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Entanglement Dynamics in a Model Tripartite Quantum System

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Abstract

A Λ-type atom interacting with two radiation fields exhibits electromagnetically induced transparency and other nonclassical effects that appear in the entanglement dynamics of the atomic subsystem and in appropriate field observables. Both EIT and field-atom entanglement are important for quantum information processing. We investigate the roles played by specific initial field states, detuning parameters, field nonlinearities and intensity-dependent field-atom couplings on EIT and the entanglement between subsystems. Departure from coherence of the initial field states produces significant effects. We investigate these aspects in a model that exhibits the salient features of entangled tripartite systems. For initial photon-added coherent states, collapses and revivals of the atomic subsystem von Neumann entropy appear as the intensity parameter varies over a narrow range of values. These features could be useful in enabling entanglement.

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References

  1. Robinett, R. W.: Quantum wave packet revivals. Phys. Rep. 392, 1 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  2. Milburn, G. J.: Quantum and classical Liouville dynamics of the anharmonic oscillator. Phys. Rev. A 33, 674 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  3. Kitagawa, M., Yamamoto, Y.: Number-phase minimum-uncertainty state with reduced number uncertainty in a Kerr nonlinear interferometer. Phys. Rev. A 34, 3974 (1986)

    Article  ADS  Google Scholar 

  4. Averbukh, I Sh, Perelman, N. F.: Fractional revivals: Universality in the long-term evolution of quantum wave packets beyond the correspondence principle dynamics. Phys. Lett. A 139, 449 (1989)

    Article  ADS  Google Scholar 

  5. Behzadi, N.: Entanglement observation among single mode bosonic field and an atom. Quantum Inf. Process. 11, 777 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  6. Miry, S. R., Tavassoly, M. K., Roknizadeh, R.: Generation of some entangled state of the cavity field. Quantum Inf. Process. 14, 593 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Zeinab, K., Saeed, G., Mohammad, M.: Maximal atom-photon entanglement in a double- Λ quantum system. Quantum Inf. Process. 14, 1907 (2015)

    Article  MATH  Google Scholar 

  8. Zeinab, K., Saeed, G., Mohammad, M.: Atom-photon entanglement beyond the multi-photon resonance condition. Quantum Inf. Process. doi:10.1007/s11128-015-1168-9 (2015)

  9. Marangos, J. P.: Topical review: Electromagnetically induced transparency. J. Mod. Opt. 45, 471 (1998)

    Article  ADS  Google Scholar 

  10. Clader, B. D., Hendrickson, S. M., Camacho, R. M., Jacobs, B. C.: All-optical micro-disk switch using EIT. Opt. Express 21, 5 (2013)

    Article  Google Scholar 

  11. Boller, K. J., Imamoğlu, A., Harris, S. E.: Observation of electromagnetically induced transparency. Phys. Rev. Lett. 66, 2593 (1991)

    Article  ADS  Google Scholar 

  12. Li, Y., Xiao, M.: Electromagnetically induced transparency in a three-level Λ-type system in rubidium atoms. Phys. Rev. A 51, R2703 (1995)

    Article  ADS  Google Scholar 

  13. Éntin, V. M., Ryabtsev, I. I., Boguslavskii, A. E., Beterov, I. M.: Experimental implementation of a four-level N-type scheme for the observation of electromagnetically induced transparency. JETP Lett. 71, 175 (2000)

    Article  ADS  Google Scholar 

  14. Sudheesh, C., Lakshmibala, S., Balakrishnan, V.: Dynamics of quantum observables in entangled states. Phys. Lett. A 329, 14 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. Sudheesh, C., Lakshmibala, S., Balakrishnan, V.: Wave packet dynamics of photon-added coherent states. Europhys. Lett. 71, 744 (2005)

    Article  ADS  Google Scholar 

  16. Lai, W. K., Buek, V., Knight, P. L.: Dynamics of a three-level atom in a two-mode squeezed vacuum. Phys. Rev. A 44, 6043 (1991)

    Article  ADS  Google Scholar 

  17. Lai, W. K., Buek, V., Knight, P. L.: Interaction of a three-level atom with an SU(2) coherent state. Phys. Rev. A 44, 2003 (1991)

    Article  ADS  Google Scholar 

  18. Wen-Jian, Y., Bao-Ming, X., Li, L., Zou, J., Li, H., Shao, B.: Influences of initial states on entanglement dynamics of two central spins in a spin environment. Int. J. Th. Phys. 55, 1460 (2016)

    Article  MATH  Google Scholar 

  19. Agarwal, G. S., Puri, R. R.: Collapse and revival phenomenon in the evolution of a resonant field in a Kerr-like medium. Phys. Rev. A 39, 2969 (1989)

    Article  ADS  Google Scholar 

  20. Sudheesh, C., Lakshmibala, S., Balakrishnan, V.: Wave packet dynamics of entangled two-mode states. J. Phys. B 39, 3345 (2006)

    Article  ADS  Google Scholar 

  21. Sudheesh, C., Lakshmibala, S., Balakrishnan, V.: Manifestations of wave packet revivals in the moments of observables. Phys. Lett. A 373, 2814 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Sudheesh, C., Lakshmibala, S., Balakrishnan, V.: Recurrence statistics of observables in quantum-mechanical wave packet dynamics. EPL 90, 50001 (2010)

    Article  ADS  Google Scholar 

  23. Shankar, A., Lakshmibala, S., Balakrishnan, V.: Dynamics of an open quantum system interacting with a quantum environment. J. Phys. B 47, 215505 (2014)

    Article  ADS  Google Scholar 

  24. Raymond Ooi, C. H., Hazmin, S. N., Sudha, S.: Nonclassical dynamics with time- and intensity-dependent coupling. Quantum Inf. Process. 11, 6 (2012)

    MATH  Google Scholar 

  25. Mahjoei, M., Golshan, M. M., Safari, H.: Collapse revival behaviour of the entanglement between V-type three-level atoms and two-mode photons in nonlinear Jaynes-Cummings model. Pramana—J. Phys. 80, 5 (2013)

    Article  Google Scholar 

  26. Baghshahi, H. R., Tavassoly, M. K.: Generation and non classicality of entangled states via the interaction of two three-level atoms with a quantised cavity field assisted by a driving external classical field. Quantum Inf. Process. 14, 1279 (2015)

    Article  ADS  MATH  Google Scholar 

  27. Tara, K., Agarwal, G. S., Chaturvedi, S.: Production of Schrödinger macroscopic quantum-superposition states in a Kerr medium. Phys. Rev. A 47, 5024 (1993)

    Article  ADS  Google Scholar 

  28. Zavatta, A., Viciani, S., Bellini, M.: Quantum-to-classical transition with single-photon-added coherent states of light. Science 306, 660 (2004)

    Article  ADS  Google Scholar 

  29. Buck, B., Sukumar, C. V.: Exactly soluble model of atom-phonon coupling showing periodic decay and revival. Phys. Lett. A 81, 132 (1981)

    Article  ADS  Google Scholar 

  30. Faghihi, M. J., Tavassoly, M. K., Harouni, M. B.: Tripartite entanglement dynamics and entropic squeezing of a three-level atom interacting with a bimodal cavity field. Laser Phys. 24, 045202 (2014)

    Article  ADS  Google Scholar 

  31. Faghihi, M. J., Tavassoly, M. K., Hooshmandasl, M. R.: 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 (2013)

    Article  ADS  Google Scholar 

  32. Buz̆ek, V.: Jaynes-Cummings model with intensity-dependent coupling interacting with squeezed vacuum. Phys. Lett. A 139, 231 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  33. Buz̆ek, V.: Jaynes-Cummings model with intensity-dependent coupling interacting with Holstein-Primakoff S U(1,1) coherent state. Phys. Rev. A 39, 3196 (1989)

    Article  ADS  Google Scholar 

  34. Zait, R. A.: 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 (2003)

    Article  ADS  Google Scholar 

  35. Sudarshan, E. C. G.: Diagonal harmonious state representations. Int. J. Th. Phys. 32, 1069 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  36. Rodríguez-Lara, B. M.: Propagation of nonclassical states of light through one-dimensional photonic lattices. J. Opt. Soc. Am. B 31, 4 (2014)

    Google Scholar 

  37. Rodríguez-Lara, B. M.: Intensity-dependent quantum Rabi model: spectrum, supersymmetric partner, and optical simulation. J. Opt. Soc. Am. B 31, 7 (2014)

    Article  Google Scholar 

  38. Sivakumar, S.: Nonlinear Jaynes-Cummings model of atom-field interaction. Int. J. Th. Phys. 43, 2405 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  39. Sivakumar, S.: Interpolating coherent states for Heisenberg-Weyl and single-photon S U(1,1) algebras. J. Phys. A: Math. Gen. 35, 6755 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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Laha, P., Sudarsan, B., Lakshmibala, S. et al. Entanglement Dynamics in a Model Tripartite Quantum System. Int J Theor Phys 55, 4044–4059 (2016). https://doi.org/10.1007/s10773-016-3033-8

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  • DOI: https://doi.org/10.1007/s10773-016-3033-8

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