OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Grover Swartzlander
  • Vol. 31, Iss. 1 — Jan. 1, 2014
  • pp: 38–44

Photon-added nonlinear coherent states for a one-mode field in a Kerr medium

R. Román-Ancheyta, C. González Gutiérrez, and J. Récamier  »View Author Affiliations

JOSA B, Vol. 31, Issue 1, pp. 38-44 (2014)

View Full Text Article

Enhanced HTML    Acrobat PDF (1654 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We construct deformed photon-added nonlinear coherent states (DPANCSs) by application of the deformed creation operator upon the nonlinear coherent states obtained as eigenstates of the deformed annihilation operator and by application of a deformed displacement operator upon the vacuum state. We evaluate some statistical properties like the Mandel parameter, Husimi, and Wigner functions for these states and analyze their differences; we give closed analytical expressions for them. We found a profound difference in the statistical properties of the DPANCSs obtained from the two abovementioned generalizations.

© 2013 Optical Society of America

OCIS Codes
(270.5290) Quantum optics : Photon statistics
(270.6570) Quantum optics : Squeezed states

ToC Category:
Quantum Optics

Original Manuscript: August 15, 2013
Revised Manuscript: November 7, 2013
Manuscript Accepted: November 13, 2013
Published: December 6, 2013

R. Román-Ancheyta, C. González Gutiérrez, and J. Récamier, "Photon-added nonlinear coherent states for a one-mode field in a Kerr medium," J. Opt. Soc. Am. B 31, 38-44 (2014)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. R. J. Glauber, “Photon correlations,” Phys. Rev. Lett. 10, 84–86 (1963). [CrossRef]
  2. R. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766–2788 (1963). [CrossRef]
  3. R. R. Puri and G. S. Agarwal, “SU(1,1) coherent states defined via a minimum-uncertainty product and an equality of quadrature variances,” Phys. Rev. A 53, 1786–1790 (1996). [CrossRef]
  4. 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). [CrossRef]
  5. A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to-classical transition with single-photon-added coherent states of light,” Science 306, 660–662 (2004). [CrossRef]
  6. H. Moya-Cessa, “Generation and properties of superpositions of displaced Fock states,” J. Mod. Opt. 42, 1741–1754 (1995). [CrossRef]
  7. A. Zavatta, S. Viciani, and M. Bellini, “Single-photon excitation of a coherent state: catching the elementary step of stimulated light emission,” Phys. Rev. A 72, 023820 (2005). [CrossRef]
  8. A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006). [CrossRef]
  9. J. Wenger, R. Tualle-Brouri, and P. Grangier, “Non-Gaussian statistics from individual pulses of squeezed light,” Phys. Rev. Lett. 92, 153601 (2004). [CrossRef]
  10. M. Barbieri, N. Spagnolo, M. G. Genoni, F. Ferreyrol, R. Blandino, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, “Non-Gaussianity of quantum states: an experimental test on single-photon-added coherent states,” Phys. Rev. A 82, 063833 (2010). [CrossRef]
  11. J. Lee, J. Kim, and H. Nha, “Demonstrating higher-order nonclassical effects by photon-added classical states: realistic schemes,” J. Opt. Soc. Am. B 26, 1363–1369 (2009). [CrossRef]
  12. M. S. Kim, H. Jeong, A. Zavatta, V. Parigi, and M. Bellini, “Scheme for proving the bosonic commutation relation using single-photon interference,” Phys. Rev. Lett. 101, 260401 (2008). [CrossRef]
  13. A. Zavatta, V. Parigi, M. S. Kim, H. Jeong, and M. Bellini, “Experimental demonstration of the bosonic commutation relation via superpositions of quantum operations on thermal light fields,” Phys. Rev. Lett. 103, 140406 (2009). [CrossRef]
  14. T. Kiesel, W. Vogel, M. Bellini, and A. Zavatta, “Nonclassicality quasiprobability of single-photon-added thermal states,” Phys. Rev. A 83, 032116 (2011). [CrossRef]
  15. V. I. Man’ko, G. Marmo, E. C. G. Sudarshan, and F. Zaccaria, “f-oscillators and nonlinear coherent states,” Phys. Scr. 55, 528–541 (1997). [CrossRef]
  16. R. L. de Matos Filho and W. Vogel, “Nonlinear coherent states,” Phys. Rev. A 54, 4560–4563 (1996). [CrossRef]
  17. J. Récamier, W. L. Mochán, M. Gorayeb, J. L. Paz, and R. Jáuregui, “Uncertainty relations for a deformed oscillator,” Int. J. Mod. Phys. B 20, 1851–1859 (2006). [CrossRef]
  18. V. V. Dodonov, “Non classical states in quantum optics: a squeezed review of the first 75 years,” J. Opt. B 4, R1–R33 (2002). [CrossRef]
  19. W.-M. Zhang, D. H. Feng, and R. Gilmore, “Coherent states: theory and some applications,” Rev. Mod. Phys. 62, 867–927 (1990). [CrossRef]
  20. J. Récamier, M. Gorayeb, W. L. Mochán, and J. L. Paz, “Nonlinear coherent states and some of their properties,” Int. J. Theor. Phys. 47, 673–683 (2008). [CrossRef]
  21. B. Roy and P. Roy, “New nonlinear coherent states and some of their nonclassical properties,” J. Opt. B 2, 65–68 (2000). [CrossRef]
  22. G. Ren, J.-M. Du, H.-J. Yu, and Y.-J. Xu, “Nonclassical properties of Hermite polynomial’s coherent state,” J. Opt. Soc. Am. B 29, 3412–3418 (2012). [CrossRef]
  23. S. Sivakumar, “Photon-added coherent states as nonlinear coherent states,” J. Phys. A 32, 3441–3447 (1999). [CrossRef]
  24. O. Safaeian and M. K. Tavassoly, “Deformed photon-added nonlinear coherent states and their non-classical properties,” J. Phys. A 44, 225301 (2011). [CrossRef]
  25. R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963). [CrossRef]
  26. S. Haroche and J.-M. Raimond, Exploring the Quantum, Atoms, Cavities, and Photons (Oxford University, 2006).
  27. J. M. Raimond, T. Meunier, P. Bertet, S. Gleyzes, P. Maioli, A. Auffeves, G. Nogues, M. Brune, and S. Haroche, “Probing a quantum field in a photon box,” J. Phys. B 38, S535–S550 (2005). [CrossRef]
  28. L.-Y. Hu, F. Jia, and Z.-M. Zhang, “Entanglement and nonclassicality of photon-added two-mode squeezed thermal state,” J. Opt. Soc. Am. B 29, 1456–1464 (2012). [CrossRef]
  29. L.-Y. Hu and Z.-M. Zhang, “Nonclassicality and decoherence of photon-added squeezed thermal state in thermal environment,” J. Opt. Soc. Am. B 29, 529–537 (2012). [CrossRef]
  30. O. de los Santos-Sánchez and J. Récamier, “Nonlinear coherent states for nonlinear systems,” J. Phys. A 44, 145307 (2011). [CrossRef]
  31. O. de los Santos-Sánchez and J. Récamier, “The f-deformed Jaynes–Cummings model and its nonlinear coherent states,” J. Phys. B 45, 015502 (2012). [CrossRef]
  32. R. Roknizadeh and M. K. Tavassoly, “The construction of some important classes of generalized coherent states: the nonlinear coherent states method,” J. Phys. A 37, 8111–8127 (2004). [CrossRef]
  33. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995), p. 1102.
  34. P. D. Drummond and D. F. Walls, “Quantum theory of optical bistability. I. Nonlinear polarisability model,” J. Phys. A 13, 725–741 (1980). [CrossRef]
  35. B. C. Sanders and G. J. Milburn, “Complementarity in a quantum nondemolition measurement,” Phys. Rev. A 39, 694–702 (1989). [CrossRef]
  36. B. Yurke and D. Stoler, “Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion,” Phys. Rev. Lett. 57, 13–16 (1986). [CrossRef]
  37. R. Román-Ancheyta, O. de los Santos-Sánchez, and J. Récamier, “Ladder operators and coherent states for nonlinear potentials,” J. Phys. A 44, 435304 (2011). [CrossRef]
  38. C. T. Lee, “Simple criterion for nonclassical two-mode states,” J. Opt. Soc. Am. B 15, 1187–1191 (1998). [CrossRef]
  39. L. Mandel, “Sub-Poissonian photon statistics in resonance fluorescence,” Opt. Lett. 4, 205–207 (1979). [CrossRef]
  40. H. M. Cessa and P. Knight, “Series representation of quantum-field quasiprobabilities,” Phys. Rev. A 48, 2479–2481 (1993). [CrossRef]
  41. H. M. Cessa, “Decoherence in atom-field interactions: a treatment using superoperator techniques,” Phys. Rep. 432, 1–41 (2006). [CrossRef]
  42. A. Royer, “Wigner function as the expectation value of a parity operator,” Phys. Rev. A 15, 449–450 (1977). [CrossRef]
  43. F. A. M. de Oliveira, M. S. Kim, P. L. Knight, and V. Buzek, “Properties of displaced number states,” Phys. Rev. A 41, 2645 (1990). [CrossRef]
  44. M. Boiteux and A. Levelut, “Semicoherent states,” J. Phys. A 6, 589–596 (1973). [CrossRef]
  45. R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical analogue of displaced Fock states and quantum correlations in Glauber–Fock photonic lattices,” Phys. Rev. Lett. 107, 103601 (2011). [CrossRef]
  46. A. I. Lvovsky and S. A. Babichev, “Synthesis and tomographic characterization of the displaced Fock state of light,” Phys. Rev. A 66, 011801 (2002). [CrossRef]
  47. F. Ziesel, T. Ruster, A. Walther, H. Kaufmann, S. Dawkins, K. Singer, F. Schmidt-Kaler, and U. G. Poschinger, “Experimental creation and analysis of displaced number states,” J. Phys. B 46, 104008 (2013). [CrossRef]

Cited By

Alert me when this paper is cited

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

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited