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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Grover Swartzlander
  • Vol. 30, Iss. 5 — May. 1, 2013
  • pp: 1109–1117

Entanglement dynamics and position-momentum entropic uncertainty relation of a Λ-type three-level atom interacting with a two-mode cavity field in the presence of nonlinearities

M. J. Faghihi, M. K. Tavassoly, and M. R. Hooshmandasl  »View Author Affiliations

JOSA B, Vol. 30, Issue 5, pp. 1109-1117 (2013)

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In this paper, the interaction between a Λ-type three-level atom and a two-mode cavity field is discussed. The detuning parameters and cross-Kerr nonlinearity are taken into account, and it is assumed that the atom–field coupling and Kerr medium are f-deformed. Even though the system seems complicated, the analytical form of the state vector of the entire system for the considered model is exactly obtained. The time evolution of nonclassical properties, such as quantum entanglement and position–momentum entropic uncertainty relation (entropy squeezing) of the field are investigated. In each case, the influences of the detuning parameters, generalized Kerr medium, and intensity-dependent coupling on the latter nonclassicality signs are analyzed in detail.

© 2013 Optical Society of America

OCIS Codes
(270.0270) Quantum optics : Quantum optics
(270.5585) Quantum optics : Quantum information and processing

ToC Category:
Image Processing

Original Manuscript: November 16, 2012
Revised Manuscript: February 12, 2013
Manuscript Accepted: February 26, 2013
Published: April 4, 2013

M. J. Faghihi, M. K. Tavassoly, and M. R. Hooshmandasl, "Entanglement dynamics and position-momentum entropic uncertainty relation of a Λ-type three-level atom interacting with a two-mode cavity field in the presence of nonlinearities," J. Opt. Soc. Am. B 30, 1109-1117 (2013)

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  1. E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE. 51, 89–109 (1963). [CrossRef]
  2. F. W. Cummings, “Stimulated emission of radiation in a single mode,” Phys. Rev. A 140, 1051–1056 (1965). [CrossRef]
  3. B. Buck and C. V. Sukumar, “Exactly soluble model of atom–phonon coupling showing periodic decay and revival,” Phys. Lett. A 81, 132–135 (1981). [CrossRef]
  4. C. V. Sukumar and B. Buck, “Multi-phonon generalisation of the Jaynes–Cummings model,” Phys. Lett. A 83, 211–213(1981). [CrossRef]
  5. V. Bužek, “Jaynes–Cummings model with intensity-dependent coupling interacting with Holstein–Primakoff SU(1, 1) coherent state, Phys. Rev. A 39, 3196–3199 (1989). [CrossRef]
  6. F. An-fu and W. Zhi-wei, “Phase, coherence properties, and the numerical analysis of the field in the nonresonant Jaynes–Cummings model,” Phys. Rev. A 49, 1509–1512 (1994). [CrossRef]
  7. R. H. Xie, G. O. Xu, and D. H. Liu, “Numerical study of non-classical effects and the effect of virtual photon fields in the Jaynes–Cummings model,” Phys. Lett. A 202, 28–33 (1995). [CrossRef]
  8. V. I. Koroli and V. V. Zalamai, “Dynamics of a laser-cooled and trapped radiator interacting with the Holstein–Primakoff SU(1,1) coherent state,” J. Phys. B 42, 035505 (2009). [CrossRef]
  9. M. K. Tavassoly and F. Yadollahi, “Dynamics of states in the nonlinear interaction regime between a three-level atom and generalized coherent states and their non-classical features,” Int. J. Mod. Phys. B 26, 1250027 (2012). [CrossRef]
  10. M. F. Fang and H. E. Liu, “Properties of entropy and phase of the field in the two-photon Jaynes–Cummings model with an added Kerr medium,” Phys. Lett. A 200, 250–256 (1995). [CrossRef]
  11. A. Y. Kazakov, “Modified Jaynes–Cummings model: interaction of the two-level atom with two modes,” Phys. Lett. A 206, 229–234 (1995). [CrossRef]
  12. J. Crnugelj, M. Martinis, and V. Mikuta-Martinis, “Properties of a deformed Jaynes–Cummings model,” Phys. Rev. A 50, 1785–1791 (1994). [CrossRef]
  13. N. H. Abdel-Wahab and M. F. Mourad, “On the interaction between two two-level atoms and a two mode cavity field in the presence of detuning and cross-Kerr nonlinearity,” Phys. Scr. 84, 015401 (2011). [CrossRef]
  14. R. A. Zait, “Nonclassical statistical properties of a three-level atom interacting with a single-mode field in a Kerr medium with intensity dependent coupling,” Phys. Lett. A 319, 461–474 (2003). [CrossRef]
  15. M. J. Faghihi and M. K. Tavassoly, “Dynamics of entropy and nonclassical properties of the state of a Λ-type three-level atom interacting with a single-mode cavity field with intensity-dependent coupling in a Kerr medium,” J. Phys. B 45, 035502 (2012). [CrossRef]
  16. J. L. Guo, Y. B. Sun, and Z. D. Li, “Entropy exchange and entanglement in Jaynes–Cummings model with Kerr-like medium and intensity-depend coupling,” Opt. Commun. 284, 896–901 (2011). [CrossRef]
  17. S. Cordero and J. Récamier, “Algebraic treatment of the time-dependent Jaynes–Cummings Hamiltonian including nonlinear terms,” J. Phys. A 45, 385303 (2012). [CrossRef]
  18. 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).
  19. M. Abdel-Aty and A. S. F. Obada, “Engineering entanglement of a general three-level system interacting with a correlated two-mode nonlinear coherent state,” Eur. Phys. J. D 23, 155–165 (2003). [CrossRef]
  20. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 2001).
  21. G. R. Honarasa and M. K. Tavassoly, “Generalized deformed Kerr states and their physical properties,” Phys. Scr. 86, 035401 (2012). [CrossRef]
  22. N. C. Lindsay, A Concrete Introduction to Higher Algebra, 3rd ed. (Springer, 2008).
  23. G. Benenti, G. Casati, and G. Strini, Principles of Quantum Computation and Information, Vols I and II (World Scientific, 2007).
  24. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).
  25. S. J. D. Phoenix and P. L. Knight, “Establishment of an entangled atom–field state in the Jaynes–Cummings model,” Phys. Rev. A 44, 6023–6029 (1991). [CrossRef]
  26. M. Araki and E. Leib, “Entropy inequalities,” Commun. Math. Phys. 18, 160–170 (1970). [CrossRef]
  27. S. M. Barnett and S. J. D. Phoenix, “Information theory, squeezing, and quantum correlations,” Phys. Rev. A 44, 535–545 (1991). [CrossRef]
  28. S. J. D. Phoenix and P. L. Knight, “Periodicity, phase, and entropy in models of two-photon resonance,” J. Opt. Soc. Am. B 7, 116–124 (1990). [CrossRef]
  29. G. S. Agarwal and S. Singh, “Effect of pump fluctuations on line shapes in coherent anti-Stokes Raman scattering,” Phys. Rev. A 25, 3195–3205 (1982). [CrossRef]
  30. B. Buck and C. V. Sukumar, “Solution of the Heisenberg equations for an atom interacting with radiation,” J. Phys. A 17, 877 (1984). [CrossRef]
  31. F. Eftekhari, and M. K. Tavassoly, “On a general formalism of nonlinear charge coherent states, their quantum statistics and nonclassical properties,” Int. J. Mod. Phys. A 25, 3481–3504 (2010). [CrossRef]
  32. O. Safaeian and M. K. Tavassoly, “Deformed photon-added nonlinear coherent states and their non-classical properties,” J. Phys. A 44, 225301 (2011). [CrossRef]
  33. 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]
  34. E. C. G. Sudarshan, “Diagonal harmonious state representations,” Int. J. Theor. Phys. 32, 1069–1076 (1993). [CrossRef]
  35. M. K. Tavassoly, “New nonlinear coherent states associated with inverse bosonic and f-deformed ladder operators,” J. Phys. A 41, 285305 (2008). [CrossRef]
  36. M. K. Tavassoly, “On the non-classicality features of new classes of nonlinear coherent states,” Opt. Commun. 283, 5081–5091 (2010). [CrossRef]
  37. E. Piroozi and M. K. Tavassoly, “Nonlinear semi-coherent states, their nonclassical features and phase properties,” J. Phys. A 45, 135301 (2012). [CrossRef]
  38. W. Heisenberg, “The actual content of quantum theoretical kinematics and mechanics,” Z. Phys. 43, 172–198 (1927). [CrossRef]
  39. I. Białynicki-Birula and J. Mycielski, “Uncertainty relations for information entropy in wave mechanics,” Commun. Math. Phys. 44, 129–132 (1975). [CrossRef]
  40. G. R. Honarasa, M. K. Tavassoly, and M. Hatami, “Number–phase entropic uncertainty relations and Wigner functions for solvable quantum systems with discrete spectra,” Phys. Lett. A 373, 3931–3936 (2009). [CrossRef]
  41. A. Orłowski, “Information entropy and squeezing of quantum fluctuations,” Phys. Rev. A 56, 2545–2548 (1997). [CrossRef]
  42. G. R. Honarasa, M. K. Tavassoly, and M. Hatami, “Quantum phase properties associated to solvable quantum systems using the nonlinear coherent states approach,” Opt. Commun. 282, 2192–2198 (2009). [CrossRef]
  43. V. I. Manko, G. Marmo, and F. Zaccaria, “Moyal and tomographic probability representations for f-oscillator quantum states,” Phys. Scr. 81, 045004 (2010). [CrossRef]
  44. M. J. Faghihi and M. K. Tavassoly, “Nonlinear quantum optical springs and their nonclassical properties,” Commun. Theor. Phys. 56, 327–332 (2011). [CrossRef]

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