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A rigorous investigation on the interaction between two three-level \(\Lambda \)-type atoms and a single-mode cavity field

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Abstract

In this paper, we study quantum entanglement and non-classical statistical aspects for a model describing two three-level \(\Lambda \) atoms interacting with a single-mode cavity field. The Hamiltonian describes multi-photon processes and includes the Kerr-like medium in the resonance case. The constants of motion are obtained from the Hamiltonian operators under the rotating wave approximation. The exact solution of the wave function for the whole system is obtained under the special initial conditions when the atom is in the ground state and the field in the coherent states. The results are used to perform some studies on the temporal evolution of collapse revival, normal squeezing function, photon antibunching and Q-function to measure the degree of entanglement between subsystems. Entanglement dynamics using von Neumann entropy and Shannon information is used to quantify the entanglement in the quantum subsystems. The numerical results show that the presence of these parameters plays an essential role in developing these aspects. The above optical schemes have many advantages and can be used in various experiments in quantum optics and information, such as trapped ions and quantum electrodynamics resonators.

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References

  1. M O Scully and M S Zubairy, Quantum optics (Cambridge University Press, Cambridge, 2001)

    MATH  Google Scholar 

  2. E T Jaynes and FW Cummings, Proc. IEEE 51, 89 (1963)

    Article  Google Scholar 

  3. B W Shore and P L Knight, J. Mod. Opt. 40, 1195 (1993)

    Article  ADS  Google Scholar 

  4. N H Abdel-Wahab and A Salah, Mod. Phys. Lett. A 34, 1950081 (2019)

  5. A Salah, L E Thabet, T M El-Shahat, N H Abd El-Wahab and M G Edin, Mod. Phys. Lett. A 37, 2250030 (2022)

  6. Q Liao, G Fang, Y Wang, M A Ahmad and S Liu, Optik 122, 1392 (2011)

    Article  ADS  Google Scholar 

  7. N H Abdel-Wahab and M F Mourad, Il Nuovo Cimento I 124, 1161 (2009)

    Google Scholar 

  8. A Salah, L E Thabet, T M El-Shahat and A El-Wahab, Pramana – J. Phys. 94, 143 (2020)

  9. T Huang, X-M Lin, Z-W Zhou, Z-L Cao and G-C Guo, Physica A 358, 313 (2005)

    Article  ADS  Google Scholar 

  10. M W Janowicz and J M A Ashbourn, Phys. Rev. A 55, 2348 (1997)

  11. A-S F Obada, M M A Ahmed, E M Khalil and S I Ali, Opt. Commun. 287, 215 (2013)

    Article  ADS  Google Scholar 

  12. A Slaoui, A Salah and M Daoud, Physica A 558, 124946 (2020)

    Article  MathSciNet  Google Scholar 

  13. N H Abdel-Wahab and M F Mourad, Phys. Scr. 8, 015401 (2011)

    Article  ADS  Google Scholar 

  14. J H Eberly, N B Narozhny and J J Sanchez-Mondragon, Phys. Rev. Lett. 44, 1323 (1980); Phys. Rev. A 23, 236 (1981)

  15. R Krivec and V B Mandelzweig, Phys. Rev. A 52, 221 (1995)

    Article  ADS  Google Scholar 

  16. K I Osman and H A Ashi, Physica A 310, 165 (2002)

    Article  ADS  Google Scholar 

  17. B P Hou, S J Wang, W L Yu and W L Sun, J. Opt. B: At. Mol. Opt. Phys. 38, 1419 (2005)

    ADS  Google Scholar 

  18. W Kai, G Ying and G Q Huang, Chin. Phys. 16, 130 (2007)

    Article  Google Scholar 

  19. B K Dutta and P K Mahapatra, Phys. Scr. 75, 345 (2007)

    Article  ADS  Google Scholar 

  20. T M El-Shahat, M Kh Ismail and A F Al Naim, J. Russ. Laser. Res. 39, 231 (2018)

  21. E K Bashkirov, Opt. Spectrosc. 100, 613 (2006)

    Article  ADS  Google Scholar 

  22. H R Baghshahi and M K Tavassoly, Eur. Phys. J. Plus 130, 37 (2015)

    Article  Google Scholar 

  23. E Faraji, M K Tavassoly and H R Baghshahi, Int. J. Theor. Phys. 55, 2573 (2016)

    Article  Google Scholar 

  24. H R Baghshahi, M K Tavassoly and S J Akhtarshenas, Quantum Inf. Process. 14, 1279 (2015)

    Article  ADS  Google Scholar 

  25. S A Abdel-Khalek, S H Halawani and A S F Obada, Int. J. Theor. Phys. 56, 2898 (2017)

    Article  Google Scholar 

  26. N H Abd El-Wahab, A S Abdel Rady, A-N A Osman and A Salah, Eur. Phys. J. Plus 130, 207 (2015)

  27. N H Abd El-Wahab and A Salah, Mod. Phys. Lett. A 34, 195008 (2019)

  28. G Benenti, G Casati and G Strini, Principles of quantum computation and information: Basic tools and special topics (World Scientific, Singapore, 2007) Vol. II

  29. M A Nielsen I L Chuang, Quantum computation and quantum information, 10th Anniversary Edn (Cambridge University Press, Cambridge, 2010)

  30. A Ekert, Phys. Rev. Lett. 67, 661 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  31. J I Cirac and N Gisin, Phys. Lett. A 229, 1 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  32. C A Fuchs, N Gisin, R B Griffiths, C-S Niu and A Peres, Phys. Rev. A 56, 1163 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  33. W Stallings, Cryptography and network security: Principles and practice, 6th Edn (Prentice Hall, 2013)

  34. C H Bennett, G Brassard, C Crepeau, R Jozsa, A Peres and W K Wootters, Phys. Rev. Lett. 70, 1895 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  35. A-S F Obada and M Abdel-Aty, Acta Phys. Pol. B 31, 589 (2000)

    ADS  Google Scholar 

  36. M Abdel-Aty, J. Phys. B: At. Mol. Opt. Phys. 33, 2665 (2000)

    Article  ADS  Google Scholar 

  37. R Loundon, The quantum theory of light (Clarendon Press, Oxford, Plenum, 1983)

    Google Scholar 

  38. M Abdel-Aty, G Abd Al-Kader and A-S F Obada, Chaos Solitons Fractals 12, 2455 (2001)

  39. L Mandel, Opt. Lett. 4, 205 (1979)

    Article  ADS  Google Scholar 

  40. M S Kim, J. Mod. Opt. 40, 1331 (1993)

    Article  ADS  Google Scholar 

  41. H P Yuen and J H Shapiro, IEEE Trans. Inform. 24, 657 (1978)

    Article  Google Scholar 

  42. H P Yuen and J H Shapiro, IEEE Trans. Inform. 25, 179 (1979)

    Article  Google Scholar 

  43. H P Yuen and J H Shapiro, IEEE Trans. Inform. 26, 78 (1980)

    Article  Google Scholar 

  44. J H Shapiro, Opt. Lett. 5, 351 (1980)

    Article  ADS  Google Scholar 

  45. C M Caves and B I Schumaker, Phys. Rev. A 31, 3068 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  46. B I Schumaker and C M Caves, Phys. Rev. A 31, 3093 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  47. G H Nilburen, Phys. Rev. A 33, 6017 (1986)

    Google Scholar 

  48. J Eiselt and H Risken, Opt. Commun. 72, 351 (1989)

    Article  ADS  Google Scholar 

  49. A Miranwicz, R Tanas and S Kelich, Opt. Commun. 2, 253 (1990)

    Google Scholar 

  50. M J Werner and H Risken, Quantum Opt. 3, 185 (1991)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

Funding was provided by Ministry of Higher Education.

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Authors and Affiliations

  1. Mathematics and Theoretical Physics Department, Nuclear Research Center, Egyptian Atomic Energy Authority, Cairo, Egypt

    Ahmed Salah

  2. Mathematics Department, Faculty of Science, Minia University, Minia, Egypt

    N H Abdel-Wahab

Authors
  1. Ahmed Salah
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  2. N H Abdel-Wahab
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Correspondence to Ahmed Salah.

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Salah, A., Abdel-Wahab, N.H. A rigorous investigation on the interaction between two three-level \(\Lambda \)-type atoms and a single-mode cavity field. Pramana - J Phys 97, 87 (2023). https://doi.org/10.1007/s12043-023-02561-w

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  • DOI: https://doi.org/10.1007/s12043-023-02561-w

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