Abstract

In this paper, we follow the model presented in our previous work [J. Opt. Soc. Am. B 30, 1109 (2013)], in which the interaction between a Λ-type three-level atom and a quantized two-mode radiation field in a cavity in the presence of nonlinearities was studied. After giving a brief review of the procedure for obtaining the state vector of the atom-field system, we investigated some further interesting and important physical features of the whole system state, which are of particular interest to the quantum optics field of research, i.e., the number-phase entropic uncertainty relation (based on the two-mode Pegg–Barnett formalism) and a few of the nonclassicality signs that consist of sub-Poissonian statistics, Cauchy–Schwartz inequality, and two types of squeezing phenomena. During our presentation, the effects of intensity-dependent coupling, deformed Kerr medium, and the detuning parameters on the depth and domain of each of the mentioned nonclassical criteria of the considered quantum system are described in detail. The results show that each of the mentioned nonclassicality aspects can be obtained by appropriately choosing the related parameters.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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. 140, A1051–A1056 (1965).
    [CrossRef]
  3. B. W. Shore and P. L. Knight, “The Jaynes–Cummings model,” J. Mod. Opt. 40, 1195–1238 (1993).
    [CrossRef]
  4. G. Rempe, H. Walther, and N. Klein, “One-atom maser,” Phys. Rev. Lett. 54, 551–554 (1987).
  5. 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]
  6. C. V. Sukumar and B. Buck, “Multi-phonon generalisation of the Jaynes–Cummings model,” Phys. Lett. A 83, 211–213 (1981).
    [CrossRef]
  7. Sh. Barzanjeh, M. H. Naderi, and M. Soltanolkotabi, “Back-action ground-state cooling of a micromechanical membrane via intensity-dependent interaction,” Phys. Rev. A 84, 023803 (2011).
    [CrossRef]
  8. Sh. Barzanjeh, M. H. Naderi, and M. Soltanolkotabi, “Steady-state entanglement and normal-mode splitting in an atom-assisted optomechanical system with intensity-dependent coupling,” Phys. Rev. A 84, 063850 (2011).
    [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. H. Naderi, “The Jaynes–Cummings model beyond the rotating-wave approximation as an intensity-dependent model: quantum statistical and phase properties,” J. Phys. A 44, 055304 (2011).
    [CrossRef]
  11. 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]
  12. S. R. Miry and M. K. Tavassoly, “Generation of a class of SU(1,1) coherent states of the Gilmore–Perelomov type and a class of SU(2) coherent states and their superposition,” Phys. Scr. 85, 035404 (2012).
    [CrossRef]
  13. S. R. Miry, M. Shahpari, and M. K. Tavassoly, “Nonlinear elliptical states: generation and nonclassical properties,” Opt. Commun. 306, 49–56 (2013).
    [CrossRef]
  14. G. R. Honarasa and M. K. Tavassoly, “Generalized deformed Kerr states and their physical properties,” Phys. Scr. 86, 035401 (2012).
    [CrossRef]
  15. 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).
    [CrossRef]
  16. M. Hillery, “Quantum cryptography with squeezed states,” Phys. Rev. A 61, 022309 (2000).
    [CrossRef]
  17. S. F. Pereira, Z. Y. Ou, and H. J. Kimble, “Quantum communication with correlated nonclassical states,” Phys. Rev. A 62, 042311 (2000).
    [CrossRef]
  18. V. V. Dodonov, “‘Nonclassical’ states in quantum optics: a ‘squeezed’ review of the first 75 years,” J. Opt. B 4, R1–R33 (2002).
    [CrossRef]
  19. R. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766–2788 (1963).
    [CrossRef]
  20. J. R. Klauder, “Continuous representation theory. I. Postulates of continuous representation theory,” J. Math. Phys. 4, 1055–1058 (1963).
    [CrossRef]
  21. E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Phys. Rev. Lett. 10, 277–279 (1963).
    [CrossRef]
  22. H. T. Dung, R. Tanaś, and A. S. Shumovsky, “Collapses, revivals, and phase properties of the field in Jaynes–Cummings type models,” Opt. Commun. 79, 462–468 (1990).
    [CrossRef]
  23. D. T. Pegg and S. M. Barnett, “Phase properties of the quantized single-mode electromagnetic field,” Phys. Rev. A 39, 1665–1675 (1989).
    [CrossRef]
  24. M. D. Reid and D. F. Walls, “Violations of classical inequalities in quantum optics,” Phys. Rev. A 34, 1260–1276 (1986).
    [CrossRef]
  25. R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903–1905 (1987).
    [CrossRef]
  26. C. M. Caves and B. L. Schumaker, “New formalism for two-photon quantum optics. I. Quadrature phases and squeezed states,” Phys. Rev. A 31, 3068–3092 (1985).
    [CrossRef]
  27. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).
  28. M. Hillery, “Sum and difference squeezing of the electromagnetic field,” Phys. Rev. A 40, 3147–3155 (1989).
    [CrossRef]
  29. 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]
  30. E. C. G. Sudarshan, “Diagonal harmonious state representations,” Int. J. Theor. Phys. 32, 1069–1076 (1993).
    [CrossRef]
  31. M. K. Tavassoly, “New nonlinear coherent states associated with inverse bosonic and f-deformed ladder operators,” J. Phys. A 41, 285305 (2008).
    [CrossRef]
  32. M. K. Tavassoly, “On the non-classicality features of new classes of nonlinear coherent states,” Opt. Commun. 283, 5081–5091 (2010).
    [CrossRef]
  33. E. Piroozi and M. K. Tavassoly, “Nonlinear semi-coherent states, their nonclassical features and phase properties,” J. Phys. A 45, 135301 (2012).
    [CrossRef]
  34. M. Nakano and K. Yamaguchi, “Quantum-phase dynamics of dimer systems interacting with a two-mode squeezed coherent field,” J. Chem. Phys. 116, 10069–10082 (2002).
    [CrossRef]
  35. 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]
  36. 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]
  37. L. Mandel, “Sub-Poissonian photon statistics in resonance fluorescence,” Opt. Lett. 4, 205–207 (1979).
    [CrossRef]
  38. G. S. Agarwal, “Nonclassical statistics of fields in pair coherent states,” J. Opt. Soc. Am. B 5, 1940–1947 (1988).
    [CrossRef]
  39. C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge University, 2005).
  40. M. K. Tavassoly, “Gazeau-Klauder squeezed states associated with solvable quantum systems,” J. Phys. A 39, 11583–11597 (2006).
    [CrossRef]
  41. G. R. Honarasa, M. K. Tavassoly, and M. Hatami, “Generalized coherent states for solvable quantum systems with degenerate discrete spectra and their nonclassical properties,” Physica A 390, 1381–1392 (2011).
    [CrossRef]
  42. M. J. Faghihi and M. K. Tavassoly, “Nonlinear quantum optical springs and their nonclassical properties,” Commun. Theor. Phys. 56, 327–332 (2011).
    [CrossRef]
  43. G. R. Honarasa, M. K. Tavassoly, and M. Hatami, “Quantum phase distribution and the number-phase Wigner function of generalized squeezed vacuum states associated with solvable quantum systems,” Chin. Phys. B 21, 054208 (2012).
    [CrossRef]

2013 (2)

2012 (6)

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

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. R. Miry and M. K. Tavassoly, “Generation of a class of SU(1,1) coherent states of the Gilmore–Perelomov type and a class of SU(2) coherent states and their superposition,” Phys. Scr. 85, 035404 (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]

G. R. Honarasa, M. K. Tavassoly, and M. Hatami, “Quantum phase distribution and the number-phase Wigner function of generalized squeezed vacuum states associated with solvable quantum systems,” Chin. Phys. B 21, 054208 (2012).
[CrossRef]

2011 (5)

G. R. Honarasa, M. K. Tavassoly, and M. Hatami, “Generalized coherent states for solvable quantum systems with degenerate discrete spectra and their nonclassical properties,” Physica A 390, 1381–1392 (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]

M. H. Naderi, “The Jaynes–Cummings model beyond the rotating-wave approximation as an intensity-dependent model: quantum statistical and phase properties,” J. Phys. A 44, 055304 (2011).
[CrossRef]

Sh. Barzanjeh, M. H. Naderi, and M. Soltanolkotabi, “Back-action ground-state cooling of a micromechanical membrane via intensity-dependent interaction,” Phys. Rev. A 84, 023803 (2011).
[CrossRef]

Sh. Barzanjeh, M. H. Naderi, and M. Soltanolkotabi, “Steady-state entanglement and normal-mode splitting in an atom-assisted optomechanical system with intensity-dependent coupling,” Phys. Rev. A 84, 063850 (2011).
[CrossRef]

2010 (1)

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

2009 (2)

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]

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]

2006 (1)

M. K. Tavassoly, “Gazeau-Klauder squeezed states associated with solvable quantum systems,” J. Phys. A 39, 11583–11597 (2006).
[CrossRef]

2002 (2)

M. Nakano and K. Yamaguchi, “Quantum-phase dynamics of dimer systems interacting with a two-mode squeezed coherent field,” J. Chem. Phys. 116, 10069–10082 (2002).
[CrossRef]

V. V. Dodonov, “‘Nonclassical’ states in quantum optics: a ‘squeezed’ review of the first 75 years,” J. Opt. B 4, R1–R33 (2002).
[CrossRef]

2000 (2)

M. Hillery, “Quantum cryptography with squeezed states,” Phys. Rev. A 61, 022309 (2000).
[CrossRef]

S. F. Pereira, Z. Y. Ou, and H. J. Kimble, “Quantum communication with correlated nonclassical states,” Phys. Rev. A 62, 042311 (2000).
[CrossRef]

1997 (1)

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]

1993 (2)

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

B. W. Shore and P. L. Knight, “The Jaynes–Cummings model,” J. Mod. Opt. 40, 1195–1238 (1993).
[CrossRef]

1990 (1)

H. T. Dung, R. Tanaś, and A. S. Shumovsky, “Collapses, revivals, and phase properties of the field in Jaynes–Cummings type models,” Opt. Commun. 79, 462–468 (1990).
[CrossRef]

1989 (2)

D. T. Pegg and S. M. Barnett, “Phase properties of the quantized single-mode electromagnetic field,” Phys. Rev. A 39, 1665–1675 (1989).
[CrossRef]

M. Hillery, “Sum and difference squeezing of the electromagnetic field,” Phys. Rev. A 40, 3147–3155 (1989).
[CrossRef]

1988 (1)

1987 (2)

R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903–1905 (1987).
[CrossRef]

G. Rempe, H. Walther, and N. Klein, “One-atom maser,” Phys. Rev. Lett. 54, 551–554 (1987).

1986 (1)

M. D. Reid and D. F. Walls, “Violations of classical inequalities in quantum optics,” Phys. Rev. A 34, 1260–1276 (1986).
[CrossRef]

1985 (1)

C. M. Caves and B. L. Schumaker, “New formalism for two-photon quantum optics. I. Quadrature phases and squeezed states,” Phys. Rev. A 31, 3068–3092 (1985).
[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]

1979 (1)

1965 (1)

F. W. Cummings, “Stimulated emission of radiation in a single mode,” Phys. Rev. 140, A1051–A1056 (1965).
[CrossRef]

1963 (4)

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]

R. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766–2788 (1963).
[CrossRef]

J. R. Klauder, “Continuous representation theory. I. Postulates of continuous representation theory,” J. Math. Phys. 4, 1055–1058 (1963).
[CrossRef]

E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Phys. Rev. Lett. 10, 277–279 (1963).
[CrossRef]

Agarwal, G. S.

Barnett, S. M.

D. T. Pegg and S. M. Barnett, “Phase properties of the quantized single-mode electromagnetic field,” Phys. Rev. A 39, 1665–1675 (1989).
[CrossRef]

Barzanjeh, Sh.

Sh. Barzanjeh, M. H. Naderi, and M. Soltanolkotabi, “Back-action ground-state cooling of a micromechanical membrane via intensity-dependent interaction,” Phys. Rev. A 84, 023803 (2011).
[CrossRef]

Sh. Barzanjeh, M. H. Naderi, and M. Soltanolkotabi, “Steady-state entanglement and normal-mode splitting in an atom-assisted optomechanical system with intensity-dependent coupling,” Phys. Rev. A 84, 063850 (2011).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

Buck, B.

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

Caves, C. M.

C. M. Caves and B. L. Schumaker, “New formalism for two-photon quantum optics. I. Quadrature phases and squeezed states,” Phys. Rev. A 31, 3068–3092 (1985).
[CrossRef]

Cummings, F. W.

F. W. Cummings, “Stimulated emission of radiation in a single mode,” Phys. Rev. 140, A1051–A1056 (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]

Dodonov, V. V.

V. V. Dodonov, “‘Nonclassical’ states in quantum optics: a ‘squeezed’ review of the first 75 years,” J. Opt. B 4, R1–R33 (2002).
[CrossRef]

Dung, H. T.

H. T. Dung, R. Tanaś, and A. S. Shumovsky, “Collapses, revivals, and phase properties of the field in Jaynes–Cummings type models,” Opt. Commun. 79, 462–468 (1990).
[CrossRef]

Faghihi, M. J.

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).
[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]

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

Gerry, C. C.

C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge University, 2005).

Ghosh, R.

R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903–1905 (1987).
[CrossRef]

Glauber, R. J.

R. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766–2788 (1963).
[CrossRef]

Hatami, M.

G. R. Honarasa, M. K. Tavassoly, and M. Hatami, “Quantum phase distribution and the number-phase Wigner function of generalized squeezed vacuum states associated with solvable quantum systems,” Chin. Phys. B 21, 054208 (2012).
[CrossRef]

G. R. Honarasa, M. K. Tavassoly, and M. Hatami, “Generalized coherent states for solvable quantum systems with degenerate discrete spectra and their nonclassical properties,” Physica A 390, 1381–1392 (2011).
[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]

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]

Hillery, M.

M. Hillery, “Quantum cryptography with squeezed states,” Phys. Rev. A 61, 022309 (2000).
[CrossRef]

M. Hillery, “Sum and difference squeezing of the electromagnetic field,” Phys. Rev. A 40, 3147–3155 (1989).
[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 distribution and the number-phase Wigner function of generalized squeezed vacuum states associated with solvable quantum systems,” Chin. Phys. B 21, 054208 (2012).
[CrossRef]

G. R. Honarasa, M. K. Tavassoly, and M. Hatami, “Generalized coherent states for solvable quantum systems with degenerate discrete spectra and their nonclassical properties,” Physica A 390, 1381–1392 (2011).
[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]

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]

Hooshmandasl, M. R.

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]

Kimble, H. J.

S. F. Pereira, Z. Y. Ou, and H. J. Kimble, “Quantum communication with correlated nonclassical states,” Phys. Rev. A 62, 042311 (2000).
[CrossRef]

Klauder, J. R.

J. R. Klauder, “Continuous representation theory. I. Postulates of continuous representation theory,” J. Math. Phys. 4, 1055–1058 (1963).
[CrossRef]

Klein, N.

G. Rempe, H. Walther, and N. Klein, “One-atom maser,” Phys. Rev. Lett. 54, 551–554 (1987).

Knight, P. L.

B. W. Shore and P. L. Knight, “The Jaynes–Cummings model,” J. Mod. Opt. 40, 1195–1238 (1993).
[CrossRef]

C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge University, 2005).

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]

Mandel, L.

R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903–1905 (1987).
[CrossRef]

L. Mandel, “Sub-Poissonian photon statistics in resonance fluorescence,” Opt. Lett. 4, 205–207 (1979).
[CrossRef]

Marmo, G.

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]

Miry, S. R.

S. R. Miry, M. Shahpari, and M. K. Tavassoly, “Nonlinear elliptical states: generation and nonclassical properties,” Opt. Commun. 306, 49–56 (2013).
[CrossRef]

S. R. Miry and M. K. Tavassoly, “Generation of a class of SU(1,1) coherent states of the Gilmore–Perelomov type and a class of SU(2) coherent states and their superposition,” Phys. Scr. 85, 035404 (2012).
[CrossRef]

Naderi, M. H.

M. H. Naderi, “The Jaynes–Cummings model beyond the rotating-wave approximation as an intensity-dependent model: quantum statistical and phase properties,” J. Phys. A 44, 055304 (2011).
[CrossRef]

Sh. Barzanjeh, M. H. Naderi, and M. Soltanolkotabi, “Back-action ground-state cooling of a micromechanical membrane via intensity-dependent interaction,” Phys. Rev. A 84, 023803 (2011).
[CrossRef]

Sh. Barzanjeh, M. H. Naderi, and M. Soltanolkotabi, “Steady-state entanglement and normal-mode splitting in an atom-assisted optomechanical system with intensity-dependent coupling,” Phys. Rev. A 84, 063850 (2011).
[CrossRef]

Nakano, M.

M. Nakano and K. Yamaguchi, “Quantum-phase dynamics of dimer systems interacting with a two-mode squeezed coherent field,” J. Chem. Phys. 116, 10069–10082 (2002).
[CrossRef]

Ou, Z. Y.

S. F. Pereira, Z. Y. Ou, and H. J. Kimble, “Quantum communication with correlated nonclassical states,” Phys. Rev. A 62, 042311 (2000).
[CrossRef]

Pegg, D. T.

D. T. Pegg and S. M. Barnett, “Phase properties of the quantized single-mode electromagnetic field,” Phys. Rev. A 39, 1665–1675 (1989).
[CrossRef]

Pereira, S. F.

S. F. Pereira, Z. Y. Ou, and H. J. Kimble, “Quantum communication with correlated nonclassical states,” Phys. Rev. A 62, 042311 (2000).
[CrossRef]

Piroozi, E.

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

Reid, M. D.

M. D. Reid and D. F. Walls, “Violations of classical inequalities in quantum optics,” Phys. Rev. A 34, 1260–1276 (1986).
[CrossRef]

Rempe, G.

G. Rempe, H. Walther, and N. Klein, “One-atom maser,” Phys. Rev. Lett. 54, 551–554 (1987).

Schumaker, B. L.

C. M. Caves and B. L. Schumaker, “New formalism for two-photon quantum optics. I. Quadrature phases and squeezed states,” Phys. Rev. A 31, 3068–3092 (1985).
[CrossRef]

Shahpari, M.

S. R. Miry, M. Shahpari, and M. K. Tavassoly, “Nonlinear elliptical states: generation and nonclassical properties,” Opt. Commun. 306, 49–56 (2013).
[CrossRef]

Shore, B. W.

B. W. Shore and P. L. Knight, “The Jaynes–Cummings model,” J. Mod. Opt. 40, 1195–1238 (1993).
[CrossRef]

Shumovsky, A. S.

H. T. Dung, R. Tanaś, and A. S. Shumovsky, “Collapses, revivals, and phase properties of the field in Jaynes–Cummings type models,” Opt. Commun. 79, 462–468 (1990).
[CrossRef]

Soltanolkotabi, M.

Sh. Barzanjeh, M. H. Naderi, and M. Soltanolkotabi, “Steady-state entanglement and normal-mode splitting in an atom-assisted optomechanical system with intensity-dependent coupling,” Phys. Rev. A 84, 063850 (2011).
[CrossRef]

Sh. Barzanjeh, M. H. Naderi, and M. Soltanolkotabi, “Back-action ground-state cooling of a micromechanical membrane via intensity-dependent interaction,” Phys. Rev. A 84, 023803 (2011).
[CrossRef]

Sudarshan, E. C. G.

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]

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

E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Phys. Rev. Lett. 10, 277–279 (1963).
[CrossRef]

Sukumar, C. V.

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]

Tanas, R.

H. T. Dung, R. Tanaś, and A. S. Shumovsky, “Collapses, revivals, and phase properties of the field in Jaynes–Cummings type models,” Opt. Commun. 79, 462–468 (1990).
[CrossRef]

Tavassoly, M. K.

S. R. Miry, M. Shahpari, and M. K. Tavassoly, “Nonlinear elliptical states: generation and nonclassical properties,” Opt. Commun. 306, 49–56 (2013).
[CrossRef]

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).
[CrossRef]

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

S. R. Miry and M. K. Tavassoly, “Generation of a class of SU(1,1) coherent states of the Gilmore–Perelomov type and a class of SU(2) coherent states and their superposition,” Phys. Scr. 85, 035404 (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]

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]

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

G. R. Honarasa, M. K. Tavassoly, and M. Hatami, “Quantum phase distribution and the number-phase Wigner function of generalized squeezed vacuum states associated with solvable quantum systems,” Chin. Phys. B 21, 054208 (2012).
[CrossRef]

G. R. Honarasa, M. K. Tavassoly, and M. Hatami, “Generalized coherent states for solvable quantum systems with degenerate discrete spectra and their nonclassical properties,” Physica A 390, 1381–1392 (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]

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]

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]

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

M. K. Tavassoly, “Gazeau-Klauder squeezed states associated with solvable quantum systems,” J. Phys. A 39, 11583–11597 (2006).
[CrossRef]

Walls, D. F.

M. D. Reid and D. F. Walls, “Violations of classical inequalities in quantum optics,” Phys. Rev. A 34, 1260–1276 (1986).
[CrossRef]

Walther, H.

G. Rempe, H. Walther, and N. Klein, “One-atom maser,” Phys. Rev. Lett. 54, 551–554 (1987).

Yadollahi, F.

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]

Yamaguchi, K.

M. Nakano and K. Yamaguchi, “Quantum-phase dynamics of dimer systems interacting with a two-mode squeezed coherent field,” J. Chem. Phys. 116, 10069–10082 (2002).
[CrossRef]

Zaccaria, F.

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]

Chin. Phys. B (1)

G. R. Honarasa, M. K. Tavassoly, and M. Hatami, “Quantum phase distribution and the number-phase Wigner function of generalized squeezed vacuum states associated with solvable quantum systems,” Chin. Phys. B 21, 054208 (2012).
[CrossRef]

Commun. Theor. Phys. (1)

M. J. Faghihi and M. K. Tavassoly, “Nonlinear quantum optical springs and their nonclassical properties,” Commun. Theor. Phys. 56, 327–332 (2011).
[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. Chem. Phys. (1)

M. Nakano and K. Yamaguchi, “Quantum-phase dynamics of dimer systems interacting with a two-mode squeezed coherent field,” J. Chem. Phys. 116, 10069–10082 (2002).
[CrossRef]

J. Math. Phys. (1)

J. R. Klauder, “Continuous representation theory. I. Postulates of continuous representation theory,” J. Math. Phys. 4, 1055–1058 (1963).
[CrossRef]

J. Mod. Opt. (1)

B. W. Shore and P. L. Knight, “The Jaynes–Cummings model,” J. Mod. Opt. 40, 1195–1238 (1993).
[CrossRef]

J. Opt. B (1)

V. V. Dodonov, “‘Nonclassical’ states in quantum optics: a ‘squeezed’ review of the first 75 years,” J. Opt. B 4, R1–R33 (2002).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. A (4)

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

M. K. Tavassoly, “Gazeau-Klauder squeezed states associated with solvable quantum systems,” J. Phys. A 39, 11583–11597 (2006).
[CrossRef]

M. H. Naderi, “The Jaynes–Cummings model beyond the rotating-wave approximation as an intensity-dependent model: quantum statistical and phase properties,” J. Phys. A 44, 055304 (2011).
[CrossRef]

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

J. Phys. B (1)

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]

Opt. Commun. (4)

S. R. Miry, M. Shahpari, and M. K. Tavassoly, “Nonlinear elliptical states: generation and nonclassical properties,” Opt. Commun. 306, 49–56 (2013).
[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]

H. T. Dung, R. Tanaś, and A. S. Shumovsky, “Collapses, revivals, and phase properties of the field in Jaynes–Cummings type models,” Opt. Commun. 79, 462–468 (1990).
[CrossRef]

Opt. Lett. (1)

Phys. Lett. A (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]

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]

Phys. Rev. (2)

F. W. Cummings, “Stimulated emission of radiation in a single mode,” Phys. Rev. 140, A1051–A1056 (1965).
[CrossRef]

R. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766–2788 (1963).
[CrossRef]

Phys. Rev. A (8)

D. T. Pegg and S. M. Barnett, “Phase properties of the quantized single-mode electromagnetic field,” Phys. Rev. A 39, 1665–1675 (1989).
[CrossRef]

M. D. Reid and D. F. Walls, “Violations of classical inequalities in quantum optics,” Phys. Rev. A 34, 1260–1276 (1986).
[CrossRef]

C. M. Caves and B. L. Schumaker, “New formalism for two-photon quantum optics. I. Quadrature phases and squeezed states,” Phys. Rev. A 31, 3068–3092 (1985).
[CrossRef]

M. Hillery, “Sum and difference squeezing of the electromagnetic field,” Phys. Rev. A 40, 3147–3155 (1989).
[CrossRef]

Sh. Barzanjeh, M. H. Naderi, and M. Soltanolkotabi, “Back-action ground-state cooling of a micromechanical membrane via intensity-dependent interaction,” Phys. Rev. A 84, 023803 (2011).
[CrossRef]

Sh. Barzanjeh, M. H. Naderi, and M. Soltanolkotabi, “Steady-state entanglement and normal-mode splitting in an atom-assisted optomechanical system with intensity-dependent coupling,” Phys. Rev. A 84, 063850 (2011).
[CrossRef]

M. Hillery, “Quantum cryptography with squeezed states,” Phys. Rev. A 61, 022309 (2000).
[CrossRef]

S. F. Pereira, Z. Y. Ou, and H. J. Kimble, “Quantum communication with correlated nonclassical states,” Phys. Rev. A 62, 042311 (2000).
[CrossRef]

Phys. Rev. Lett. (3)

G. Rempe, H. Walther, and N. Klein, “One-atom maser,” Phys. Rev. Lett. 54, 551–554 (1987).

R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903–1905 (1987).
[CrossRef]

E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Phys. Rev. Lett. 10, 277–279 (1963).
[CrossRef]

Phys. Scr. (3)

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]

S. R. Miry and M. K. Tavassoly, “Generation of a class of SU(1,1) coherent states of the Gilmore–Perelomov type and a class of SU(2) coherent states and their superposition,” Phys. Scr. 85, 035404 (2012).
[CrossRef]

Physica A (1)

G. R. Honarasa, M. K. Tavassoly, and M. Hatami, “Generalized coherent states for solvable quantum systems with degenerate discrete spectra and their nonclassical properties,” Physica A 390, 1381–1392 (2011).
[CrossRef]

Proc. IEEE (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]

Other (2)

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge University, 2005).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

Time evolution of the entropy squeezing in-phase versus the scaled time τ=λt according to the relation obtained in Eq. (19) 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 upside plots correspond to the absence of the intensity-dependent atom–field coupling: f(n)=1, and the downside plots show the presence of the intensity-dependent atom–field coupling: fi(ni)=1/ni. Also, (a) χ=0 and Δ2=Δ3=0; (b) χ=0.4λ, Δ2=Δ3=0 and gi(ni)=1/ni; (c) χ=0.4λ, Δ2=7λ, Δ3=15λ and gi(ni)=1/ni.

Fig. 2.
Fig. 2.

Time evolution of the Mandel’s Q parameter according to the relation obtained in Eq. (20) for chosen parameters similar to Fig. 1.

Fig. 3.
Fig. 3.

Time evolution of the Cauchy–Schwartz inequality according to the relation obtained in Eq. (21) for chosen parameters similar to Fig. 1.

Fig. 4.
Fig. 4.

Time evolution of two-mode squeezing according to the relation obtained in Eq. (23) for chosen parameters similar to Fig. 1.

Fig. 5.
Fig. 5.

Time evolution of sum squeezing according to the relation obtained in Eq. (25) for chosen parameters similar to Fig. 1.

Equations (25)

Equations on this page are rendered with MathJax. Learn more.

H^0=j=13ωjσ^jj+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).
|ψ(t)=n1=0+n2=0+qn1qn2[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],
γ1ω1+n1Ω1+n2Ω2,γ2ω2+(n1+1)Ω1+n2Ω2,γ3ω3+n1Ω1+(n2+1)Ω2.
A(n1,n2,t)=eiΔ2tj=13(μj+VB)bjeiμjt,B(n1+1,n2,t)=j=13κ1bjeiμjt,C(n1,n2+1,t)=ei(Δ3Δ2)tκ2j=13[(μj+VB)×(μj+VAΔ2)κ12]bjeiμjt,
μj=13x1+23x123x2cos[θ+23(j1)π],j=1,2,3,θ=13cos1[9x1x22x1327x32(x123x2)3/2]
x1=˙VA+VB+VC+Δ32Δ2,x2=˙(VA+VBΔ2)(VC+Δ3Δ2)+VB(VAΔ2)κ12κ22,x3=˙VB[(VAΔ2)(VC+Δ3Δ2)κ22]κ12(VC+Δ3Δ2).
VA=˙V(n1,n2),VB=˙V(n1+1,n2),VC=˙V(n1,n2+1),κ1=˙λ1n1+1f1(n1+1),κ2=˙λ2n2+1f2(n2+1),Δ2=ω2ω1+Ω1,Δ3=ω3ω1+Ω2
V(n1,n2)=˙χn1n2g12(n1)g22(n2).
|ψ(0)AF=|1n1=0+n2=0+qn1qn2|n1,n2,
bj=μk+μl+VA+VBΔ2μjkμjl,jkl=1,2,3,
|θp=1s+1n=0sexp(inθp)|n,
θp=θ0+2πps+1,p=0,1,,s,
|θp,θq=1s+1n=0sm=0sexp(inθp)exp(imθq)|n,m
θk=θ0+2πks+1,k=p,q,
Pθ(θp,θq)=lims+(s+12π)2θp,θq|ρ^F|θp,θq.
Pθ(θ1,θ2)=14π2|n1=0+n2=0+qn1qn2A(n1,n2,t)exp(in1θ1)exp(in2θ2)|2+14π2|n1=0+n2=0+qn1qn2B(n1+1,n2,t)exp(in1θ1)exp(in2θ2)|2+14π2|n1=0+n2=0+qn1qn2C(n1,n2+1,t)exp(in1θ1)exp(in2θ2)|2.
Rn(t)=n1=0+n2=0+Pn(n1,n2)lnPn(n1,n2),Rθ(t)=θ0θ0+2πdθ1θ0θ0+2πdθ2Pθ(θ1,θ2)lnPθ(θ1,θ2),
Sn(t)=12πexp(Rn(t))1,Sθ(t)=12πexp(Rθ(t))1.
Q=(Δn^)2n^n^,
I0=(a12a12a22a22)1/2|a1a1a2a2|1,
X^1=122(a^1+a^1+a^2+a^2),X^2=12i2(a^1a^1+a^2a^2).
SX1=Re(a^12+a^22+2a^1a^2+2a^1a^2)+a^1a^1+a^2a^22[Re(a^1+a^2)]2,SX2=Re(2a^1a^22a^1a^2a^12a^22)+a^1a^1+a^2a^22[Im(a^1+a^2)]2.
Y^1=12(a^1a^2+a^1a^2),Y^2=12i(a^1a^2a^1a^2),
SY1=2Rea^12a^22+2a^1a^1a^2a^24(Rea^1a^2)2a^1a^1+a^2a^2+1,SY2=2a^1a^1a^2a^22Rea^12a^224(Ima^1a^2)2a^1a^1+a^2a^2+1.

Metrics