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Superposition of two-mode “Near” coherent states: non-classicality and entanglement

  • A. DehghaniEmail author
  • B. Mojaveri
  • M. Aryaie
  • A. A. Alenabi
Article
  • 44 Downloads

Abstract

In this paper, we introduce quasi-Bell states as a result of two-mode superposition of two “Near” coherent states, \(|\alpha ,\delta \theta \rangle \), shifted in phase by \(\pi \) and \(\frac{\pi }{2}\), where the latter introduced by Othman et al. as a new class of quantum states attached to the simple harmonic oscillator which generated via a Mach–Zehnder interferometer. To gain insight into useful attributes to quantum information theory, we present a general analysis of non-classical properties such as photon counting probability, photon statistics, squeezing effect and quantum polarization. We also derive the concurrence measure to quantify entanglement of these states and look for conditions that provide information on which these become maximally entangled. Comparing with some cases already discussed in the literature, we find that the phase angle \(\delta \theta \) plays an important role in non-classical effects. We also get a connection between entanglement and the polarization degree of the introduced states.

Keywords

Quantum optics Coherent states Photon statistics Photon counting Squeezing Entanglement 

Notes

References

  1. 1.
    Schrödinger, E.: The current situation in quantum mechanics. Natur wissen schaften 23, 807, 823, 844 (1935)zbMATHGoogle Scholar
  2. 2.
    Barenco, A., Deutsch, D., Ekert, A., Jozsa, R.: Conditional quantum dynamics and logic gates. Phys. Rev. Lett. 74, 4083 (1995)ADSCrossRefGoogle Scholar
  3. 3.
    Divincenzo, D.P.: Quantum computation. Science 270, 255 (1995)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Bengtsson, I., Zyczkowski, K.: Geometry of Quantum States: An Introduction to Quantum Entanglement. Cambridge University Press, Cambridge (2006)CrossRefGoogle Scholar
  5. 5.
    Bennett, C.H., Brassard, G., Crepeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Li, X., Pan, Q., Jing, J., Zhang, J., Xie, C., Peng, K.: Quantum dense coding exploiting a bright Einstein–Podolsky–Rosen beam. Phys. Rev. Lett. 88, 047904 (2002)ADSCrossRefGoogle Scholar
  7. 7.
    Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein–Podolsky–Rosen states. Phys. Rev. Lett. 69, 2881 (1992)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    Bennett, C.H.: Quantum cryptography using any two non-orthogonal states. Phys. Rev. Lett. 68, 3121 (1992)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661 (1991)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    Horne, M.A., Shimony, A., Zeilinger, A.: Two-particle interferometry. Phys. Rev. Lett. 62, 2209 (1989)ADSCrossRefGoogle Scholar
  11. 11.
    Sanders, B.C.: Entangled coherent states. Phys. Rev. A 45, 6811 (1992)ADSCrossRefGoogle Scholar
  12. 12.
    Van Enk, S.J., Hirota, O.: Entangled coherent states: teleportation and decoherence. Phys. Rev. A 64, 022313 (2000)CrossRefGoogle Scholar
  13. 13.
    Wang, X., Sanders, B.C.: Multipartite entangled coherent states. Phys. Rev. A 65, 012303 (2001)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    Fakhri, H., Dehghani, A.: Coherency of \(su(1,1)\)-Barut-Girardello type and entanglement for spherical harmonics. J. Math. Phys. 50, 052104 (2009)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    Ping, Yun-Xia, Zhang, Bo, Cheng, Ze, Xu, Q.: Two-mode entanglement via superposition of two-mode coherent states. Mod. Phys. Lett. B 21, 1253 (2007)ADSCrossRefGoogle Scholar
  16. 16.
    Chai, Chin-lin: Two-mode nonclassical state via superpositions of two-mode coherent states. Phys. Rev. A 46, 7187 (1992)ADSCrossRefGoogle Scholar
  17. 17.
    Cai, X.H., Kuang, L.M.: Preparation of entangled squeezed states and quantification of their entanglement. Chin. Phys. 11, 876 (2002)ADSCrossRefGoogle Scholar
  18. 18.
    Zhou, L., Kuang, L.M.: Optical preparation of entangled squeezed vacuum states. Phys. Lett. A 302, 273 (2002)ADSCrossRefGoogle Scholar
  19. 19.
    Lu, H., Chen, L., Lin, J.: Entangled squeezed states: Bell state measurement and teleportation. Chin. Opt. Lett. 2, 618 (2004)ADSGoogle Scholar
  20. 20.
    Dey, S., Hussin, V.: Entangled squeezed states in noncommutative spaces with minimal length uncertainty relations. Phys. Rev. D 91, 124017 (2015)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    Dey, S., Fring, A., Hussin, V.: Nonclassicality versus entanglement in a noncommutative space. Int. J. Mod. Phys. B 31, 1650248 (2017)ADSCrossRefGoogle Scholar
  22. 22.
    Xu, L., Kuang, L.M.J.: Single-mode excited entangled coherent states. J. Phys. A Math. Gen. 39, L191 (2006)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    Wang, X.G.: Two-mode nonlinear coherent states. Opt. Commun. 178, 365 (2000)ADSCrossRefGoogle Scholar
  24. 24.
    Afshar, D., Anbaraki, A.: Nonclassical properties and entanglement of superposition of two-mode separable nonlinear coherent states. J. Opt. Soc. Am. B 33, 558 (2016)ADSCrossRefGoogle Scholar
  25. 25.
    Karimi, A.: Two-mode photon-added entangled coherent-squeezed states: their entanglement and nonclassical properties. Appl. Phys. B 123, 181 (2017)ADSCrossRefGoogle Scholar
  26. 26.
    Hyunseok, J., Nguyen, B.A.: GHZ-type and W-type entangled coherent states: generation and Bell-type inequality tests without photon counting. Phys. Rev. A 74, 022104 (2006)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Kwiat, P.G., Mattle, K., Weinfurter, H., Zeilinger, A., Sergienko, A.V., Shih, Y.: New high-intensity source of polarization-entangled photon pairs. Phys. Rev. Lett. 75, 4337 (1995)ADSCrossRefGoogle Scholar
  28. 28.
    Pan, J.W., Chen, Z.-B., Lu, C.Y., Weinfurter, H., Zeilinger, A., Zukowski, M.: Multiphoton entanglement and interferometry. Rev. Mod. Phys. 84, 777 (2012)ADSCrossRefGoogle Scholar
  29. 29.
    Mair, A., Vaziri, A., Weihs, G., Zeilinger, A.: Entanglement of the orbital angular momentum states of photons. Nature 412, 313 (2001)ADSCrossRefGoogle Scholar
  30. 30.
    Franke-Arnold, S., Allen, L., Padgett, M.: Advances in optical angular momentum. Laser Photon. Rev. 2, 299 (2008)ADSCrossRefGoogle Scholar
  31. 31.
    Okamoto, R., Hofmann, H.F., Nagata, T., O’Brien, J.L., Sasaki, K., Takeuchi, S.: Beating the standard quantum limit: phase super-sensitivity of N-photon interferometers. New J. Phys. 10, 073033 (2008)ADSCrossRefGoogle Scholar
  32. 32.
    Leach, J., Jack, B., Romero, J., Ritsch-Marte, M., Boyd, R.W., Jha, A.K., Barnett, S.M., Franke-Arnold, S., Padgett, M.J.: Violation of a Bell inequality in two-dimensional orbital angular momentum state-spaces. Opt. Express 17, 8287 (2009)ADSCrossRefGoogle Scholar
  33. 33.
    Karimi, E., Leach, J., Slussarenko, S., Piccirillo, B., Marrucci, L., Chen, L., She, W., Franke-Arnold, S., Padgett, M.J., Santamato, E.: Spin-orbit hybrid entanglement of photons and quantum contextuality. Phys. Rev. A 82, 022115 (2010)ADSCrossRefGoogle Scholar
  34. 34.
    Leach, J., Jack, B., Romero, J., Jha, A.K., Yao, A.M., Franke-Arnold, S., Ireland, D.G., Boyd, R.W., Barnett, S.M., Padgett, M.J.: Quantum correlations in optical angle-orbital angular momentum variables. Science 329, 662 (2010)ADSCrossRefGoogle Scholar
  35. 35.
    Simon, D.S., Sergienko, A.V.: High-capacity quantum key distribution via hyperentangled degrees of freedom. New J. Phys. 16, 063052 (2014)ADSCrossRefGoogle Scholar
  36. 36.
    Bhatti, D., von Zanthier, J., Agarwal, G.S.: Entanglement of polarization and orbital angular momentum. Phys. Rev. A 91, 062303 (2015)ADSCrossRefGoogle Scholar
  37. 37.
    Ahmad, M.A., Liu, S.T.: Superposition of two coherent states p out of phase with average photon number as relative phase. Optik 120, 68 (2009)ADSCrossRefGoogle Scholar
  38. 38.
    Zeng, R., Ahmad, M.A., Liu, S.: Nonclassical state via superposition of two coherent states (\(\frac{pi}{2}\) out of phase) and related entangled states. Opt. Commun. 271, 162 (2007)ADSCrossRefGoogle Scholar
  39. 39.
    Prakash, H., Kumar, P.: Non-classical properties of superposition of two coherent states having phase difference \(\phi \). Optik 122, 1058 (2011)ADSCrossRefGoogle Scholar
  40. 40.
    Kim, M.S., Son, W., Buek, V., Knight, P.L.: Entanglement by a beam splitter: nonclassicality as a prerequisite for entanglement. Phys. Rev. A 65, 032323 (2002)ADSCrossRefGoogle Scholar
  41. 41.
    Buzek, V., Vidiella-Barranco, A., Knight, P.L.: Superpositions of coherent states: squeezing and dissipation. Phys. Rev. A 45, 6570 (1992)ADSCrossRefGoogle Scholar
  42. 42.
    Short, R., Mandel, L.: Observation of sub-Poissonian photon statistics. Phys. Rev. Lett. 51, 384 (1983)ADSCrossRefGoogle Scholar
  43. 43.
    Simon, R., Selvadoray, M., Mukunda, N.: Nonclassicality and the concept of local constraints on the photon number distribution, 112 (1997). arXiv:quant-ph/9709030v1
  44. 44.
    Kimble, H.J., Dagenais, M., Mandel, L.: Photon antibunching in resonance fluorescence. Phys. Rev. Lett. 39, 691 (1977)ADSCrossRefGoogle Scholar
  45. 45.
    Othman, Anas, Yevick, D.: Quantum properties of the superposition of two nearly identical coherent states. Int. J. Theor. Phys. 57, 2293 (2018)MathSciNetCrossRefGoogle Scholar
  46. 46.
    Bennett, C.H., Bessette, F., Brassard, G., Salvail, L., Smolin, J.: Experimental quantum cryptography. J. Cryptol. 5, 3 (1992)CrossRefGoogle Scholar
  47. 47.
    Mattle, K., Weinfurter, H., Kwiat, P.G., Zeilinger, A.: Dense coding in experimental quantum communication. Phys. Rev. Lett. 76, 4656 (1996)ADSCrossRefGoogle Scholar
  48. 48.
    Bouwmeester, D., Pan, J.W., Mattle, K., Eibl, M., Weinfurter, H., Zeilinger, A.: Experimental quantum teleportation. Nature 390, 575 (1997)ADSCrossRefGoogle Scholar
  49. 49.
    Barbieri, M., De Martini, F., Di Nepi, G., Mataloni, P., D’Ariano, G.M., Macchiavello, C.: Detection of entanglement with polarized photons: experimental realization of an entanglement witness. Phys. Rev. Lett. 91, 227901 (2003)ADSCrossRefGoogle Scholar
  50. 50.
    Luis, A., Korolkova, N.: Polarization squeezing and nonclassical properties of light. Phys. Rev. A 74, 043817 (2006)ADSCrossRefGoogle Scholar
  51. 51.
    Wootters, W.K.: Entanglement of formation and concurrence. Quantum Inf. Comput. 1, 27 (2001)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • A. Dehghani
    • 1
    Email author
  • B. Mojaveri
    • 2
  • M. Aryaie
    • 2
  • A. A. Alenabi
    • 2
  1. 1.Department of PhysicsPayame Noor UniversityTehranIslamic Republic of Iran
  2. 2.Department of PhysicsAzarbaijan Shahid Madani UniversityTabrizIslamic Republic of Iran

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