Skip to main content
SpringerLink
Log in

The improvement of lasing without inversion in the presence of multi-photon transition in a three-level atom confined in an optical cavity in the steady-state regime

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract.

A three-level atom in \( \Lambda\) configuration trapped in a single-mode Fabry-Pérot optical cavity is investigated. It is assumed that the transition between levels 2 and 3 in the atom is accomplished through the number of q photons. To solve the steady-state master equation for the atom-cavity system, the matrix continued-fraction method for applied physical quantities is used. The results show that by raising the number of transitions, the curves of the population inversion finally overlap with one another and the output mean photon number from the optical cavity rises and moreover the laser effect appears in the system. On the other hand, the outcomes reveal that by increasing the number of transitions despite the negativity of the population inversion, the number of output photons from the cavity grows and lasing interval becomes larger. Eventually the steps of the transformation from the three-level atom to two-level one in the case of multi-photon transition under several specific conditions have been studied. The obtained results of the simulations confirm the accuracy of the used approximations in the two-level pattern appropriately. In summary, the lasing process without population inversion along with the multi-photon transition in the three-level atom is discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R.-H. Xie, Q. Rao, Physica A 319, 233 (2003)

    Article  ADS  Google Scholar 

  2. L.A. Lugiato, G. Strini, Opt. Commun. 41, 447 (1982)

    Article  ADS  Google Scholar 

  3. A.-S.F. Obada, M.M.A. Ahmed, F.K. Faramawy, E.M. Khalil, Chaos, Solitons Fractals 28, 983 (2006)

    Article  ADS  Google Scholar 

  4. F.J. Bermejo, J. Santoro, L.S. de los Terreros, Comput. Phys. Commun. 43, 245 (1987)

    Article  ADS  Google Scholar 

  5. P. Garcia-Fernandez, L.S. de los Terreros, F.J. Bermejo, J. Santoro, Phys. Lett. A 118, 400 (1986)

    Article  ADS  Google Scholar 

  6. K.J. McNeil, D.F. Walls, J. Phys. A: Math. Nucl. Gen. 7, 617 (1974)

    Article  ADS  Google Scholar 

  7. G.S. Agarwal, Phys. Rev. A 1, 1445 (1970)

    Article  ADS  Google Scholar 

  8. S.X. Huang, R.M. Lin, Phys. Rev. A 39, 221 (1989)

    Article  ADS  Google Scholar 

  9. M. Reid, K.J. McNeil, D.F. Walls, Phys. Rev. A 24, 2029 (1981)

    Article  ADS  Google Scholar 

  10. M.S. Zubairy, J.J. Yeh, Phys. Rev. A 21, 1624 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  11. E.S. Guerra, B.M. Garraway, P.L. Knight, Phys. Rev. A 55, 3842 (1997)

    Article  ADS  Google Scholar 

  12. C.C. Gerry, P.J. Moyer, Phys. Rev. A 38, 5665 (1988)

    Article  ADS  Google Scholar 

  13. A. Joshi, R.R. Puri, Phys. Rev. A 45, 5056 (1992)

    Article  ADS  Google Scholar 

  14. T. Gantsog, A. Joshi, R. Tanas, Quantum Semiclass. Opt. 8, 445 (1996)

    Article  ADS  Google Scholar 

  15. R.H. Xie, V.H. Smith jr., Physica A 307, 207 (2002)

    Article  ADS  Google Scholar 

  16. P. Galatola, L.A. Lugiato, M. Vadacchino, N.B. Abraham, Opt. Commun. 69, 414 (1989)

    Article  ADS  Google Scholar 

  17. H.D. Simaan, R. Loudon, J. Phys. A: Math. Gen. 8, 539 (1975)

    Article  ADS  Google Scholar 

  18. V.V. Dodonov, S.S. Mizrahi, Phys. Lett. A 223, 404 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  19. L. Gilles, P.L. Knight, Phys. Rev. A 48, 1582 (1993)

    Article  ADS  Google Scholar 

  20. L.S. de los Terreros, F.J. Bermejo, Phys. Lett. A 114, 121 (1986)

    Article  ADS  Google Scholar 

  21. H.D. Simaan, R. Loudon, J. Phys. A: Math. Gen. 11, 435 (1978)

    Article  ADS  Google Scholar 

  22. M.D. Reid, D.F. Walls, Phys. Rev. A 28, 332 (1983)

    Article  ADS  Google Scholar 

  23. S. Carusotto, Opt. Acta 27, 1567 (1980)

    Article  MathSciNet  Google Scholar 

  24. S. Carusotto, Physica A 107, 509 (1981)

    Article  ADS  Google Scholar 

  25. L.A. Lugiato, G. Strini, Opt. Commun. 41, 374 (1982)

    Article  ADS  Google Scholar 

  26. P.G. Fernandez, L. Lugiato, F.J. Bermejo, Quantum Opt. 3, 49 (1991)

    Article  ADS  Google Scholar 

  27. F.-L. Li, Q. Huang, Generation of higher-order squeezing in multiphoton micromaser, in 4th International Conference on Squeezed States and Uncertainty Relations (Shanxi University, China, 1996) pp. 51--60

  28. F.L. Kien, H.T. Dung, A.S. Shumovsky, Physica A 153, 492 (1988)

    Article  ADS  Google Scholar 

  29. E.I. Aliskenderov, K.A. Rustamov, A.S. Shumovsky, T. Quang, J. Phys. A: Math. Gen. 20, 6265 (1987)

    Article  ADS  Google Scholar 

  30. C.V. Sukumar, B. Buck, Phys. Lett. A 83, 211 (1981)

    Article  ADS  Google Scholar 

  31. L. Davidovich, J.M. Raimond, M. Brune, S. Haroche, Phys. Rev. A 36, 3771 (1987)

    Article  ADS  Google Scholar 

  32. M. Brune, J.M. Raimond, P. Goy, L. Davidovich, S. Haroche, Phys. Rev. Lett. 59, 1899 (1987)

    Article  ADS  Google Scholar 

  33. M. Majeed, M.S. Zubairy, Phys. Rev. A 44, 4688 (1991)

    Article  ADS  Google Scholar 

  34. F.L. Kien, G.M. Meyer, U.W. Rathe, M.O. Scully, H. Walther, S.-Y. Zhu, Phys. Rev. A 52, 3279 (1995) and references therein for progress in the two-photon micromaser

    Article  ADS  Google Scholar 

  35. B. NikoIaus, D.Z. Zhang, P.E. Toschek, Phys. Rev. Lett. 47, 171 (1981)

    Article  ADS  Google Scholar 

  36. A.D. Boozer, Phys. Rev. A 78, 053814 (2008)

    Article  ADS  Google Scholar 

  37. B. Jones, S. Ghose, J.P. Clemens, P.R. Rice, L.M. Pedrotti, Phys. Rev. A 60, 3267 (1999)

    Article  ADS  Google Scholar 

  38. G.M. Meyer, H.-J. Briegel, Phys. Rev. A 58, 3210 (1998)

    Article  ADS  Google Scholar 

  39. T. Pellizzari, H. Ritsch, Phys. Rev. Lett. 72, 3973 (1994)

    Article  ADS  Google Scholar 

  40. T. Pellizzari, H. Ritsch, J. Mod. Opt. 41, 609 (1994)

    Article  ADS  Google Scholar 

  41. B. Parvin, R. Malekfar, Eur. Phys. J. D 66, 126 (2012)

    Article  ADS  Google Scholar 

  42. M.J. Gagen, G.J. Milburn, Phys. Rev. A 47, 1467 (1993)

    Article  ADS  Google Scholar 

  43. M. Orszag, Quantum Optics: Including Noise Reduction, Trapped Ions, Quantum Trajectories, and Decoherence (Springer-Verlag, Berlin, 2008)

  44. C.C. Gerry, P.L. Knight, Introductory Quantum Optics (Cambridge University Press, New York, 2005)

  45. M.A. Parker, Physics of Optoelectronics (CRC Press, Boca Raton, 2005)

  46. D.A. Steck, Quantum and Atom Optics (2007) http://steck.us/teaching

  47. T. Maier, Superradiant clock laser on an optical lattice (Masterarbeit, Universität Innsbruck, 2014)

  48. H.G. de Barros, Raman spectroscopy and single-photon source in an ion-cavity system, dissertation (Leopold-Franzens-Universität Innsbruck, 2010)

  49. H.J. Carmichael, Statistical Methods in Quantum Optics 1: Master Equations and Fokker-Planck Equations (Springer-Verlag, Berlin, 1999)

  50. H.J. Carmichael, Statistical Methods in Quantum Optics 2: Non-Classical Fields (Springer-Verlag, Berlin, 2008)

  51. B. Parvin, Eur. Phys. J. Plus 131, 1 (2016)

    Article  Google Scholar 

  52. V. Bernat, I. Jex, Quantum Opt. 4, 9 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  53. G. Adam, J. Seke, O. Hittmair, Opt. Commun. 73, 121 (1989)

    Article  ADS  Google Scholar 

  54. B. Parvin, R. Malekfar, J. Mod. Opt. 59, 1841 (2012)

    Article  ADS  Google Scholar 

  55. H. Risken, The Fokker-Planck Equation, Methods of Solution and Applications (Springer-Verlag, Berlin, 1989)

  56. N. Nayak, R.K. Bullough, B.V. Thompson, G.S. Agarwal, IEEE J. Quantum Electron. 24, 1331 (1988)

    Article  ADS  Google Scholar 

  57. G.S. Agarwal, S.D. Gupta, Phys. Rev. A 42, 1737 (1990)

    Article  ADS  Google Scholar 

  58. S.M. Tan, J. Opt. B: Quantum Semiclass. Opt. 1, 424 (1999)

    Article  ADS  Google Scholar 

  59. C. Ginzel, H.-J. Briegel, U. Martini, B.-G. Englert, A. Schenzle, Phys. Rev. A 48, 732 (1993)

    Article  ADS  Google Scholar 

  60. L. Florescu, S. John, T. Quang, R. Wang, Phys. Rev. A 69, 013816 (2004)

    Article  ADS  Google Scholar 

  61. L. Davidovich, Rev. Mod. Phys. 68, 127 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  62. B. Parvin, R. Malekfar, J. Mod. Opt. 59, 848 (2012)

    Article  ADS  Google Scholar 

  63. Y. Mu, C.M. Savage, Phys. Rev. A 46, 5944 (1992)

    Article  ADS  Google Scholar 

  64. H.-J. Briegel, G.M. Meyer, B.-G. Englert, Phys. Rev. A 53, 1143 (1996)

    Article  ADS  Google Scholar 

  65. G.M. Meyer, H.-J. Briegel, H. Walther, Europhys. Lett. 37, 317 (1997)

    Article  ADS  Google Scholar 

  66. M. Loffler, G.M. Meyer, H. Walther, Phys. Rev. A 55, 3923 (1997)

    Article  ADS  Google Scholar 

  67. S.Y. Kilin, T.B. Karlovich, J. Exp. Theor. Phys. 95, 805 (2002)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physics Department, Faculty of Basic Sciences, University of Maragheh, P.O. Box 55181-83111, Maragheh, Iran

    Babak Parvin

Authors
  1. Babak Parvin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Babak Parvin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Parvin, B. The improvement of lasing without inversion in the presence of multi-photon transition in a three-level atom confined in an optical cavity in the steady-state regime. Eur. Phys. J. Plus 132, 180 (2017). https://doi.org/10.1140/epjp/i2017-11479-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2017-11479-7

Search

Navigation