Abstract

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

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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]
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    [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]

2012 (6)

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]

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]

S. Cordero and J. Récamier, “Algebraic treatment of the time-dependent Jaynes–Cummings Hamiltonian including nonlinear terms,” J. Phys. A 45, 385303 (2012).
[CrossRef]

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).

G. R. Honarasa and M. K. Tavassoly, “Generalized deformed Kerr states and their physical properties,” Phys. Scr. 86, 035401 (2012).
[CrossRef]

E. Piroozi and M. K. Tavassoly, “Nonlinear semi-coherent states, their nonclassical features and phase properties,” J. Phys. A 45, 135301 (2012).
[CrossRef]

2011 (4)

O. Safaeian and M. K. Tavassoly, “Deformed photon-added nonlinear coherent states and their non-classical properties,” J. Phys. A 44, 225301 (2011).
[CrossRef]

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]

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]

M. J. Faghihi and M. K. Tavassoly, “Nonlinear quantum optical springs and their nonclassical properties,” Commun. Theor. Phys. 56, 327–332 (2011).
[CrossRef]

2010 (3)

V. I. Manko, G. Marmo, and F. Zaccaria, “Moyal and tomographic probability representations for f-oscillator quantum states,” Phys. Scr. 81, 045004 (2010).
[CrossRef]

M. K. Tavassoly, “On the non-classicality features of new classes of nonlinear coherent states,” Opt. Commun. 283, 5081–5091 (2010).
[CrossRef]

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]

2009 (3)

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]

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]

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]

2008 (1)

M. K. Tavassoly, “New nonlinear coherent states associated with inverse bosonic and f-deformed ladder operators,” J. Phys. A 41, 285305 (2008).
[CrossRef]

2003 (2)

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]

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]

1997 (2)

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]

A. Orłowski, “Information entropy and squeezing of quantum fluctuations,” Phys. Rev. A 56, 2545–2548 (1997).
[CrossRef]

1995 (3)

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]

A. Y. Kazakov, “Modified Jaynes–Cummings model: interaction of the two-level atom with two modes,” Phys. Lett. A 206, 229–234 (1995).
[CrossRef]

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]

1994 (2)

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]

J. Crnugelj, M. Martinis, and V. Mikuta-Martinis, “Properties of a deformed Jaynes–Cummings model,” Phys. Rev. A 50, 1785–1791 (1994).
[CrossRef]

1993 (1)

E. C. G. Sudarshan, “Diagonal harmonious state representations,” Int. J. Theor. Phys. 32, 1069–1076 (1993).
[CrossRef]

1991 (2)

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]

S. M. Barnett and S. J. D. Phoenix, “Information theory, squeezing, and quantum correlations,” Phys. Rev. A 44, 535–545 (1991).
[CrossRef]

1990 (1)

1989 (1)

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]

1984 (1)

B. Buck and C. V. Sukumar, “Solution of the Heisenberg equations for an atom interacting with radiation,” J. Phys. A 17, 877 (1984).
[CrossRef]

1982 (1)

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]

1981 (2)

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]

C. V. Sukumar and B. Buck, “Multi-phonon generalisation of the Jaynes–Cummings model,” Phys. Lett. A 83, 211–213(1981).
[CrossRef]

1975 (1)

I. Białynicki-Birula and J. Mycielski, “Uncertainty relations for information entropy in wave mechanics,” Commun. Math. Phys. 44, 129–132 (1975).
[CrossRef]

1970 (1)

M. Araki and E. Leib, “Entropy inequalities,” Commun. Math. Phys. 18, 160–170 (1970).
[CrossRef]

1965 (1)

F. W. Cummings, “Stimulated emission of radiation in a single mode,” Phys. Rev. A 140, 1051–1056 (1965).
[CrossRef]

1963 (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]

1927 (1)

W. Heisenberg, “The actual content of quantum theoretical kinematics and mechanics,” Z. Phys. 43, 172–198 (1927).
[CrossRef]

Abdel-Aty, M.

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]

Abdel-Wahab, N. H.

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]

Agarwal, G. S.

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]

An-fu, F.

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]

Araki, M.

M. Araki and E. Leib, “Entropy inequalities,” Commun. Math. Phys. 18, 160–170 (1970).
[CrossRef]

Barnett, S. M.

S. M. Barnett and S. J. D. Phoenix, “Information theory, squeezing, and quantum correlations,” Phys. Rev. A 44, 535–545 (1991).
[CrossRef]

Benenti, G.

G. Benenti, G. Casati, and G. Strini, Principles of Quantum Computation and Information, Vols I and II (World Scientific, 2007).

Bialynicki-Birula, I.

I. Białynicki-Birula and J. Mycielski, “Uncertainty relations for information entropy in wave mechanics,” Commun. Math. Phys. 44, 129–132 (1975).
[CrossRef]

Buck, B.

B. Buck and C. V. Sukumar, “Solution of the Heisenberg equations for an atom interacting with radiation,” J. Phys. A 17, 877 (1984).
[CrossRef]

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]

C. V. Sukumar and B. Buck, “Multi-phonon generalisation of the Jaynes–Cummings model,” Phys. Lett. A 83, 211–213(1981).
[CrossRef]

Bužek, V.

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]

Casati, G.

G. Benenti, G. Casati, and G. Strini, Principles of Quantum Computation and Information, Vols I and II (World Scientific, 2007).

Chuang, I. L.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).

Cordero, S.

S. Cordero and J. Récamier, “Algebraic treatment of the time-dependent Jaynes–Cummings Hamiltonian including nonlinear terms,” J. Phys. A 45, 385303 (2012).
[CrossRef]

Crnugelj, J.

J. Crnugelj, M. Martinis, and V. Mikuta-Martinis, “Properties of a deformed Jaynes–Cummings model,” Phys. Rev. A 50, 1785–1791 (1994).
[CrossRef]

Cummings, F. W.

F. W. Cummings, “Stimulated emission of radiation in a single mode,” Phys. Rev. A 140, 1051–1056 (1965).
[CrossRef]

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]

de los Santos-Sánchez, O.

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).

Eftekhari, F.

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]

Faghihi, M. J.

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]

M. J. Faghihi and M. K. Tavassoly, “Nonlinear quantum optical springs and their nonclassical properties,” Commun. Theor. Phys. 56, 327–332 (2011).
[CrossRef]

Fang, M. F.

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]

Guo, J. L.

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]

Hatami, M.

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]

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]

Heisenberg, W.

W. Heisenberg, “The actual content of quantum theoretical kinematics and mechanics,” Z. Phys. 43, 172–198 (1927).
[CrossRef]

Honarasa, G. R.

G. R. Honarasa and M. K. Tavassoly, “Generalized deformed Kerr states and their physical properties,” Phys. Scr. 86, 035401 (2012).
[CrossRef]

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]

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]

Jaynes, E. T.

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]

Kazakov, A. Y.

A. Y. Kazakov, “Modified Jaynes–Cummings model: interaction of the two-level atom with two modes,” Phys. Lett. A 206, 229–234 (1995).
[CrossRef]

Knight, P. L.

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]

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]

Koroli, V. I.

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]

Leib, E.

M. Araki and E. Leib, “Entropy inequalities,” Commun. Math. Phys. 18, 160–170 (1970).
[CrossRef]

Li, Z. D.

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]

Lindsay, N. C.

N. C. Lindsay, A Concrete Introduction to Higher Algebra, 3rd ed. (Springer, 2008).

Liu, D. H.

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]

Liu, H. E.

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]

Man’ko, V. I.

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]

Manko, V. I.

V. I. Manko, G. Marmo, and F. Zaccaria, “Moyal and tomographic probability representations for f-oscillator quantum states,” Phys. Scr. 81, 045004 (2010).
[CrossRef]

Marmo, G.

V. I. Manko, G. Marmo, and F. Zaccaria, “Moyal and tomographic probability representations for f-oscillator quantum states,” Phys. Scr. 81, 045004 (2010).
[CrossRef]

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]

Martinis, M.

J. Crnugelj, M. Martinis, and V. Mikuta-Martinis, “Properties of a deformed Jaynes–Cummings model,” Phys. Rev. A 50, 1785–1791 (1994).
[CrossRef]

Mikuta-Martinis, V.

J. Crnugelj, M. Martinis, and V. Mikuta-Martinis, “Properties of a deformed Jaynes–Cummings model,” Phys. Rev. A 50, 1785–1791 (1994).
[CrossRef]

Mourad, M. F.

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]

Mycielski, J.

I. Białynicki-Birula and J. Mycielski, “Uncertainty relations for information entropy in wave mechanics,” Commun. Math. Phys. 44, 129–132 (1975).
[CrossRef]

Nielsen, M. A.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).

Obada, A. S. F.

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]

Orlowski, A.

A. Orłowski, “Information entropy and squeezing of quantum fluctuations,” Phys. Rev. A 56, 2545–2548 (1997).
[CrossRef]

Phoenix, S. J. D.

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]

S. M. Barnett and S. J. D. Phoenix, “Information theory, squeezing, and quantum correlations,” Phys. Rev. A 44, 535–545 (1991).
[CrossRef]

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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).

S. Cordero and J. Récamier, “Algebraic treatment of the time-dependent Jaynes–Cummings Hamiltonian including nonlinear terms,” J. Phys. A 45, 385303 (2012).
[CrossRef]

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O. Safaeian and M. K. Tavassoly, “Deformed photon-added nonlinear coherent states and their non-classical properties,” J. Phys. A 44, 225301 (2011).
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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).
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[CrossRef]

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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).
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C. V. Sukumar and B. Buck, “Multi-phonon generalisation of the Jaynes–Cummings model,” Phys. Lett. A 83, 211–213(1981).
[CrossRef]

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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]

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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).
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E. Piroozi and M. K. Tavassoly, “Nonlinear semi-coherent states, their nonclassical features and phase properties,” J. Phys. A 45, 135301 (2012).
[CrossRef]

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]

G. R. Honarasa and M. K. Tavassoly, “Generalized deformed Kerr states and their physical properties,” Phys. Scr. 86, 035401 (2012).
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O. Safaeian and M. K. Tavassoly, “Deformed photon-added nonlinear coherent states and their non-classical properties,” J. Phys. A 44, 225301 (2011).
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M. K. Tavassoly, “On the non-classicality features of new classes of nonlinear coherent states,” Opt. Commun. 283, 5081–5091 (2010).
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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).
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Int. J. Mod. Phys. A (1)

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]

Int. J. Mod. Phys. B (1)

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]

Int. J. Theor. Phys. (1)

E. C. G. Sudarshan, “Diagonal harmonious state representations,” Int. J. Theor. Phys. 32, 1069–1076 (1993).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. A (5)

B. Buck and C. V. Sukumar, “Solution of the Heisenberg equations for an atom interacting with radiation,” J. Phys. A 17, 877 (1984).
[CrossRef]

M. K. Tavassoly, “New nonlinear coherent states associated with inverse bosonic and f-deformed ladder operators,” J. Phys. A 41, 285305 (2008).
[CrossRef]

E. Piroozi and M. K. Tavassoly, “Nonlinear semi-coherent states, their nonclassical features and phase properties,” J. Phys. A 45, 135301 (2012).
[CrossRef]

O. Safaeian and M. K. Tavassoly, “Deformed photon-added nonlinear coherent states and their non-classical properties,” J. Phys. A 44, 225301 (2011).
[CrossRef]

S. Cordero and J. Récamier, “Algebraic treatment of the time-dependent Jaynes–Cummings Hamiltonian including nonlinear terms,” J. Phys. A 45, 385303 (2012).
[CrossRef]

J. Phys. B (3)

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).

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]

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]

Opt. Commun. (3)

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]

M. K. Tavassoly, “On the non-classicality features of new classes of nonlinear coherent states,” Opt. Commun. 283, 5081–5091 (2010).
[CrossRef]

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]

Phys. Lett. A (7)

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]

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]

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).
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[CrossRef]

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]

C. V. Sukumar and B. Buck, “Multi-phonon generalisation of the Jaynes–Cummings model,” Phys. Lett. A 83, 211–213(1981).
[CrossRef]

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[CrossRef]

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).
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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]

S. M. Barnett and S. J. D. Phoenix, “Information theory, squeezing, and quantum correlations,” Phys. Rev. A 44, 535–545 (1991).
[CrossRef]

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]

A. Orłowski, “Information entropy and squeezing of quantum fluctuations,” Phys. Rev. A 56, 2545–2548 (1997).
[CrossRef]

Phys. Scr. (4)

V. I. Manko, G. Marmo, and F. Zaccaria, “Moyal and tomographic probability representations for f-oscillator quantum states,” Phys. Scr. 81, 045004 (2010).
[CrossRef]

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]

G. R. Honarasa and M. K. Tavassoly, “Generalized deformed Kerr states and their physical properties,” Phys. Scr. 86, 035401 (2012).
[CrossRef]

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).
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Other (4)

N. C. Lindsay, A Concrete Introduction to Higher Algebra, 3rd ed. (Springer, 2008).

G. Benenti, G. Casati, and G. Strini, Principles of Quantum Computation and Information, Vols I and II (World Scientific, 2007).

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 2001).

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Figures (3)

Fig. 1.
Fig. 1.

Three-level atomic structure for Λ-type configuration.

Fig. 2.
Fig. 2.

Entropy evolution of the field versus scaled time τ=λt, when the atom and field are assumed to be initially in the excited state and in a coherent state with |α1|2=10=|α2|2, respectively. The left plots correspond to the absence of the intensity-dependent atom–field coupling, f(n)=1, and the right plots show the presence of the intensity-dependent atom–field coupling, fi(ni)=ni. Also, (a) χ=0 and Δ2=Δ3=0; (b) χ=0.4λ, Δ2=Δ3=0, and gi(ni)=1; (c) χ=0.4λ, Δ2=Δ3=0, and gi(ni)=1/ni; (d) χ=0, Δ2=7λ, and Δ3=15λ; (e) χ=0.4λ, Δ2=7λ, Δ3=15λ, and gi(ni)=1; (f) χ=0.4λ, Δ2=7λ, Δ3=15λ, and gi(ni)=1/ni.

Fig. 3.
Fig. 3.

Entropy squeezing in the position component for chosen parameters similar to Fig. 2.

Equations (32)

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H^=H^0+H^1,
H^0=i=13ωiσ^ii+j=12Ωja^ja^j,
H^1=χR^1R^1R^2R^2+λ1(A^1σ^12+σ^21A^1)+λ2(A^2σ^13+σ^31A^2),
[R^j,n^j]=R^j,[R^j,n^j]=R^j,[R^i,R^j]=0,
[A^j,n^j]=A^j,[A^j,n^j]=A^j,[A^i,A^j]=0,
H^1int=χ+λ1(a^1a^1a^1σ^12+σ^21a^1a^1a^1)+λ2(a^2a^2a^2σ^13+σ^31a^2a^2a^2).
|ψ(t)=n1=0n2=0qn1qn2[A(n1,n2,t)eiγ1t|1,n1,n2+B(n1+1,n2,t)eiγ2t|2,n1+1,n2+C(n1,n2+1,t)eiγ3t|3,n1,n2+1],
γ1=ω1+n1Ω1+n2Ω2,γ2=ω2+(n1+1)Ω1+n2Ω2,γ3=ω3+n1Ω1+(n2+1)Ω2.
it|ψ(t)=H^|ψ(t),
iA˙=VAA+κ1BeiΔ2t+κ2CeiΔ3t,iB˙=VBB+κ1AeiΔ2t,iC˙=VCC+κ2AeiΔ3t,
Δ2=ω2ω1+Ω1,Δ3=ω3ω1+Ω2,
VA=V(n1,n2),VB=V(n1+1,n2),VC=V(n1,n2+1),κ1=λ1n1+1f1(n1+1),κ2=λ2n2+1f2(n2+1),
V(n1,n2)=χn1n2g12(n1)g22(n2).
μ3+x1μ2+x2μ+x3=0,
x1=VA+VB+VC+Δ32Δ2,x2=(VA+VBΔ2)(VC+Δ3Δ2)+VB(VAΔ2)κ12κ22,x3=VB[(VAΔ2)(VC+Δ3Δ2)κ22]κ12(VC+Δ3Δ2).
B(t)=j=13b˜jeiμjt,b˜j=κ1bj.
μj=13x1+23x123x2cos[θ+23(j1)π],j=1,2,3,θ=13cos1[9x1x22x1327x32(x123x2)3/2],
A(n1,n2,t)=eiΔ2tj=13(μj+VB)bjeiμjt,B(n1+1,n2,t)=j=13κ1bjeiμjt,C(n1,n2+1,t)=1κ2ei(Δ3Δ2)tj=13[(μj+VB)(μj+VAΔ2)κ12]bjeiμjt,
bj=μk+μl+VA+VBΔ2μjkμjl,jkl=1,2,3,
|SA(t)SF(t)|SAF(t)SA(t)+SF(t),
SA(F)(t)=TrA(F)(ρ^A(F)(t)lnρ^A(F)(t)).
ρ^A(t)=TrF(|ψ(t)ψ(t)|)=(ρ11ρ12ρ13ρ21ρ22ρ23ρ31ρ32ρ33),
ρ11=n1=0+n2=0+qn1qn1*qn2qn2*A(n1,n2,t)A*(n1,n2,t),ρ12=n1=0+n2=0+qn1+1qn1*qn2qn2*A(n1+1,n2,t)B*(n1+1,n2,t)exp(iΔ2t)=ρ21*,ρ13=n1=0+n2=0+qn1qn1*qn2+1qn2*A(n1,n2+1,t)C*(n1,n2+1,t)exp(iΔ3t)=ρ31*,ρ22=n1=0+n2=0+qn1qn1*qn2qn2*B(n1+1,n2,t)B*(n1+1,n2,t),
ρ23=n1=0+n2=0+qn1qn1+1*qn2+1qn2*B(n1+1,n2+1,t)C*(n1+1,n2+1,t)exp(i(Δ3Δ2)t)=ρ32*,ρ33=n1=0+n2=0+qn1qn1*qn2qn2*C(n1,n2+1,t)C*(n1,n2+1,t),
DEM(t)=SF(t)=SA(t)=j=13ξjlnξj,
ξj=13α1+23α123α2cos[β+23(j1)π],β=13cos1[9α1α22α1327α32(α123α2)3/2],
α1=ρ11ρ22ρ33,α2=ρ11ρ22+ρ22ρ33+ρ33ρ11ρ12ρ21ρ23ρ32ρ31ρ13,α3=ρ11ρ22ρ33ρ12ρ23ρ31ρ13ρ32ρ21+ρ11ρ23ρ32+ρ22ρ31ρ13+ρ33ρ12ρ21.
|αi=ni=0+qni|ni,qni=exp(|αi|22)αinini!,i=1,2.
δx=exp(Ex)=exp(+x|ρ^F|xlnx|ρ^F|xdx),δp=exp(Ep)=exp(+p|ρ^F|plnp|ρ^F|pdp),
x|ρ^F|x=|n1=0+n2=0+qn1qn2A(n1,n2,t)x|n1|2+|n1=0+n2=0+qn1qn2B(n1+1,n2,t)x|n1+1|2+|n1=0+n2=0+qn1qn2C(n1,n2+1,t)x|n1|2,
x|n1=[exp(x2)π2n1n1!]1/2Hn1(x),
EX(t)=(πe)1/2exp(Ex(t))1,EP(t)=(πe)1/2exp(Ep(t))1.

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