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Dynamical symmetry breaking of lambda- and vee-type three-level systems on quantization of the field modes

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Abstract

We develop a scheme to construct the Hamiltonians of the lambda-, vee- and cascade-type three-level configurations using the generators of SU(3) group. It turns out that this approach provides a well-defined selection rule to give different Hamiltonians for each configuration. The lambda- and vee-type configurations are exactly solved with different initial conditions while taking the two-mode classical and quantized fields. For the classical field, it is shown that the Rabi oscillation of the lambda model is similar to that of the vee model and the dynamics of the vee model can be recovered from lambda model and vice versa simply by inversion. We then proceed to solve the quantized version of both models by introducing a novel Euler matrix formalism. It is shown that this dynamical symmetry exhibited in the Rabi oscillation of two configurations for the semiclassical models is completely destroyed on quantization of the field modes. The symmetry can be restored within the quantized models when both field modes are in the coherent states with large average photon number which is depicted through the collapse and revival of the Rabi oscillations.

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References

  1. A Joshi and S V Lawande, Curr. Sci. 82, 816 (2002); 82, 958 (2002)

    Google Scholar 

  2. L Hollberg, L Lugiato, A Oraevski, A Sergienko and V Zadkov (Eds), J. Opt. B: Quant. Semiclass. Opt. 5, 457 (2003)

    Google Scholar 

  3. A Nielsen and I L Chuang, Quantum computation (Cambridge University Press, Cambridge, 2002)

    Google Scholar 

  4. E T Jaynes and F W Cummings, Proc. IEEE 51, 89 (1963)

    Article  Google Scholar 

  5. G Rempe, H Walther and N Klien, Phys. Rev. Lett. 58, 353 (1987)

    Article  ADS  Google Scholar 

  6. R G Brewer and E L Hahn, Phys. Rev. A11, 1641 (1975)

    Google Scholar 

  7. P W Milloni and J H Eberly, J. Chem. Phys. 68, 1602 (1978)

    Article  ADS  Google Scholar 

  8. E M Belanov and I A Poluktov, JETP Lett. 29, 758 (1969)

    Google Scholar 

  9. D Grischkowsky, M M T Loy and P F Liao, Phys. Rev. A12, 2514 (1975) and references therein

    Google Scholar 

  10. B Sobolewska, Opt. Commun. 19, 185 (1976)

    Article  Google Scholar 

  11. C Cohen-Tannoudji and S Raynaud, J. Phys. B10, 365 (1977)

    ADS  Google Scholar 

  12. R M Whitley and C R Stroud Jr, Phys. Rev. A14, 1498 (1976)

    ADS  Google Scholar 

  13. E Arimondo, Coherent population trapping in laser spectroscopy, Prog in Optics XXXV edited by E Wolf (Elsevier Science, Amsterdam, 1996) p. 257

    Google Scholar 

  14. C M Bowden and C C Sung, Phys. Rev. A18, 1588 (1978)

    ADS  Google Scholar 

  15. T Mossberg, A Flusberg, R Kachru and S R Hartman, Phys. Rev. Lett. 39, 1523 (1984)

    Article  ADS  Google Scholar 

  16. T W Mossberg and S R Hartman, Phys. Rev. A39, 1271 (1981)

    ADS  Google Scholar 

  17. K Bergman, H Theuer and B W Shore, Rev. Mod. Phys. 70, 1003 (1998)

    Article  Google Scholar 

  18. R J Cook and H J Kimble, Phys. Rev. Lett. 54, 1023 (1985)

    Article  ADS  Google Scholar 

  19. R J Cook, Phys. Scr. T21, 49 (1988)

    Article  ADS  Google Scholar 

  20. B Misra and E C G Sudarshan, J. Math. Phys. 18, 756 (1977)

    Article  MathSciNet  ADS  Google Scholar 

  21. C B Chiu, E C G Sudarshan and B Misra, Phys. Rev. D16, 520 (1977)

    MathSciNet  Google Scholar 

  22. R J Cook, Phys. Scr. T21, 49 (1988)

    Article  ADS  Google Scholar 

  23. S E Harris, Phys. Today 50, 36 (1997)

    Article  Google Scholar 

  24. L V Lau, S E Harris, Z Dutton and C H Behroozi, Nature (London) 397, 594 (1999)

    Article  ADS  Google Scholar 

  25. C C Gerry and J H Eberly, Phys. Rev. A42, 6805 (1990)

    ADS  Google Scholar 

  26. F T Hioe and J H Eberly, Phys. Rev. A25, 2168 (1982)

    MathSciNet  ADS  Google Scholar 

  27. H I Yoo and J H Eberly, Phys. Rep. 118, 239 (1985)

    Article  ADS  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  29. F T Hioe and J H Eberly, Phys. Rev. Lett. 47, 838 (1981)

    Article  MathSciNet  ADS  Google Scholar 

  30. F T Hioe, Phys. Rev. A28, 879 (1983)

    MathSciNet  ADS  Google Scholar 

  31. X Li and N Bei, Phys. Lett. A101, 169 (1984)

    Google Scholar 

  32. J N Elgin, Phys. Lett. A80, 140 (1980)

    ADS  Google Scholar 

  33. R J Cook and B W Shore, Phys. Rev. A20, 539 (1979)

    ADS  Google Scholar 

  34. F T Hioe and J H Eberly, Phys. Rev. 29, 1164 (1984)

    Article  ADS  Google Scholar 

  35. B Buck and C V Sukumar, J. Phys. A17, 877 (1984)

    MathSciNet  ADS  Google Scholar 

  36. T Nikajima, M Elk and Lambropoulos, Phys. Rev. A50, R913 (1994)

    ADS  Google Scholar 

  37. Tak-San Ho and Shih-I Chu, Phys. Rev. A31, 659 (1985)

    ADS  Google Scholar 

  38. F Li, X Li, D L Lin and T F George, Phys. Rev. A40, 5129 (1989) and references therein

    ADS  Google Scholar 

  39. F T Hioe, Phys. Lett. A99, 150 (1983)

    MathSciNet  ADS  Google Scholar 

  40. N V Kancheva, D Pushkarov and S Rashev, J. Phys. B: Mol. Opt. Phys. 14, 539 (1981)

    Article  Google Scholar 

  41. N V Vitanov, J. Phys. B: Mol. Opt. Phys. 31, 709 (1998)

    Article  Google Scholar 

  42. S Y Chu and D C Su, Phys. Rev. A25, 3169 (2003)

    ADS  Google Scholar 

  43. N N Bogolubov Jr, F L Kien and A S Shumovsky, Phys. Lett. A101, 201 (1984); A107, 173 (1985)

    ADS  Google Scholar 

  44. M R Nath, S Sen and G Gangopadhyay, Pramana — J. Phys. 61, 1089 (2003), quantph: 0711.3884

    Article  ADS  Google Scholar 

  45. M R Nath, T K Dey, S Sen and G Gangopadhyay, Pramana — J. Phys. 70, 141 (2008), quant-ph:0712.2649v2

    Article  ADS  Google Scholar 

  46. M S Scully and M O Zubairy, Quantum optics (Cambridge University Press, Cambridge, 1997) p. 16

    Google Scholar 

  47. D B Litchenberg, Unitary symmetry and elementary particles (Academic Press, New York, 1970)

    Google Scholar 

  48. M R Nath, S Sen and G Gangopadhyay, in preparation

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Authors and Affiliations

  1. Department of Physics, Guru Charan College, Silchar, 788 004, India

    Mihir Ranjan Nath & Surajit Sen

  2. Department of Physics, Assam University, Silchar, 788 011, India

    Asoke Kumar Sen

  3. JD Block, Sector III, S.N. Bose National Centre for Basic Sciences, Salt Lake City, Kolkata, 700 098, India

    Gautam Gangopadhyay

Authors
  1. Mihir Ranjan Nath
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  2. Surajit Sen
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  3. Asoke Kumar Sen
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  4. Gautam Gangopadhyay
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Correspondence to Gautam Gangopadhyay.

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Nath, M.R., Sen, S., Sen, A.K. et al. Dynamical symmetry breaking of lambda- and vee-type three-level systems on quantization of the field modes. Pramana - J Phys 71, 77–97 (2008). https://doi.org/10.1007/s12043-008-0143-8

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  • DOI: https://doi.org/10.1007/s12043-008-0143-8

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