scholar 

  47. C. A. R. Sá de Melo, “Squeezed boson states in condensed matter,” Phys. Rev. B, 44, 11911–11917 (1991).

    Google Scholar 

  48. J. Peřina, M. Kárská, and J. Křepelka, “Stimulated Raman scattering of nonclassical light by squeezed phonons,” Acta Phys. Polon., 79, 817–828 (1991).

    Google Scholar 

  49. J. Janszky and A. V. Vinogradov, “Phonon squeezing,” in: Mol. Cryst. Liq. Cryst. Sci. Technol.-Sec. B: Nonlinear Optics, Gordon & Breach, London (1992), Vol. 2, pp. 317–329.

    Google Scholar 

  50. C. F. Lo and R. Sollie, “Correlated squeezed phonon states,” Phys. Lett. A, 169, 91–98 (1992).

    Article  ADS  Google Scholar 

  51. M. Sonnek, H. Eiermann, and M. Wagner, “Squeezed excited states in exciton-phonon systems,” Phys. Rev. B, 51, 905–915 (1995).

    Article  ADS  Google Scholar 

  52. X. D. Hu and F. Nori, “Squeezed phonon states: modulating quantum fluctuations of atomic displacements,” Phys. Rev. Lett., 76, 2294–2297 (1996).

    Article  ADS  Google Scholar 

  53. X. D. Hu and F. Nori, “Phonon squeezed states generated by second-order Raman scattering,” Phys. Rev. Lett., 79, 4605–4608 (1997).

    Article  ADS  Google Scholar 

  54. G. A. Garrett, A. G. Rojo, A. K. Sood, J. F. Whitaker, and R. Merlin, “Vacuum squeezing of solids; macroscopic quantum states driven by light pulses,” Science, 275, 1638–1640 (1997).

    Article  Google Scholar 

  55. M. Blencowe, “Quantum electromechanical systems,” Phys. Rep., 395, 159–222 (2004).

    Article  ADS  Google Scholar 

  56. A. Zazunov, D. Feinberg, and T. Martin, “Phonon squeezing in a superconducting molecular transistor,” Phys. Rev. Lett., 97, 196801 (2006).

    Google Scholar 

  57. A. V. Vinogradov and J. Janszky, “Excitation of squeezed vibrational wave packets associated with Franck-Condon transitions in molecules,” Zh. Éksp. Teor. Fiz., 100, 386–399 (1991) [Sov. Phys.-JETP, 73, 211–217 (1991)].

    Google Scholar 

  58. I. Averbukh, and M. Shapiro, “Optimal squeezing of molecular wave packets,” Phys. Rev. A, 47, 5086–5092 (1993).

    Article  ADS  Google Scholar 

  59. J. Janszky, A. V. Vinogradov, I. A. Walmsley, and J. Mostowski, “Competition between geometrical and dynamical squeezing during a Franck-Condon transition,” Phys. Rev. A, 50, 732–740 (1994).

    Article  ADS  Google Scholar 

  60. M. V. Korolkov, J. Manz, and G. K. Paramonov, “Theory of ultrafast laser control for state-selective dynamics of diatomic molecules in the ground electronic state: Vibrational excitation, dissociation, spatial squeezing and association,” Chem. Phys., 217, 341–374 (1997).

    Article  Google Scholar 

  61. G. Alber and P. Zoller, “Laser excitation of electronic wave packets in Rydberg atoms,” Phys. Rep., 199, 232–280 (1991).

    Article  ADS  Google Scholar 

  62. M. M. Nieto, “Rydberg wave packets are squeezed states,” Quantum Opt., 6, 9–14 (1994).

    Article  ADS  Google Scholar 

  63. R. Bluhm and V. A. Kostelecký, “Atomic supersymmetry, Rydberg wave packets, and radial squeezed states,” Phys. Rev. A, 49, 4628–4640 (1994).

    Article  ADS  Google Scholar 

  64. R. Bluhm, V. A. Kostelecký, and B. Tudose, “Elliptical squeezed states and Rydberg wave packets,” Phys. Rev. A, 52, 2234–2244 (1995).

    Article  ADS  Google Scholar 

  65. L. Michel and B. I. Zhilinskii, “Rydberg states of atoms and molecules. Basic group theoretical and topological analysis,” Phys. Rep., 341, 173–264 (2001).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  66. J. R. R. Verlet and H. H. Fielding, “Manipulating electron wave packets,” Int. Rev. Phys. Chem., 20, 283–312 (2001).

    Article  Google Scholar 

  67. R. W. Robinett, “Quantum wave packet revivals,” Phys. Rep., 392, 1–119 (2004).

    Article  ADS  MathSciNet  Google Scholar 

  68. S. Ghosh and J. Banerji, “A time-frequency analysis of wave packet fractional revivals,” J. Phys. B: At. Mol. Opt. Phys., 40, 3545–3553 (2007).

    Article  ADS  Google Scholar 

  69. G. S. Agarwal and R. R. Puri, “Atomic states with spectroscopic squeezing,” Phys. Rev. A, 49, 4968–4971 (1994).

    Article  ADS  Google Scholar 

  70. D. J. Wineland, J. J. Bollinger, W. M. Itano, and D. J. Heinzen, “Squeezed atomic states and projection noise in spectroscopy,” Phys. Rev. A, 50, 67–88 (1994).

    Article  ADS  Google Scholar 

  71. K. Saito and M. Ueda, “Quantum-controlled few-photon state generated by squeezed atoms,” Phys. Rev. Lett., 79, 3869–3872 (1997).

    Article  ADS  Google Scholar 

  72. L.-M. Duan, A. Srensen, J. I. Cirac, and P. Zoller, “Squeezing and entanglement of atomic beams,” Phys. Rev. Lett., 85, 3991–3994 (2000).

    Article  ADS  Google Scholar 

  73. K. Burnett, M. Edwards, C. W. Clark, and M. Shotter, “The Bogoliubov approach to number squeezing of atoms in an optical lattice,” J. Phys. B: At. Mol. Opt. Phys., 35, 1671–1678 (2002).

    Article  ADS  Google Scholar 

  74. D. J. Wineland, J. J. Bollinger, W. M. Itano, F. L. Moore, and D. J. Heinzen, “Spin squeezing and reduced quantum noise in spectroscopy,” Phys. Rev. A, 46, R6797–R6800 (1992).

    Google Scholar 

  75. M. Kitagawa and M. Ueda, “Squeezed spin states,” Phys. Rev. A, 47, 5138–5143 (1993).

    Article  ADS  Google Scholar 

  76. D. A. Trifonov, “Generalized intelligent states and squeezing,” J. Math. Phys., 35, 2297–2308 (1994).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  77. A. Kuzmich, K. Mølmer, and E. S. Polzik, “Spin squeezing in an ensemble of atoms illuminated with squeezed light,” Phys. Rev. Lett., 79, 4782–4785 (1997).

    Article  ADS  Google Scholar 

  78. T. Altanhan and S. Bilge, “Squeezed spin states and Heisenberg interaction,” J. Phys. A: Math. Gen., 32, 115–121 (1999).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  79. J. Hald, J. L. Sørensen, C. Schori, and E. S. Polzik, “Spin squeezed atoms: A macroscopic entangled ensemble created by light,” Phys. Rev. Lett., 83, 1319–1322 (1999).

    Article  ADS  Google Scholar 

  80. A. Sørensen and K. Mølmer, “Spin-spin interaction and spin squeezing in an optical lattice,” Phys. Rev. Lett., 83, 2274–2277 (1999).

    Article  ADS  Google Scholar 

  81. A. Kuzmich, L. Mandel, and N. P. Bigelow, “Generation of spin squeezing via continuous quantum nondemolition measurement,” Phys. Rev. Lett., 85, 1594–1597 (2000).

    Article  ADS  Google Scholar 

  82. L. Vernac, M. Pinard, and E. Giacobino, “Spin squeezing in two-level systems,” Phys. Rev. A, 62, 063812 (2000).

    Google Scholar 

  83. A. S. Sørensen and K. Mølmer, “Entanglement and extreme spin squeezing,” Phys. Rev. Lett., 86, 4431–4434 (2001).

    Article  ADS  Google Scholar 

  84. A. André and M. D. Lukin, “Atom correlations and spin squeezing near the Heisenberg limit: Finite-size effect and decoherence,” Phys. Rev. A, 65, 053819 (2002).

    Google Scholar 

  85. L. K. Thomsen, S. Mancini, and H. M. Wiseman, “Continuous quantum nondemolition feedback and unconditional atomic spin squeezing,” J. Phys. B: At. Mol. Opt. Phys., 35, 4937–4952 (2002).

    Article  ADS  Google Scholar 

  86. J. M. Geremia, J. K. Stockton, and H. Mabuchi, “Real-time quantum feedback control of atomic spin-squeezing,” Science, 304, 270–273 (2004).

    Article  ADS  Google Scholar 

  87. L. B. Madsen and K. Mølmer, “Spin squeezing and precision probing with light and samples of atoms in the Gaussian description,” Phys. Rev. A, 70, 052324 (2004).

    Google Scholar 

  88. M. Reboiro, O. Civitarese, and L. Rebon, “Study of squeezing in spin clusters,” Phys. Lett. A, 266, 241–245 (2007).

    Article  ADS  Google Scholar 

  89. B. Yurke, “Squeezed-state generation using a Josephson parametric amplifier,” J. Opt. Soc. Am. B, 4, 1551–1557 (1987).

    ADS  Google Scholar 

  90. T. P. Spiller, T. D. Clark, R. J. Prance, H. Prance, and D. A. Poulton, “Macroscopic superposition in superconducting circuits,” Int. J. Mod. Phys. B, 4, 1423–1435 (1990).

    Article  ADS  Google Scholar 

  91. V. V. Dodonov, V. I. Man’ko, and O. V. Man’ko, “Correlated states and quantum noise of an oscillatory contour,” Measurement Techniques USSR, 33, 102–104 (1990).

    Article  Google Scholar 

  92. S. T. Pavlov and A. V. Prokhorov, “Correlated and compressed states in a parametrized Josephson junction,” Sov. Phys.-Solid State, 33, 1384–1386 (1991).

    Google Scholar 

  93. S. T. Pavlov and A. V. Prokhorov, “Time-dependent theory of the single-contact quantum interferometer. Correlated and squeezed states,” Sov. Phys.-Solid State, 34, 50–53 (1992).

    Google Scholar 

  94. O. V. Man’ko, “Correlated squeezed states of a Josephson junction,” J. Kor. Phys. Soc., 27, 1–4 (1994).

    MathSciNet  Google Scholar 

  95. A. Vourdas, “Mesoscopic Josephson junctions in the presence of nonclassical electromagnetic fields.” Phys. Rev. B, 49, 12040-12046 (1994).

    Google Scholar 

  96. A. Vourdas and T. P. Spiller, “Quantum theory of the interaction of Josephson junctions with nonclassical microwaves,” J. Phys. B: At. Mol. Opt. Phys., 102, 43–54 (1997).

    Google Scholar 

  97. J. Zou and B. Shao, “Superpositions of coherent states and squeezing effects in a mesoscopic Josephson junction,” Int. J. Mod. Phys. B, 13, 917–924 (1999).

    Article  ADS  Google Scholar 

  98. M. J. Everitt, T. D. Clark, P. B. Stiffell, A. Vourdas, J. F. Ralph, R. J. Prance, and H. Prance, “Superconducting analogs of quantum optical phenomena: Macroscopic quantum superpositions and squeezing in a superconducting quantum-interference device ring,” Phys. Rev. A, 69, 043804 (2004).

    Google Scholar 

  99. P. Rabl, A. Shnirman, and P. Zoller, “Generation of squeezed states of nanomechanical resonators by reservoir engineering,” Phys. Rev. B, 70, 205304 (2004).

    Google Scholar 

  100. P. Zhang, Y. D. Wang, and C. P. Sun, “Cooling mechanism for a nanomechanical resonator by periodic coupling to a Cooper pair box,” Phys. Rev. Lett., 95, 097204 (2005).

    Google Scholar 

  101. X. Zhou and A. Mizel, “Nonlinear coupling of nanomechanical resonators to Josephson quantum circuits,” Phys. Rev. Lett., 97, 267201 (2006).

    Google Scholar 

  102. F. Xue, Y.-X. Liu, C. P. Sun, and F. Nori, “Two-mode squeezed states and entangled states of two mechanical resonators,” Phys. Rev. B, 76, 064305 (2007).

    Google Scholar 

  103. V. V. Dodonov, A. B. Klimov, and V. I. Man’ko, “Generation of squeezed states in a resonator with a moving wall,” Phys. Lett. A, 149, 225–228 (1990).

    Article  ADS  Google Scholar 

  104. V. V. Dodonov, A. B. Klimov, and D. E. Nikonov, “Quantum phenomena in resonators with moving walls,” J. Math. Phys., 34, 2742–2756 (1993).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  105. V. V. Dodonov and A. B. Klimov, “Generation and detection of photons in a cavity with a resonantly oscillating boundary,” Phys. Rev. A, 53, 2664–2682 (1996).

    Article  ADS  Google Scholar 

  106. S. Mancini, V. I. Man’ko, and P. Tombesi, “Ponderomotive control of quantum macroscopic coherence,” Phys. Rev. A, 55, 3042–3050 (1997).

    Article  ADS  Google Scholar 

  107. S. Bose, K. Jacobs, and P. L. Knight, “Preparation of nonclassical states in cavities with a moving mirror,” Phys. Rev. A, 56, 4175–4186 (1997).

    Article  ADS  Google Scholar 

  108. W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, “Towards quantum superpositions of a mirror,” Phys. Rev. Lett., 91, 130401 (2003).

    Google Scholar 

  109. A. Bassi, E. Ippoliti, and S. L. Adler, “Towards quantum superpositions of a mirror: An exact open systems analysis,” Phys. Rev. Lett., 94, 030401 (2005).

    Google Scholar 

  110. V. V. Dodonov, “Nonstationary Casimir effect and analytical solutions for quantum fields in cavities with moving boundaries,” in: M. W. Evans (ed.), Modern Nonlinear Optics, Advances in Chemical Physics Series, Wiley, New York (2001), Vol. 119, Pt. 1, pp. 309–394.

    Google Scholar 

  111. V. V. Dodonov and A. V. Dodonov, “Quantum harmonic oscillator and nonstationary Casimir effect,” J. Russ. Laser Res., 26, 445–483 (2005).

    Article  Google Scholar 

  112. C. Braggio, G. Bressi, G. Carugno, C. Del Noce, G. Galeazzi, A. Lombardi, A. Palmieri, G. Ruoso, and D. Zanello, “A novel experimental approach for the detection of the dynamic Casimir effect,” Europhys. Lett., 70, 754–60 (2005).

    Article  ADS  Google Scholar 

  113. W.-J. Kim, J. H. Brownell, and R. Onofrio, “Detectability of dissipative motion in quantum vacuum via superradiance,” Phys. Rev. Lett., 96, 200402 (2006).

    Google Scholar 

  114. V. P. Karassiov, “Polarization structure of quantum light fields-a new insight. 1. General outlook,” J. Phys. A: Math. Gen., 26, 4345–4354 (1993).

    Article  ADS  MathSciNet  Google Scholar 

  115. V. P. Karassiov, “Polarization squeezing and new states of light in quantum optics,” Phys. Lett. A, 190, 387–392 (1994).

    Article  ADS  Google Scholar 

  116. N. V. Korolkova and A. S. Chirkin, “Formation and conversion of the polarization-squeezed light,” J. Mod. Opt., 43, 869–878 (1996).

    MATH  MathSciNet  ADS  Google Scholar 

  117. J. Lehner, U. Leonhardt, and H. Paul, “Unpolarized light: Classical and quantum states,” Phys. Rev. A, 53, 2727–2735 (1996).

    Article  ADS  Google Scholar 

  118. J. Lehner, H. Paul, and G. S. Agarwal, “Generation and physical properties of a new form of unpolarized light,” Opt. Commun., 139, 262–269 (1997).

    Article  ADS  Google Scholar 

  119. A. P. Alodjants, S. M. Arakelian, and A. S. Chirkin, “Polarization quantum states of light in nonlinear distributed feedback systems; quantum nondemolition measurements of the Stokes parameters of light and atomic angular momentum,” Appl. Phys. B, 66, 53–65 (1998).

    Article  ADS  Google Scholar 

  120. A. P. Alodjants and S. M. Arakelian, “Quantum phase measurements and nonclassical polarization states of light,” J. Mod. Opt., 46, 475–507 (1999).

    MATH  ADS  MathSciNet  Google Scholar 

  121. V. P. Karassiov, “Symmetry approach to reveal hidden coherent structures in quantum optics. General outlook and examples,” J. Russ. Laser Res., 21, 370–410 (2000).

    Article  Google Scholar 

  122. N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, “Polarization squeezing and continuous-variable polarization entanglement,” Phys. Rev. A, 65, 052306 (2002).

    Google Scholar 

  123. A. Luis, “Degree of polarization in quantum optics,” Phys. Rev. A, 66, 013806 (2002).

    Google Scholar 

  124. W. P. Bowen, R. Schnabel, H.-A. Bachor, and P. K. Lam, “Polarization squeezing of continuous variable Stokes parameters,” Phys. Rev. Lett., 88, 093601 (2002).

    Google Scholar 

  125. V. Josse, A. Dantan, L. Vernac, A. Bramati, M. Pinard, and E. Giacobino, “Polarization squeezing with cold atoms,” Phys. Rev. Lett., 91, 103601 (2003).

    Google Scholar 

  126. A. Luis, “Polarization distributions and degree of polarization for quantum Gaussian light fields,” Opt. Commun., 273, 173–181 (2007).

    Article  ADS  Google Scholar 

  127. V. V. Dodonov, E. V. Kurmyshev, and V. I. Man’ko, “Generalized uncertainty relation and correlated coherent states,” Phys. Lett. A, 79, 150–152 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  128. D. L. Jacobson, S. A. Werner, and H. Rauch, “Spectral modulation and squeezing at high-order neutron interferences,” Phys. Rev. A, 49, 3196–3200 (1994).

    Article  ADS  Google Scholar 

  129. P. B. Lerner, H. Rauch, and M. Suda, “Wigner-function calculations for the coherent superposition of matter wave,” Phys. Rev. A, 51, 3889–3895 (1995).

    Article  ADS  Google Scholar 

  130. G. Badurek, H. Rauch, M. Suda, and H. Weinfurter, “Identification of nonclassical states in neutron spin precession experiments,” Opt. Commun., 179, 13–18 (2000).

    Article  ADS  Google Scholar 

  131. A. Vourdas and R. M. Weiner, “Multiplicity distributions and Bose-Einstein correlations in highenergy multiparticle production in the presence of squeezed coherent states,” Phys. Rev. D, 38, 2209–2217 (1988).

    Article  ADS  Google Scholar 

  132. I. M. Dremin and R. C. Hwa, “Multiplicity distributions of squeezed isospin states,” Phys. Rev. D, 53, 1216–1223 (1996).

    Article  ADS  Google Scholar 

  133. V. V. Dodonov, I. M. Dremin, O. V. Man’ko, V. I. Man’ko, and P. G. Polynkin, “Nonclassical field states in quantum optics and particle physics,” J. Russ. Laser Res., 19, 427–463 (1998).

    Google Scholar 

  134. V. Kuvshinov and V. Shaporov, “Gluon squeezed states in QCD jet,” Acta Phys. Pol. B, 30, 59–68 (1999).

    ADS  Google Scholar 

  135. Y. Tsue, A. Koike, and N. Ikezi, “Time-evolution of a collective meson field by use of a squeezed state,” Prog. Theor. Phys., 106, 807–822 (2001).

    Article  ADS  Google Scholar 

  136. L. P. Grishchuk, H. A. Haus, and K. Bergman, “Generation of squeezed radiation from vacuum in the cosmos and the laboratory,” Phys. Rev. D, 46, 1440–1449 (1992).

    Article  ADS  Google Scholar 

  137. A. Albrecht, P. Ferreira, M. Joyce, and T. Prokopec, “Inflation and squeezed quantum states,” Phys. Rev. D, 50, 4807–4820 (1994).

    Article  ADS  Google Scholar 

  138. B. L. Hu, G. Kang, and A. Matacz, “Squeezed vacua and the quantum statistics of cosmological particle creation,” Int. J. Mod. Phys. A, 9, 991–1007 (1994).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  139. A. O. Barvinsky and A. Y. Kamenshchik, “Preferred basis in quantum theory and the problem of classicalization of the quantum universe,” Phys. Rev. D, 52, 743–757 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  140. D. Polarski and A. A. Starobinsky, “Semiclassicality and decoherence of cosmological perturbations,” Class. Quantum Grav., 13, 377–391 (1996).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  141. P. K. Suresh and V. C. Kuriakose, “Squeezed states, black holes and entropy generation,” Mod. Phys. Lett. A, 12, 1435–1445 (1997).

    Article  ADS  Google Scholar 

  142. M. Giovannini, “Backgrounds of squeezed relic photons and their spatial correlations,” Phys. Rev. D, 61, 087306 (2000).

    Google Scholar 

  143. M. B. Einhorn and F. Larsen, “Squeezed states in the de Sitter vacuum,” Phys. Rev. D, 68, 064002 (2003).

    Google Scholar 

  144. D. Ahn and M. S. Kim, “Hawking-Unruh effect and the entanglement of two-mode squeezed states in Riemannian space-time,” Phys. Lett. A, 366, 202–205 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  145. K. Vogel, V. M. Akulin, and W. P. Schleich, “Quantum state engineering of the radiation field,” Phys. Rev. Lett., 71, 1816–1819 (1993).

    Article  ADS  Google Scholar 

  146. A. S. Parkins, P. Marte, P. Zoller, and H. J. Kimble, “Synthesis of arbitrary quantum states via adiabatic transfer of Zeeman coherence,” Phys. Rev. Lett., 71, 3095–3098 (1993).

    Article  ADS  Google Scholar 

  147. C. K. Law and J. H. Eberly, “Arbitrary control of a quantum electromagnetic field,” Phys. Rev. Lett., 76, 1055–1058 (1996).

    Article  ADS  Google Scholar 

  148. W. P. Schleich and M. G. Raymer (eds.), Quantum state preparation and measurement, J. Mod. Opt., 44, special issue No. 11/12 (1997).

  149. M. Dakna, L. Knöll, and D.-G. Welsch, “Quantum state engineering using conditional measurement on a beam splitter,” Europ. Phys. J. D, 3, 295–308 (1998).

    Article  ADS  Google Scholar 

  150. V. Peřinová and A. Lukš, “Continuous measurements in quantum optics,” in: E. Wolf (ed.), Progress in Optics, North Holland, Amsterdam (2000), Vol. XL, pp. 115–269.

    Google Scholar 

  151. A. I. Lvovsky and J. Mlynek, “Quantum-optical catalysis: generating nonclassical states of light by means of linear optics,” Phys. Rev. Lett., 88, 250401 (2002).

    Google Scholar 

  152. O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hansch, and I. Bloch, “Coherent transport of neutral atoms in spin-dependent optical lattice potentials,” Phys. Rev. Lett., 91, 010407 (2003).

    Google Scholar 

  153. F. DellAnno, S. De Siena, and F. Illuminati, “Multiphoton quantum optics and quantum state engineering,” Phys. Rep., 428, 53–168 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  154. M. Brune, S. Haroche, J. M. Raimond, L. Davidovich, and N. Zagury, “Manipulation of photons in a cavity by dispersive atom-field coupling. Quantum-nondemolition measurements and generation of ’schrödinger cat’ states,” Phys. Rev. A, 45, 5193–5214 (1992).

    Article  ADS  Google Scholar 

  155. S. Haroche, “Mesoscopic coherences in cavity QED,” Nuovo Cimento B, 110, 545–556 (1995).

    Article  ADS  Google Scholar 

  156. J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys., 73, 565–582 (2001).

    Article  ADS  MathSciNet  Google Scholar 

  157. A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, “Generation of optical ’schrodinger cats’ from photon number states,” Nature, 448, 784–786 (2007).

    Article  ADS  Google Scholar 

  158. R. L. de Matos Filho and W. Vogel, “Even and odd coherent states of the motion of a trapped ion,” Phys. Rev. Lett., 76, 608–611 (1996).

    Article  ADS  Google Scholar 

  159. D. M. Meekhof, C. Monroe, B. E. King, W. M. Itano, and D. J. Wineland, “Generation of nonclassical motional states of a trapped atom,” Phys. Rev. Lett., 76, 1796–1799 (1996).

    Article  ADS  Google Scholar 

  160. J. I. Cirac, A. S. Parkins, R. Blatt, and P. Zoller, “Nonclassical states of motion in ion traps,” Adv. At. Mol. Opt. Phys., 37 237–296 (1996).

    Google Scholar 

  161. D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” J. Res. Nat. Inst. Stand. Technol., 103, 259–328 (1998).

    Google Scholar 

  162. P. Adam, J. Janszky, and A. V. Vinogradov, “Amplitude squeezed and number-phase intelligent states via coherent states superposition,” Phys. Lett. A, 160, 506–510 (1991).

    Article  ADS  Google Scholar 

  163. A. Ben-Kish, B. DeMarco, V. Meyer V, et al., “Experimental demonstration of a technique to generate arbitrary quantum superposition states of a harmonically bound spin-1/2 particle,” Phys. Rev. Lett., 90, 037902 (2003).

  164. M. D. Reid and L. Krippner, “Macroscopic quantum superposition states in nondegenerate parametric oscillation,” Phys. Rev. A, 47, 552–555 (1993).

    Article  ADS  Google Scholar 

  165. V. Bužek and P. L. Knight, “Quantum interference, superposition states of light, and nonclassical effects,” in: E. Wolf, (ed.), Progress in Optics, North Holland, Amsterdam (1995), Vol. XXXIV, pp. 1–158.

    Google Scholar 

  166. C. C. Gerry, “Generation of four-photon coherent states in dispersive cavity QED,” Phys. Rev. A, 53, 3818–3821 (1996).

    Article  ADS  Google Scholar 

  167. G. S. Agarwal, R. R. Puri, and R. P. Singh, “Atomic Schrödinger cat states,” Phys. Rev. A, 56, 2249–2254 (1997).

    Article  ADS  Google Scholar 

  168. C. C. Gerry and R. Grobe, “Generation and properties of collective atomic Schrödinger-cat states,” Phys. Rev. A, 56, 2390–2396 (1997).

    Article  ADS  Google Scholar 

  169. A. Delgado, A. B. Klimov, J. C. Retamal, and C. Saavedra, “Macroscopic field superpositions from collective interactions,” Phys. Rev. A, 58, 655–662 (1998).

    Article  ADS  Google Scholar 

  170. A. Vidiella-Barranco and J. A. Roversi, “Quantum state engineering via unitary transformations,” Phys. Rev. A, 58, 3349–3352 (1998).

    Article  ADS  Google Scholar 

  171. H. Moya-Cessa, S. Wallentowitz, and W. Vogel, “Quantum-state engineering of a trapped ion by coherent-state superpositions,” Phys. Rev. A, 59, 2920–2925 (1999).

    Article  ADS  Google Scholar 

  172. S. Massar and E. S. Polzik, “Generating a superposition of spin states in an atomic ensemble,” Phys. Rev. Lett., 91, 060401 (2003).

    Google Scholar 

  173. M. G. A. Paris, M. Cola, and R. Bonifacio, “Quantum-state engineering assisted by entanglement,” Phys. Rev. A, 67, 042104 (2003).

    Google Scholar 

  174. M. Paternostro, M. S. Kim, and B. S. Ham, “Perspectives for quantum state engineering via high nonlinearity in a double-EIT regime,” J. Mod. Opt., 50, 2565–2582 (2003).

    ADS  Google Scholar 

  175. L. P. A. Maia, B. Baseia, A. T. Avelar, J. M. C. Malbouisson, “Sculpturing coherent states to get highly excited Fock states for stationary and travelling fields,” J. Opt. B: Quantum Semiclass. Opt., 6, 351–359 (2004).

    Article  ADS  Google Scholar 

  176. A. T. Avelar, L. A. de Souza, T. M. da Rocha Filho, and B. Baseia, “Generation of superposed phase states via Raman interaction,” J. Opt. B: Quantum Semiclass. Opt., 6, 383–386 (2004).

    Article  ADS  Google Scholar 

  177. K. T. Kapale and J. P. Dowling, “Vortex phase qubit: Generating arbitrary, counterrotating, coherent superpositions in Bose-Einstein condensates via optical angular momentum beams,” Phys. Rev. Lett., 95, 173601 (2005).

    Google Scholar 

  178. M. Takeoka and M. Sasaki, “Conditional generation of an arbitrary superposition of coherent states,” Phys. Rev. A, 75, 064302 (2007).

    Google Scholar 

  179. S.B. Zheng, “Generation of strongly squeezed states for a cavity field with a single atom,” Opt. Commun., 273, 460–463 (2007).

    Article  ADS  Google Scholar 

  180. V. Bužek, A. Vidiella-Barranco, and P. L. Knight, “Superpositions of coherent states: Squeezing and dissipation,” Phys. Rev. A, 45, 6570–6585 (1992).

    Article  ADS  Google Scholar 

  181. S. L. Braunstein, “Damping of quantum superpositions,” Phys. Rev. A, 45, 6803–6810 (1992).

    Article  ADS  Google Scholar 

  182. M. S. Kim and V. Bužek, “Schrödinger-cat states at finite temperature: Influence of a finite temperature heat bath on quantum interferences,” Phys. Rev. A, 46, 4239–4251 (1992).

    Article  ADS  Google Scholar 

  183. M. R. Gallis, “Emergence of classicality via decoherence described by Lindblad operators,” Phys. Rev. A, 53, 655–660 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  184. H. Saito and H. Hyuga, “Relaxation of Schrödinger cat states and displaced thermal states in a density operator representation,” J. Phys. Soc. Jpn, 65, 1648–1654 (1996).

    Article  ADS  Google Scholar 

  185. M. G. Benedict and A. Czirjak, “Wigner functions, squeezing properties, and slow decoherence of a mesoscopic superposition of two-level atoms,” Phys. Rev. A, 60, 4034–4044 (1999).

    Article  ADS  Google Scholar 

  186. V. V. Dodonov, S. S. Mizrahi, and A. L. de Souza Silva, “Decoherence and thermalization dynamics of a quantum oscillator,” J. Opt. B: Quantum Semiclass. Opt., 2, 271–281 (2000).

    Article  ADS  Google Scholar 

  187. P. Marian and T. A. Marian, “Environment-induced nonclassical behaviour,” Eur. Phys. J. D, 11, 257–265 (2000).

    Article  ADS  Google Scholar 

  188. T. Hiroshima, “Decoherence and entanglement in two-mode squeezed vacuum states,” Phys. Rev. A, 63, 022305 (2001).

    Google Scholar 

  189. W. T. Strunz, F. Haake, and D. Braun, “Universality of decoherence for macroscopic quantum superpositions,” Phys. Rev. A, 67, 022101 (2003).

    Google Scholar 

  190. W. H. Zurek, “Decoherence, einselection, and the quantum origins of the classical,” Rev. Mod. Phys., 75, 715–775 (2003).

    Article  ADS  MathSciNet  Google Scholar 

  191. S. Banerjee, “Decoherence and dissipation of an open quantum system with a squeezed and frequency-modulated heat bath,” Physica A, 337, 67–80 (2004).

    Article  ADS  Google Scholar 

  192. M. Hein, W. Dr, and H.-J. Briegel, “Entanglement properties of multipartite entangled states under the influence of decoherence,” Phys. Rev. A, 71, 032350 (2005).

    Google Scholar 

  193. A. Serafini, M. G. A. Paris, F. Illuminati, and S. De Siena, “Quantifying decoherence in continuous variable systems,” J. Opt. B: Quantum Semiclass. Opt., 7, R19–R36 (2005).

    Article  ADS  Google Scholar 

  194. H. Moya-Cessa, “Decoherence in atom-field interactions: A treatment using superoperator techniques,” Phys. Rep., 432, 1–41 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  195. B. Bellomo, S. M. Barnett, and J. Jeffers, “Frictional quantum decoherence,” J. Phys. A: Math. Gen., 40, 9437–9453 (2007).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  196. L. Davidovich, M. Brune, J. M. Raimond, and S. Haroche, “Mesoscopic quantum coherences in cavity QED: Preparation and decoherence monitoring schemes,” Phys. Rev. A, 53, 1295–1309 (1996).

    Article  ADS  Google Scholar 

  197. Q. A. Turchette, C.J. Myatt, B.E. King, C.A. Sackett, D. Kielpinski, W. M. Itano, C. Monroe, and D. J. Wineland, “Decoherence and decay of motional quantum states of a trapped atom coupled to engineered reservoirs,” Phys. Rev. A, 62, 053807 (2000).

    Google Scholar 

  198. C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett., 70, 1895–1899 (1993).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  199. D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature, 390, 575–579 (1997).

    Article  ADS  Google Scholar 

  200. S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett., 80, 869–872 (1998).

    Article  ADS  Google Scholar 

  201. A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “ Unconditional quantum teleportation,” Science, 282, 706–709 (1998).

    Article  ADS  Google Scholar 

  202. T. C. Ralph and P. K. Lam, “Teleportation with bright squeezed light,” Phys. Rev. Lett., 81, 5668–5671 (1998).

    Article  ADS  Google Scholar 

  203. G. J. Milburn and S. L. Braunstein, “Quantum teleportation with squeezed vacuum states,” Phys. Rev. A, 60, 937–942 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  204. W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A, 67, 032302 (2003).

    Google Scholar 

  205. T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, “Quantum teleportation of light beams,” Phys. Rev. A, 67, 033802 (2003).

    Google Scholar 

  206. N. Takei, T. Aoki, S. Koike, et al., “Experimental demonstration of quantum teleportation of a squeezed state,” Phys. Rev. A, 72, 042304 (2005).

    Google Scholar 

  207. H. Yonezawa, S. L. Braunstein, and A. Furusawa, “Experimental demonstration of quantum teleportation of broadband squeezing,” Phys. Rev. Lett., 99, 110503 (2007).

    Google Scholar 

  208. V. Vedral and M. B. Plenio, “Basics of quantum computation,” Prog. Quantum Electron., 22, 1–39 (1998).

    Article  ADS  Google Scholar 

  209. H. E. Brandt, “Qubit devices and the issue of quantum decoherence,” Prog. Quantum Electron., 22, 257–370 (1998).

    Article  ADS  Google Scholar 

  210. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge Univ. Press, Cambridge, UK (2000).

    MATH  Google Scholar 

  211. M. Keyl, “Fundamentals of quantum information theory,” Phys. Rep., 369, 431–548 (2002).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  212. S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys., 77, 513–577 (2005).

    Article  ADS  Google Scholar 

  213. A. S. Holevo, M. Sohma, and O. Hirota, “Capacity of quantum Gaussian channels,” Phys. Rev. A, 59, 1820 (1999).

    Article  ADS  Google Scholar 

  214. A. S. Holevo and R. F. Werner, “Evaluating capacities of bosonic Gaussian channels,” Phys. Rev. A, 63, 03231 (2001).

    Google Scholar 

  215. F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature, 421, 238–241 (2003).

    Article  ADS  Google Scholar 

  216. X.-B. Wang, T. Hiroshima, A. Tomita, and M. Hayashi, “Quantum information with Gaussian states,” Phys. Rep., 448, 1–111 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  217. J. DiGuglielmo, B. Hage, A. Franzen, J. Fiurek, and R. Schnabel, “Experimental characterization of Gaussian quantum-communication channels,” Phys. Rev. A, 76, 012323 (2007).

    Google Scholar 

  218. B. C. Sanders, “Entangled coherent states,” Phys. Rev. A, 45, 6811–6815 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  219. C. L. Chai, “Two-mode nonclassical state via superpositions of two-mode coherent states,” Phys. Rev. A, 46, 7187–7191 (1992).

    Article  ADS  Google Scholar 

  220. N.A. Ansari and V. I. Man’ko, “Photon statistics of multimode even and odd coherent light,” Phys. Rev. A, 50, 1942–1945 (1994).

    Article  ADS  Google Scholar 

  221. V. V. Dodonov, V. I. Man’ko, and D. E. Nikonov, “Even and odd coherent states for multimode parametric systems,” Phys. Rev. A, 51, 3328–3336 (1995).

    Article  ADS  Google Scholar 

  222. C. C. Gerry, “Generation of Schrödinger cats and entangled coherent states in the motion of a trapped ion by a dispersive interaction,” Phys. Rev. A, 55, 2478–2481 (1997).

    Article  ADS  Google Scholar 

  223. F. De Martini, M. Fortunato, P. Tombesi, and D. Vitali, “Generating entangled superpositions of macroscopically distinguishable states within a parametric oscillator,” Phys. Rev. A, 60, 1636–1651 (1999).

    Article  ADS  Google Scholar 

  224. J. Recamier, O. Castaños, R. Jáuregui, and A. Frank, “Entanglement and generation of superpositions of atomic coherent states,” Phys. Rev. A, 61, 063808 (2000).

    Google Scholar 

  225. M. Massini, M. Fortunato, S. Mancini, and P. Tombesi, “Synthesis and characterization of entangled mesoscopic superpositions for a trapped electron,” Phys. Rev. A, 62, 041401 (2000).

    Google Scholar 

  226. H. Fu, X. Wang, and A. I. Solomon, “Maximal entanglement of nonorthogonal states: classification,” Phys. Lett. A, 291, 73–76 (2001).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  227. S. J. van Enk and O. and Hirota, “Entangled coherent states: Teleportation and decoherence,” Phys. Rev. A, 64, 022313 (2001).

    Google Scholar 

  228. A. Luis, “Equivalence between macroscopic quantum superpositions and maximally entangled states: Application to phase-shift detection,” Phys. Rev. A, 64, 054102 (2001).

    Google Scholar 

  229. X. G. Wang and B. C. Sanders, “Multipartite entangled coherent states,” Phys. Rev. A, 65, 012303 (2002).

    Google Scholar 

  230. M. Paternostro, M. S. Kim, and B. S. Ham, “Generation of entangled coherent states via crossphase-modulation in a double electromagnetically induced transparency regime,” Phys. Rev. A, 67, 023811 (2003).

    Google Scholar 

  231. S. J. van Enk, “Entanglement capabilities in infinite dimensions: Multidimensional entangled coherent states,” Phys. Rev. Lett., 91, 017902 (2003).

    Google Scholar 

  232. L. M. Kuang and L. Zhou, “Generation of atom-photon entangled states in atomic Bose-Einstein condensate via electromagnetically induced transparency,” Phys. Rev. A, 68, 043606 (2003).

    Google Scholar 

  233. Y. W. Cheong, H. Kim, and H.-W. Lee, “Near-complete teleportation of a superposed coherent state,” Phys. Rev. A, 70, 032327 (2004).

    Google Scholar 

  234. H. Prakash, N. Chandra, R. Prakash, and Shivani, “Improving the teleportation of entangled coherent states,” Phys. Rev. A, 75, 044305 (2007).

  235. R. L. de Matos Filho and W. Vogel, “Nonlinear coherent states,” Phys. Rev. A, 54, 4560–4563 (1996).

    Article  ADS  Google Scholar 

  236. V. I. Man’ko, G. Marmo, E. C. G. Sudarshan, and F. Zaccaria, “f-oscillators and nonlinear coherent states,” Phys. Scripta, 55, 528–541 (1997).

    Article  ADS  Google Scholar 

  237. S. Mancini, “Even and odd nonlinear coherent states,” Phys. Lett. A, 233, 291–296 (1997).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  238. V. Manko, G. Marmo, A. Porzio, S. Solimeno, and F. Zaccaria, “Trapped ions in laser fields: A benchmark for deformed quantum oscillators,” Phys. Rev. A, 62, 053407 (2000).

    Google Scholar 

  239. S. Sivakumar, “Studies on nonlinear coherent states,” J. Opt. B: Quantum Semiclass. Opt., 2, R61–R75 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  240. Z. Kis, W. Vogel, and L. Davidovich, “Nonlinear coherent states of trapped-atom motion,” Phys. Rev. A, 64, 033401 (2001).

    Google Scholar 

  241. L. C. Kwek and D. Kiang, “Nonlinear squeezed states,” J. Opt. B: Quantum Semiclass. Opt., 5, 383–386 (2003).

    Article  ADS  Google Scholar 

  242. M. K. Tavassoly and A. Parsaiean, “Quantum statistical properties of some new classes of intelligent states associated with special quantum systems,” J. Phys. A: Math. Gen., 40, 9905–9917 (2007).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  243. E. C. Lerner, H. W. Huang, and G. E. Walters, “Some mathematical properties of oscillator phase operator,” J. Math. Phys., 11, 1679–1684 (1970).

    Article  ADS  MathSciNet  Google Scholar 

  244. E. K. Ifantis, “States minimizing the uncertainty product of the oscillator phase operator,” J. Math. Phys., 13, 568–575 (1972).

    Article  ADS  MathSciNet  Google Scholar 

  245. Y. Aharonov, E. C. Lerner, H. W. Huang, and J. M. Knight, “Oscillator phase states, thermal equilibrium and group representations,” J. Math. Phys., 14, 746–756 (1973).

    Article  ADS  MathSciNet  Google Scholar 

  246. G. Brodimas, A. Jannussis, D. Sourlas, V. Zisis, and P. Poulopoulos, “Para-Bose operators,” Lett. Nuovo Cimento, 31, 177–182 (1981).

    MathSciNet  Google Scholar 

  247. G. S. Agarwal and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A, 43, 492–497 (1991).

    Article  ADS  Google Scholar 

  248. Z. Zhang and H. Fan, “Properties of states generated by excitations on a squeezed vacuum state,” Phys. Lett. A, 165, 14–18 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  249. Z. Kis, P. Adam, and J. Janszky, “Properties of states generated by excitations on the amplitude squeezed states,” Phys. Lett. A, 188, 16–20 (1994).

    Article  ADS  Google Scholar 

  250. Z. Z. Xin, Y. B. Duan, H.M. Zhang, W.J. Qian, M. Hirayama, and K. I. Matumoto, “Excited even and odd coherent states of the radiation field,” J. Phys. B: At. Mol. Opt. Phys., 29, 2597–2606 (1996).

    Article  ADS  Google Scholar 

  251. V. V. Dodonov, Y. A. Korennoy, V. I. Man’ko, and Y. A. Moukhin, “Nonclassical properties of states generated by the excitation of even/odd coherent states of light,” Quant. Semiclass. Opt., 8, 413–427 (1996).

    Article  ADS  Google Scholar 

  252. V. I. Man’ko and A. Wünsche, “Properties of squeezed-state excitations,” Quantum Semiclass. Opt., 9, 381–409 (1997).

    Article  ADS  Google Scholar 

  253. M. Dakna, L. Knöll, and D.-G. Welsch, “Photon-added state preparation via conditional measurement on a beam splitter,” Opt. Commun., 145, 309–321 (1998).

    Article  ADS  Google Scholar 

  254. H. Moya-Cessa, S. Chavez-Cerda, and W. Vogel, “Adding and subtracting energy quanta of the harmonic oscillator,” J. Mod. Opt., 46, 1641–1656 (1999).

    MATH  ADS  MathSciNet  Google Scholar 

  255. J. M. Sixdeniers and K. A. Penson, “On the completeness of photon-added coherent states,” J. Phys. A: Math. Gen., 34, 2859–2866 (2001).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  256. S. S. Mizrahi and V. V. Dodonov, “Creating quanta with an ‘annihilation’ operator,” J. Phys. A: Math. Gen., 35, 8847–8857 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  257. A. Zavatta, S. Viciani, and M. Bellini, “Quanturn-to-classical transition with single-photon-added coherent states of light,” Science, 306, 660–662 (2004).

    Article  ADS  Google Scholar 

  258. A. Biswas and G. S. Agarwal, “Nonclassicality and decoherence of photon-subtracted squeezed states,” Phys. Rev. A, 75, 032104 (2007).

    Google Scholar 

  259. 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).

    Google Scholar 

  260. A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and P. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett., 98, 030502 (2007).

    Google Scholar 

  261. E. E. Hach III and C. C. Gerry, “Four photon coherent states. Properties and generation,” J. Mod. Opt., 39, 2501–2517 (1992).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  262. M. Paprzycka and R. Tanaś, “Discrete superpositions of coherent states and phase properties of the m-photon anharmonic oscillator,” Quantum Opt., 4, 331–342 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  263. I. Jex and V. Bužek, “Multiphoton coherent states and the linear superposition principle,” J. Mod. Opt., 40, 771–783 (1993).

    Article  MATH  ADS  Google Scholar 

  264. J. Janszky, P. Domokos, and P. Adam, “Coherent states on a circle and quantum interference,” Phys. Rev. A, 48, 2213–2219 (1993).

    Article  ADS  Google Scholar 

  265. P. Shanta, S. Chaturvedi, V. Srinivasan, G. S. Agarwal, and C. L. Mehta, “Unified approach to multiphoton coherent states,” Phys. Rev. Lett., 72, 1447–1450 (1994).

    Article  ADS  Google Scholar 

  266. M. M. Nieto and D. R. Truax, “Holstein-Primakoff/Bogoliubov transformations and the multiboson system,” Fortschr. Phys., 45, 145–156 (1997).

    Article  MATH  MathSciNet  Google Scholar 

  267. J. Janszky, Z. Kis, and P. Adam, “Star states,” Fortschr. Phys., 46, 829–835 (1998).

    Article  MathSciNet  Google Scholar 

  268. S. Chountasis and A. Vourdas, “Weyl functions and their use in the study of quantum interference,” Phys. Rev. A, 58, 848–855 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  269. M. M. Nieto and D. R. Truax, “Higher-power coherent and squeezed states,” Opt. Commun., 179, 197–213 (2000).

    Article  ADS  Google Scholar 

  270. W. D. José and S. S. Mizrahi, “Generation of circular states and Fock states in a trapped ion,” J. Opt. B: Quantum Semiclass. Opt., 2, 306–314 (2000).

    Article  ADS  Google Scholar 

  271. C. Quesne, “Spectrum generating algebra of the C λ-extended oscillator and multiphoton coherent states,” Phys. Lett. A, 272, 313–325 (2000).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  272. Z. Bialynicka-Birula, “Properties of the generalized coherent state,” Phys. Rev., 173, 1207–1209 (1968).

    Article  ADS  Google Scholar 

  273. D. Stoler, “Generalized coherent states,” Phys. Rev. D, 4, 2309–2312 (1971).

    Article  ADS  Google Scholar 

  274. O. Castaños, R. López-Peña, and V. I. Man’ko, “Crystallized Schrödinger cat states,” J. Russ. Laser Res., 16, 477–525 (1995).

    Article  Google Scholar 

  275. V. Spiridonov, “Universal superpositions of coherent states and self-similar potentials,” Phys. Rev. A, 52, 1909–1935 (1995).

    Article  ADS  Google Scholar 

  276. C. Brif, “Two-photon algebra eigenstates. A unified approach to squeezing,” Ann. Phys. (New York), 251, 180–207 (1996).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  277. C. Brif, A. Mann, and A. Vourdas, “Parity-dependent squeezing of light,” J. Phys. A: Math. Gen., 29, 2053–2067 (1996).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  278. C. Quesne, “Generalized coherent states associated with the C λ-extended oscillator,” Ann. Phys. (New York), 293, 147–188 (2001).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  279. V. V. Dodonov, “Nonclassical states in quantum optics: a ’squeezed’ review of the first 75 years,” J. Opt. B: Quantum Semiclass. Opt., 4, R1–R33 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  280. V. V. Dodonov and V. I. Man’ko, “Nonclassical states in quantum physics: brief historical review,” in: V. V. Dodonov and V. I. Man’ko (eds.), Theory of Nonclassical States of Light, Taylor & Francis, London (2003), pp. 1–94.

    Google Scholar 

  281. K. Vogel and H. Risken, “Determinantion of quasiprobability distribution in terms of probability distributions for the rotated quadrature phase,” Phys. Rev. A, 40, 2847–2849 (1989).

    Article  ADS  Google Scholar 

  282. U. Leonhardt and H. Paul, “Measuring the quantum state of light,” Prog. Quantum Electron., 19, 89–130 (1995).

    Article  ADS  Google Scholar 

  283. V. Bužek, G. Adam, and G. Drobný, “Reconstruction of Wigner functions on different observation levels,” Ann. Phys. (New York), 245, 37–97 (1996).

    Article  ADS  MATH  Google Scholar 

  284. S. Mancini, V. I. Man’ko, and P. Tombesi, “Symplectic tomography as classical approach to quantum systems,” Phys. Lett. A, 213, 1–6 (1996).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  285. A. Wünsche, “Radon transform and pattern functions in quantum tomography,” J. Mod. Opt., 44, 2293–2331 (1997).

    Article  MATH  ADS  Google Scholar 

  286. V. Bužek, R. Derka, G. Adam, and P. L. Knight, “Reconstruction of quantum states of spin systems: From quantum Bayesian inference to quantum tomography,” Ann. Phys. (New York), 266, 454–496 (1998).

    Article  ADS  MATH  Google Scholar 

  287. D.-G. Welsch, W. Vogel, and T. Opatrný, “Homodyne detection and quantum state reconstruction,” in: E. Wolf (ed.), Progress in Optics, North Holland, Amsterdam (1999), Vol. XXXIX, pp. 63–211.

    Google Scholar 

  288. C. Brif and A. Mann, “Phase-space formulation of quantum mechanics and quantum-state reconstruction for physical systems with Lie-group symmetries,” Phys. Rev. A, 59, 971–987 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  289. V. Bužek, G. Drobný, R. Derka, G. Adam, and H. Wiedemann, “Quantum state reconstruction from incomplete data,” Chaos Solitons Fract., 10, 981–1074 (1999).

    Article  MATH  Google Scholar 

  290. A. B. Klimov, O. V. Man’ko, V. I. Man’ko, Y. F. Smirnov, and V. N. Tolstoy, “Tomographic representation of spin and quark states,” J. Phys. A: Math. Gen., 35, 6101–6123 (2002).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  291. G. M. D’Ariano, M. G. A. Paris, and M. F. Sacchi, “Quantum tomography,” Adv. Imag. Elect. Phys., 128, 205–308 (2003).

    Google Scholar 

  292. M. Baron, H. Rauch, and M. Suda, “First attempt of neutron quantum state reconstruction,” J. Opt. B: Quantum Semiclass. Opt., 5, S241–S244 (2003).

    Article  ADS  Google Scholar 

  293. Y. I. Bogdanov, E. V. Moreva, G. A. Maslennikov, R. F. Galeev, S. S. Straupe, and S. P. Kulik, “ Polarization states of four-dimensional systems based on biphotons,” Phys. Rev. A, 73, 063810 (2006).

    Google Scholar 

  294. J. V. Corbett, “The Pauli problem, state reconstruction and quantum-real numbers,” Rep. Math. Phys., 57, 53–68 (2006).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  295. P. Kumar, “Quantum frequency conversion,” Opt. Lett., 15, 1476–1478 (1990).

    ADS  Google Scholar 

  296. V. Peřinová, A. Lukš, J. Křepelka, C. Sibilia, and M. Bertolotti, “ Quantum statistics of light in a lossless linear coupler,” J. Mod. Opt., 38, 2429–2457 (1991).

    Article  ADS  MATH  Google Scholar 

  297. J. Huang and P. Kumar, “Observation of quantum frequency conversion,” Phys. Rev. Lett., 68, 2153–2156 (1992).

    Article  ADS  Google Scholar 

  298. C. A. Bonato and B. Baseia, “Transference of squeezing in coupled oscillators,” Int. J. Theor. Phys., 33, 1445–1460 (1994).

    Article  MATH  Google Scholar 

  299. J. Peiina and J. Pefina Jr., “Quantum statistics of a nonlinear asymmetric coupler with strong pumping,” Quantum Semiclass. Opt., 7, 541–552 (1995).

    Article  ADS  Google Scholar 

  300. J. Fu, X. C. Gao, J. B. Xu, and X. B. Zou, “Exchange of nonclassical properties between two interacting modes of light and mutual conversion of the Fock and coherent states,” Can. J. Phys., 77, 211–220 (1999).

    Article  ADS  Google Scholar 

  301. A. S. Parkins and H. J. Kimble, “Quantum state transfer between motion and light, J. Opt. B: Quantum Semiclass. Opt., 1, 496–504 (1999).

    Article  ADS  Google Scholar 

  302. M. C. de Oliveira, S. S. Mizrahi, and V. V. Dodonov, “Information transfer in the course of a quantum interaction,” J. Opt. B: Quantum Semiclass. Opt., 1 610–617 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  303. J. Lee, M. S. Kim, and H. Jeong, “Transfer of nonclassical features in quantum teleportation via a mixed quantum channel,” Phys. Rev. A, 62, 032305 (2000).

    Google Scholar 

  304. A. S. M. de Castro, V. V. Dodonov, and S. S. Mizrahi, “Quantum state exchange between coupled modes,” J. Opt. B: Quantum Semiclass. Opt., 4, S191–S199 (2002).

    Article  Google Scholar 

  305. S. Mancini, D. Vitali, and P. Tombesi, “Scheme for teleportation of quantum states onto a mechanical resonator,” Phys. Rev. Lett., 90, 137901 (2003).

    Google Scholar 

  306. J. Zhang, K. Peng, and S. L. Braunstein, “Quantum-state transfer from light to macroscopic oscillators,” Phys. Rev. A, 68, 013808 (2003).

    Google Scholar 

  307. M. D. Lukin, “Colloquium: Trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys., 75, 457–472 (2003).

    Article  ADS  Google Scholar 

  308. M. Christandl, N. Datta, A. Ekert, and A. J. Landahl, “Perfect state transfer in quantum spin networks,” Phys. Rev. Lett., 92, 187902 (2004).

    Google Scholar 

  309. J. Eisert, M. B. Plenio, S. Bose, and J. Hartley, “Towards quantum entanglement in nanoelectromechanical devices,” Phys. Rev. Lett., 93, 190402 (2004).

    Google Scholar 

  310. A. Dantan and M. Pinard, “Quantum-state transfer between fields and atoms in electromagnetically induced transparency,” Phys. Rev. A, 69, 043810 (2004).

    Google Scholar 

  311. D. N. Matsukevich and A. Kuzmich, “Quantum state transfer between matter and light,” Science, 306, 663–666 (2004).

    Article  ADS  Google Scholar 

  312. A. S. M. de Castro and V. V. Dodonov, “Purity and squeezing exchange between coupled bosonic modes,” Phys. Rev. A, 73, 065801 (2006).

    Google Scholar 

  313. S. Bose, “Quantum communication through spin chain dynamics: an introductory overview,” Contemp. Phys., 48, 13–30 (2007).

    Article  ADS  Google Scholar 

  314. Y. S. Kim and V. I. Man’ko, “Time-dependent mode coupling and generation of two-mode squeezed states,” Phys. Lett. A, 157, 226–228 (1991).

    Article  ADS  Google Scholar 

  315. H. Y. Fan, “Squeezing in the triatomic linear molecule model revealed by virtue of the IWOP technique,” J. Phys. A: Math. Gen., 26, 151–158 (1993).

    Article  Google Scholar 

  316. M. S. Abdalla, “Statistical properties of the time evolution operator for two coupled oscillators,” J. Mod. Opt., 40, 1369–1385 (1993).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  317. V. V. Dodonov, O. V. Man’ko, and V. I. Man’ko, “Quantum nonstationary oscillator: models and applications,” J. Russ. Laser Res., 16, 1–56 (1995).

    Article  Google Scholar 

  318. M. S. Abdalla, “Quantum treatment of the time-dependent coupled oscillators,” J. Phys. A: Math. Gen., 29, 1997–2012 (1996).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  319. J. M. Cerveró and J. D. Lejarreta, “Generalized two-mode harmonic oscillator: SO(3, 2) dynamical group and squeezed states,” J. Phys. A: Math. Gen., 29, 7545–7560 (1996).

    Article  ADS  Google Scholar 

  320. A. V. Dodonov and V. V. Dodonov, “Nonstationary Casimir effect in cavities with two resonantly coupled modes,” Phys. Lett. A, 289, 291–300 (2001).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  321. A. K. Rajagopal and R. W. Rendell, “Decoherence, correlation, and entanglement in a pair of coupled quantum dissipative oscillators,” Phys. Rev. A, 63, 022116 (2001).

    Google Scholar 

  322. Y. S. Kim and M. E. Noz, “Coupled oscillators, entangled oscillators, and Lorentz-covariant harmonic oscillators,” J. Opt. B: Quantum Semiclass. Opt., 7, S458–S467 (2005).

    Article  ADS  Google Scholar 

  323. K. Audenaert, J. Eisert, M. B. Plenio, and R. F. Werner, “Entanglement properties of the harmonic chain,” Phys. Rev. A, 66, 042327 (2002).

    Google Scholar 

  324. M. B. Plenio, J. Hartley, and J. Eisert, “Dynamics and manipulation of entanglement in coupled harmonic systems with many degrees of freedom,” New J. Phys., 6, 36 (2004).

    Article  ADS  Google Scholar 

  325. M. B. Plenio and F. L. Semião, “High efficiency transfer of quantum information and multiparticle entanglement generation in translation-invariant quantum chains,” New J. Phys., 7, 73 (2005).

    Article  ADS  Google Scholar 

  326. V. V. Dodonov, “Parametric excitation and generation of nonclassical states in linear media,” in: V. V. Dodonov and V. I. Man’ko (eds.), Theory of Nonclassical States of Light, Taylor & Francis, London (2003), pp. 153–218.

    Google Scholar 

  327. A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory, North-Holland, Amsterdam (1982).

    MATH  Google Scholar 

  328. B. L. Schumaker, “Quantum-mechanical pure states with Gaussian wave-functions,” Phys. Rep., 135, 317–408 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  329. R. G. Littlejohn, “The semiclassical evolution of wave packets,” Phys. Rep., 138, 193–291 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  330. G. S. Agarwal, “Wigner-function description of quantum noise in interferometers,” J. Mod. Opt., 34, 909–921 (1987).

    Article  MATH  ADS  Google Scholar 

  331. V. V. Dodonov and V. I. Man’ko, “Evolution of multidimensional systems. Magnetic properties of ideal gases of charged particles,” in: M. A. Markov (ed.), Invariants and the Evolution of Nonstationary Quantum Systems, Proceedings of the P. N. Lebedev Physical Institute, Nova Science, Commack, New York (1989), Vol. 183, pp. 263–414.

    Google Scholar 

  332. L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett., 84, 2722–2725 (2000).

    Article  ADS  Google Scholar 

  333. R. Simon, “Peres-Horodecki separability criterion for continuous variable systems,” Phys. Rev. Lett., 84, 2726–2729 (2000).

    Article  ADS  Google Scholar 

  334. R. F. Werner and M. M. Wolf, “Bound entangled Gaussian states,” Phys. Rev. Lett., 86, 3658–3661 (2001).

    Article  ADS  Google Scholar 

  335. P. Marian, T. A. Marian, and H. Scutaru, “Inseparability of mixed two-mode Gaussian states generated with a SU(1, 1) interferometer,” J. Phys. A: Math. Gen., 34, 6969–6980 (2001).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  336. G. Giedke, B. Kraus, M. Lewenstein, and J. I. Cirac, “Entanglement criteria for all bipartite Gaussian states,” Phys. Rev. Lett., 87, 167904 (2001).

    Google Scholar 

  337. S. Scheel and D.-G. Welsch, “Entanglement generation and degradation by passive optical devices,” Phys. Rev. A, 64, 063811 (2001).

    Google Scholar 

  338. M. S. Kim, W. Son, V. Bužek, and P. L. Knight, “Entanglement by a beam splitter: Nonclassicality as a prerequisite for entanglement,” Phys. Rev. A, 65, 032323 (2002).

    Google Scholar 

  339. B.-G. Englert and K. Wódkiewicz, “Separability of two-party Gaussian states,” Phys. Rev. A, 65, 054303 (2002).

    Google Scholar 

  340. G. Giedke, M. M. Wolf, O. Krüger, R. F. Werner, and J. I. Cirac, “Entanglement of formation for symmetric Gaussian states,” Phys. Rev. Lett., 91, 107901 (2003).

    Google Scholar 

  341. G. iedke, J. Eisert, J. I. Cirac, and M. B. Plenio, “Entanglement transformations of pure Gaussian states,” Quantum Inform. Comput., 3, 211–223 (2003).

    Google Scholar 

  342. A. S. M. de Castro and V. V. Dodonov, “Covariance measures of intermode correlations and inseparability for continuous variable quantum systems,” J. Opt. B: Quantum Semiclass. Opt., 5, S593–S608 (2003).

    Article  Google Scholar 

  343. P. Marian, T. A. Marian, and H. Scutaru, “Bures distance as a measure of entanglement for two-mode squeezed thermal states,” Phys. Rev. A, 68, 062309 (2003).

    Google Scholar 

  344. A. Serafini, F. Illuminati, and S. De Siena, “Symplectic invariants, entropic measures and correlations of Gaussian states,” J. Phys. B: At. Mol. Opt. Phys., 37, L21–L28 (2004).

    Article  ADS  Google Scholar 

  345. A. V. Dodonov, V. V. Dodonov, and S. S. Mizrahi, “Separability dynamics of two-mode Gaussian states in parametric conversion and amplification,” J. Phys. A: Math. Gen., 38, 683–696 (2005).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  346. C. M. Caves, C. Zhu, G. J. Milburn, and W. Schleich, “Photon statistics of two-mode squeezed states and interference in four-dimensional phase space,” Phys. Rev. A, 43, 3854–3861 (1991).

    Article  ADS  Google Scholar 

  347. M. Artoni, U. P. Ortiz, and J. L. Birman, “Photocount distribution of two-mode squeezed states,” Phys. Rev. A, 43, 3954–3965 (1991).

    Article  ADS  Google Scholar 

  348. G. Schrade, V. M. Akulin, V. I. Man’ko, and W. Schleich, “Photon distribution for two-mode squeezed vacuum,” Phys. Rev. A, 48, 2398–2406 (1993).

    Article  ADS  Google Scholar 

  349. V. V. Dodonov, O. V. Man’ko, and V. I. Man’ko, “Photon distribution for one-mode mixed light with a generic Gaussian Wigner function,” Phys. Rev. A, 49, 2993–3001 (1994).

    Article  ADS  Google Scholar 

  350. M. Selvadoray, M. S. Kumar, and R. Simon, “Photon distribution in two-mode squeezed coherent states with complex displacement and squeeze parameters,” Phys. Rev. A, 49, 4957–4967 (1994).

    Article  ADS  Google Scholar 

  351. V. V. Dodonov, O. V. Man’ko, and V. I. Man’ko, “Multidimensional Hermite polynomials and photon distribution for polymode mixed light,” Phys. Rev. A, 50, 813–817 (1994).

    Article  ADS  Google Scholar 

  352. P. Marian and T. A. Marian, “Photon number and counting statistics for a field with Gaussian characteristic function,” Ann. Phys. (New York), 245, 98–112 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  353. S. Y. Kalmykov and M. E. Veisman, “Quantum-statistical properties of two coupled modes of electromagnetic field,” Phys. Rev. A, 57, 3943–3951 (1998).

    Article  ADS  Google Scholar 

  354. V. V. Dodonov and M. A. Andreata, “Squeezing and photon distribution in a vibrating cavity,” J. Phys. A: Math. Gen., 32, 6711–6726 (1999).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  355. Y. S. Kim and M. E. Noz, Phase Space Picture of Quantum Mechanics, World Scientific, Singapore (1991).

    Google Scholar 

  356. J. Katriel and A. I. Solomon, “Generalised q-bosons and their squeezed states,” J. Phys. A: Math. Gen., 24, 2093–2105 (1991).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  357. M. M. Nieto and D. R. Truax, “Squeezed states for general systems,” Phys. Rev. Lett., 71, 2843–2846 (1993).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  358. H. Huang and G. S. Agarwal, “General linear transformations and entangled states,” Phys. Rev. A, 49, 52–60 (1994).

    Article  ADS  Google Scholar 

  359. J. Twamley, “Bures and statistical distance for squeezed thermal states,” J. Phys. A: Math. Gen., 29, 3723–3731 (1996).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  360. A. Wünsche, “The complete Gaussian class of quasiprobabilities and its relation to squeezed states and their discrete excitations,” Quantum Semiclass. Opt., 8, 343–379 (1996).

    Article  ADS  Google Scholar 

  361. W. S. Liu and X. P. Li, “BCS states as squeezed fermion-pair states,” Europ. Phys. J. D, 2, 1–4 (1998).

    Article  MATH  ADS  Google Scholar 

  362. V. V. Dodonov, “Universal integrals of motion and universal invariants of quantum systems,” J. Phys. A: Math. Gen., 33, 7721–7738 (2000).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  363. A. Wünsche, “Symplectic groups in quantum optics,” J. Opt. B, 2, 73–80 (2000).

    ADS  Google Scholar 

  364. H. Y. Fan, “Operator ordering in quantum optics theory and the development of Dirac’s symbolic method,” J. Opt. B: Quantum Semiclass. Opt., 5, R147–R163 (2003).

    Article  ADS  Google Scholar 

  365. I. I. Hirschman, “A note on entropy,” Am. J. Math., 79, 152–156 (1957).

    Article  MATH  MathSciNet  Google Scholar 

  366. V. V. Dodonov and V. I. Man’ko, “Generalization of the uncertainty relations in quantum mechanics,” in: M. A. Markov (ed.), Invariants and the Evolution of Nonstationary Quantum Systems, Proceedings of the P. N. Lebedev Physical Institute, Nova Science, Commack, New York (1989), Vol. 183, pp. 3–101.

    Google Scholar 

  367. G. B. Folland and A. Sitaram, “The uncertainty principle: A mathematical survey,” J. Fourier Anal. Appl., 3, 207–238 (1997).

    Article  MATH  MathSciNet  Google Scholar 

  368. V. Majerník and L. Richterek, “Entropic uncertainty relations.” Eur. J. Phys., 18, 79–89 (1997).

    Article  Google Scholar 

  369. C. H. Keitel and K. Wdkiewicz, “On the information entropy of squeezed states and the entropic uncertainty relation,” Phys. Lett. A, 167, 151–160 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  370. J. Sánchez-Ruiz, “Improved bounds in the entropic uncertainty and certainty relations for complementary observables,” Phys. Lett. A, 201, 125–131 (1995).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  371. A. K. Rajagopal, “The Sobolev inequality and the Tsallis entropic uncertainty relation,” Phys. Lett. A, 205, 32–36 (1995).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  372. V. Majernik and T. Opatrný, “Entropic uncertainty relations for a quantum oscillator,” J. Phys. A: Math. Gen., 29, 2187–2197 (1996).

    Article  MATH  ADS  Google Scholar 

  373. E. C. G. Sudarshan, C. B. Chiu, and G. Bhamathi, “Generalized uncertainty relations and characteristic invariants for the multimode states,” Phys. Rev. A, 52, 43–54 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  374. N. V. Karelin and A. M. Lazaruk, “Uncertainty relation for multidimensional correlation functions,” Theor. Math. Phys., 117, 1447–1452 (1998).

    Article  MATH  Google Scholar 

  375. D. A. Trifonov, “State extended uncertainty relations,” J. Phys. A: Math. Gen., 33, L299–L304 (2000).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  376. D. A. Trifonov, “Generalized uncertainty relations and coherent and squeezed states,” J. Opt. Soc. Am. A, 17, 2486–2495 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  377. A. D. Sukhanov, “Schrödinger uncertainty relations and physical features of correlated coherent states,” Theor. Math. Phys., 132, 1277–1294 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  378. D. T. Smithey, M. Beck, J. Cooper, and M. G. Raymer, “Measurement of number-phase uncertainty relations of optical fields,” Phys. Rev. A, 48, 3159–3167 (1993).

    Article  ADS  Google Scholar 

  379. T. Opatrný, “Number-phase uncertainty relations,” J. Phys. A: Math. Gen., 28, 6961–6975 (1995).

    Article  MATH  ADS  Google Scholar 

  380. S. L. Braunstein, C. M. Caves, and G. J. Milburn, “Generalized uncertainty relations: Theory, examples, and Lorentz invariance,” Ann. Phys. (New York), 247, 135–173 (1996).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  381. E. Celeghini, M. Rasetti, and G. Vitiello, “Squeezing and quantum groups,” Phys. Rev. Lett., 66, 2056–2059 (1991).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  382. A. Kempf, “Uncertainty relation in quantum mechanics with quantum group symmetry,” J. Math. Phys., 35, 4483–4496 (1994).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  383. J.-Z. Zhang, “A q-deformed uncertainty relation,” Phys. Lett. A, 262, 125–130 (1999).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  384. A. Kempf, G. Mangano, and R. B. Mann, “Hilbert space representation of the minimal length uncertainty relation,” Phys. Rev. D, 52, 1108–1118 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  385. M. Li and T. Yoneya, “Pointlike D-brane dynamics and space-time uncertainty relation,” Phys. Rev. Lett., 78, 1219–1222 (1997).

    Article  ADS  Google Scholar 

  386. J. Y. Bang and M. S. Berger, “Quantum mechanics and the generalized uncertainty principle,” Phys. Rev. D, 74, 125012 (2006).

    Google Scholar 

  387. M. U. Karelin and A. M. Lazaruk, “Structure of the density matrix providing the minimum generalized uncertainty relation for mixed states,” J. Phys. A: Math. Gen., 33, 6807–6816 (2000).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  388. V. V. Dodonov, “Purity-and entropy-bounded uncertainty relations for mixed quantum states,” J. Opt. B: Quantum Semiclass. Opt., 4, S98–S108 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  389. U. Leonhardt, B. Böhmer, and H. Paul, “Uncertainty relations for realistic joint measurements of position and momentum in quantum optics,” Opt. Commun., 119, 296–300 (1995).

    Article  ADS  Google Scholar 

  390. M. Ozawa, “Conservation laws, uncertainty relations, and quantum limits of measurements,” Phys. Rev. Lett., 88, 050402 (2002).

    Google Scholar 

  391. M. Ozawa, “Uncertainty relations for noise and disturbance in generalized quantum measurements,” Ann. Phys. (New York), 311, 350–416 (2004).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  392. M. Ozawa, “Universal uncertainty principle in the measurement operator formalism,” J. Opt. B: Quantum Semiclass. Opt., 7, S672–S681 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  393. C. A. Fuchs and A. Peres, “Quantum-state disturbance versus information gain: Uncertainty relations for quantum information,” Phys. Rev. A, 53, 2038–2045 (1996).

    Article  ADS  Google Scholar 

  394. D. C. Brody and L. I. Hughston, “Generalized Heisenberg relations for quantum statistical estimation,” Phys. Lett. A, 236, 257–262 (1997).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  395. M. J. W. Hall, “Universal geometric approach to uncertainty, entropy, and information,” Phys. Rev. A, 59, 2602–2615 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  396. S. L. Luo, “Fisher information, kinetic energy and uncertainty relation inequalities,” J. Phys. A: Math. Gen., 35, 5181–5187 (2002).

    Article  MATH  ADS  Google Scholar 

  397. S. L. Luo, “Wigner-Yanase skew information and uncertainty relations,” Phys. Rev. Lett., 91, 180403 (2003).

    Google Scholar 

  398. M. O. Scully, B.-G. Englert, and H. Walther, “Quantum optical tests of complementarity,” Nature, 351, 111–116 (1991).

    Article  ADS  Google Scholar 

  399. G. Björk, J. Söderholm, A. Trifonov, T. Tsegaye, and A. Karlsson, “Complementarity and the uncertainty relations,” Phys. Rev. A, 60, 1874–1882 (1999).

    Article  ADS  Google Scholar 

  400. J. L. Garretson, H. M. Wiseman, D. T. Pope, and D. T. Pegg, “The uncertainty relation in ‘whichway’ experiments: how to observe directly the momentum transfer using weak values,” J. Opt. B: Quantum Semiclass. Opt., 6, S506–S517 (2004).

    Article  ADS  Google Scholar 

  401. B. L. Hu and Y. H. Zhang, “Squeezed states and uncertainty relation at finite temperature,” Mod. Phys. Lett. A, 8, 3575–3584 (1993).

    Article  ADS  Google Scholar 

  402. J. Uffink and J. van Lith, “Thermodynamic uncertainty relations,” Found. Phys., 29, 655–692 (1999).

    Article  MathSciNet  Google Scholar 

  403. M. J. W. Hall, “Exact uncertainty relations,” Phys. Rev. A, 64, 052103 (2001).

    Google Scholar 

  404. V. Giovannetti, “Separability conditions from entropic uncertainty relations,” Phys. Rev. A, 70, 012102 (2004).

    Google Scholar 

  405. O. Guhne and M. Lewenstein, “Entropic uncertainty relations and entanglement,” Phys. Rev. A, 70, 022316 (2004).

    Google Scholar 

  406. O. Guhne, “Characterizing entanglement via uncertainty relations,” Phys. Rev. Lett., 92, 117903 (2004).

    Google Scholar 

  407. H. Nha and J. Kim, “Entanglement criteria via the uncertainty relations in su(2) and su(1, 1) algebras: Detection of non-Gaussian entangled states,” Phys. Rev. A, 74, 012317 (2006).

    Google Scholar 

  408. A. Serafini, “Multimode uncertainty relations and separability of continuous variable states,” Phys. Rev. Lett., 96, 110402 (2006).

    Google Scholar 

  409. M. I. Kolobov and I. V. Sokolov, “Multimode squeezing, antibunching in space and noise-free optical images,” Europhys. Lett., 15, 271–276 (1991).

    Article  ADS  Google Scholar 

  410. I. V. Sokolov, “Imaging of faint phase objects at the Heisenberg limit with quadrature-squeezed light,” J. Opt. B: Quantum Semiclass. Opt., 2, 179–183 (2000).

    Article  ADS  Google Scholar 

  411. L. A. Lugiato, A. Gatti, and E. Brambilla, “Quantum imaging,” J. Opt. B: Quantum Semiclass. Opt., 4, S176–S183 (2002).

    Article  ADS  Google Scholar 

  412. M. Hillery, “Quantum cryptography with squeezed states,” Phys. Rev. A, 61, 022309 (2000).

    Google Scholar 

  413. D. Gottesman and J. Preskill, “Secure quantum key distribution using squeezed states,” Phys. Rev. A, 63, 022309 (2001).

    Google Scholar 

  414. N. J. Cerf, M. Levy, and G. Van Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A, 63, 052311 (2001).

    Google Scholar 

  415. D. Han, Y. S. Kim, and W. W. Zachary (eds.), Workshop on Squeezed States and Uncertainty Relations (University of Maryland at College Park, Maryland, March 28–30, 1991), NASA Conference Publication 3135, NASA, Greenbelt (1992).

    Google Scholar 

  416. D. Han, Y. S. Kim, and V. I. Man’ko (eds.), Second International Workshop on Squeezed States and Uncertainty Relations (P. N. Lebedev Physical Institute, Moscow, May 25–29, 1992), NASA Conference Publication 3219, NASA, Greenbelt (1993).

    Google Scholar 

  417. D. Han, Y. S. Kim, N. H. Rubin, Y. Shih, and W. W. Zachary (eds.), Third International Workshop on Squeezed States and Uncertainty Relations (University of Maryland at Baltimore County, Baltimore, Maryland, August 10–13, 1993), NASA Conference Publication 3270, NASA, Greenbelt (1994).

    Google Scholar 

  418. D. Han, K. Peng, Y. S. Kim, and V. I. Man’ko (eds.), Fourth International Conference on Squeezed States and Uncertainty Relations (Shanxi University, Taiyuan, Shanxi, P. R. China, June 5–8, 1995), NASA Conference Publication 3322, NASA, Greenbelt (1996).

    Google Scholar 

  419. D. Han, J. Janszky, Y. S. Kim, and V. I. Man’ko (eds.), Fifth International Conference on Squeezed States and Uncertainty Relations (Balatonfüred, Hungary, May 27–31, 1997), NASA/CP-1998-206855, NASA, Greenbelt (1998).

  420. D. Han, Y. S. Kim, and S. Solimeno (Eds.), Sixth International Conference on Squeezed States and Uncertainty Relations (University of Naples “Federico II” Naples, Italy, May 24–29, 1999), NASA/CP-2000-209899, NASA, Greenbelt (2000) [on CD-ROM].

    Google Scholar 

  421. D. Han, Y. S. Kim, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich (Eds.), Proceedings of the Seventh International Conference on Squeezed States and Uncertainty Relations (Boston University, Boston, USA, June 4–8, 2002) [online publication: http://ysfine.com/index.html].

    Google Scholar 

  422. H. Moya-Cessa, R. Jáuregui, S. Hacyan, and O. Castaños (eds.), Proceedings of the 8th International Conference on Squeezed States and Uncertainty Relations (Puebla, Mexico, June 9–13, 2003), Rinton Press, Princeton (2003).

    MATH  Google Scholar 

  423. C. Fabre and S. Solimeno (eds), Quantum Correlations and Fluctuations, J. Opt. B: Quantum Semiclass. Opt., 2, special issue No. 2 (2000).

  424. Y. S. Kim, M. A. Man’ko, and A. Sergienko (eds), Uncertainty Relations, Quantum Phase Space, Quantum Optics, Quantum Information, Imaging, and Computing, J. Opt. B: Quantum Semiclass. Opt., 4, special issue No. 3 (2002).

  425. O. Castaños, R. Jauregue-Renaud, Y. S. Kim, M. A. Man’ko, and G. Moya Cessa (eds), Special Issue on Squeezed States and Uncertainty Relations, J. Opt. B: Quantum Semiclass. Opt., 6, No. 3 (2004).

  426. Y. S. Kim, M. A. Man’ko, and M. Planat (eds.), Squeeze Transformation and Optics after Einstein, J. Opt. B: Quantum Semiclass. Opt., 7, No. 12 (2005).

  427. M. Planat, V. Laude, G. Kurizki, H. Rosu, W. Schleich, and A. Vourdas (eds.), 9th International Conference on Squeezed States and Uncertainty Relations (Besançon, France, May 2–6, 2005), Int. J. Mod. Phys. B, 20, special issues Nos. 11–13 (2006).

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Authors and Affiliations

  1. Instituto de Física, Universidade de Brasília, Caixa Postal 04455, 70910-900, Brasília, DF, Brazil

    Victor V. Dodonov

  2. P. N. Lebedev Physical Institute, Russian Academy of Sciences, Leninskii Prospect 53, Moscow, 119991, Russia

    Margarita A. Man’ko

  3. Department of Computing, University of Bradford, Bradford BD7 1DB, UK

    Vladimir I. Man’ko & Apostol Vourdas

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  1. Victor V. Dodonov
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  2. Margarita A. Man’ko
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  3. Vladimir I. Man’ko
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Dedicated to the memory of our friends and colleagues Prof. Vladimir A. Isakov, Prof. Alexander S. Shumovsky, and Dr. Andrey Vinogradov.

Manuscript submitted by the authors in English on 20 September 2007.

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Dodonov, V.V., Man’ko, M.A., Man’ko, V.I. et al. Squeezed states and uncertainty relations since 1991. J Russ Laser Res 28, 404–428 (2007). https://doi.org/10.1007/s10946-007-0031-6

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