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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry Van Driel
  • Vol. 26, Iss. 4 — Apr. 1, 2009
  • pp: 830–835

Nonclassicality of photon-subtracted and photon-added-then-subtracted Gaussian states

Yang Yang and Fu-Li Li  »View Author Affiliations

JOSA B, Vol. 26, Issue 4, pp. 830-835 (2009)

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By the use of nonclassical depth as a criterion for nonclassicality, we show that states generated by first adding (subtracting) multiphotons to an arbitrary state and then subtracting (adding) multiphotons from the resulting state is certainly nonclassical if the addition number of photons is equal to or larger than the subtraction number. The explicit expressions of nonclassical depth are found for both the single-photon-subtracted Gaussian state and the photon-added-then-subtracted thermal state. Based on the expressions, we show that the nonclassicality of the initial Gaussian state can be enhanced by the photon subtraction process. We also notice that the photon-added-then-subtracted thermal state is nonclassical if the initial thermal mean photon number is not zero, and the nonclassicality increases monotonously as the initial thermal mean photon number increases.

© 2009 Optical Society of America

OCIS Codes
(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in
(270.0270) Quantum optics : Quantum optics
(160.3918) Materials : Metamaterials
(190.6135) Nonlinear optics : Spatial solitons

ToC Category:
Quantum Optics

Original Manuscript: January 21, 2009
Revised Manuscript: February 26, 2009
Manuscript Accepted: March 4, 2009
Published: March 27, 2009

Yang Yang and Fu-Li Li, "Nonclassicality of photon-subtracted and photon-added-then-subtracted Gaussian states," J. Opt. Soc. Am. B 26, 830-835 (2009)

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  1. M. O. Scully, M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997).
  2. S. L. Braunstein, P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005). [CrossRef]
  3. A. Zavatta, S. Viciani, M. Bellini, “Quantum-to-classical transition with single-photon-added coherent states of light,” Science 306, 660–662 (2004). [CrossRef] [PubMed]
  4. A. Zavatta, S. Viciani, M. Bellini, “Single-photon excitation of a coherent state: catching the elementary step of stimulated light emission,” Phys. Rev. A 72, 023820 (2005). [CrossRef]
  5. A. Zavatta, V. Parigi, M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (2007). [CrossRef]
  6. V. Parigi, A. Zavatta, M. Kim, M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890–1893 (2007). [CrossRef] [PubMed]
  7. J. Wenger, R. Tualle-Brouri, P. Grangier, “Non-Gaussian statistics from individual pulses of squeezed light,” Phys. Rev. Lett. 92, 153601 (2004). [CrossRef] [PubMed]
  8. A. R. Usha Devi, R. Prabhu, M. S. Uma, “Non-classicality of photon added coherent and thermal radiations,” Eur. Phys. J. D 40, 133–138 (2006). [CrossRef]
  9. M. S. Kim, E. Park, P. L. Knight, H. Jeong, “Nonclassicality of a photon-subtracted Gaussian field,” Phys. Rev. A 71, 043805 (2005). [CrossRef]
  10. A. Biswas, G. S. Agarwal, “Nonclassicality and decoherence of photon-subtracted squeezed states,” Phys. Rev. A 75, 032104 (2007). [CrossRef]
  11. S. S. Mizrahi, V. V. Dodonov, “Creating quanta with an ‘annihilation’ operator,” J. Phys. A 35, 8847–8857 (2002). [CrossRef]
  12. G. S. Agarwal, K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492–497 (1991). [CrossRef] [PubMed]
  13. L. Y. Hu, H. Y. Fan, “Statistical properties of photon-subtracted squeezed vacuum in thermal environment,” J. Opt. Soc. Am. B 25, 1955–1964 (2008). [CrossRef]
  14. G. S. Agarwal, K. Tara, “Nonclassical character of states exhibiting no squeezing or sub-Poissonian statistics,” Phys. Rev. A 46, 485–488 (1992). [CrossRef] [PubMed]
  15. W. Vogel, “Nonclassical states: an observable criterion,” Phys. Rev. Lett. 84, 1849–1852 (2000). [CrossRef] [PubMed]
  16. Th. Richter, W. Vogel, “Nonclassicality of quantum states: a hierarchy of observable conditions,” Phys. Rev. Lett. 89, 283601 (2002). [CrossRef]
  17. D. N. Klyshko, “Observable signs of nonclassical light,” Phys. Lett. A 213, 7–15 (1996). [CrossRef]
  18. Arvind, N. Mukunda, R. Simon, “Characterizations of classical and nonclassical states of quantized radiation,” J. Phys. A 31, 565–583 (1998). [CrossRef]
  19. G. M. D’Ariano, M. F. Sacchi, “Tomographic measurements of nonclassical radiation states,” Phys. Rev. A 59, 826–830 (1999). [CrossRef]
  20. M. S. Kim, W. Son, V. Bužek, P. L. Knight, “Entanglement by a beam splitter: nonclassicality as a prerequisite for entanglement,” Phys. Rev. A 65, 032323 (2002). [CrossRef]
  21. Wang Xiang-bin, “Theorem for the beam-splitter entangler,” Phys. Rev. A 66, 024303 (2002). [CrossRef]
  22. J. K. Asbóth, J. Calsamiglia, H. Ritsch, “Computable measure of nonclassicality for light,” Phys. Rev. Lett. 94, 173602 (2005). [CrossRef] [PubMed]
  23. G. Vidal, R. F. Werner, “Computable measure of entanglement,” Phys. Rev. A 65, 032314 (2002). [CrossRef]
  24. V. Vedral, M. B. Plenio, M. A. Rippin, P. L. Knight, “Quantifying entanglement,” Phys. Rev. Lett. 78, 2275–2279 (1997). [CrossRef]
  25. R. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766–2788 (1963). [CrossRef]
  26. E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Phys. Rev. Lett. 10, 277–279 (1963). [CrossRef]
  27. C. T. Lee, “Measure of the nonclassicality of nonclassical states,” Phys. Rev. A 44, R2775–R2778 (1991). [CrossRef] [PubMed]
  28. C. T. Lee, “Theorem on nonclassical states,” Phys. Rev. A 52, 3374–3376 (1995). [CrossRef] [PubMed]
  29. A. Ferraro, S. Olivares, M. G. A. Paris, “Gaussian states in continuous variable quantum information,” quant-ph/0503237, p. 38.
  30. H. R. Li, F. L. Li, Y. Yang, “Entangling two single-mode Gaussian states by use of a beam splitter,” Chin. Phys. 15, 2947–2952 (2006). [CrossRef]
  31. E. Shchukin, Th. Richter, W. Vogel, “Nonclassicality criteria in terms of moments,” Phys. Rev. A 71, 011802(R) (2005). [CrossRef]
  32. E. V. Shchukin, W. Vogel, “Nonclassical moments and their measurement,” Phys. Rev. A 72, 043808 (2005). [CrossRef]
  33. T. Kiesel, W. Vogel, V. Parigi, A. Zavatta, M. Bellini, “Experimental determination of a nonclassical Glauber–Sudarshan P function,” Phys. Rev. A 78, 021804(R) (2008). [CrossRef]

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