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Cooperative emission from an ensemble of three-level Λ radiators in a cavity: An insight from the viewpoint of dynamics of nonlinear systems

  • Atoms, Molecules, Optics
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Abstract

Cooperative radiation emitted by an ensemble of three-level optical systems with a doublet in the ground state (Λ scheme), which is placed into a cyclic cavity, is studied theoretically. In contrast to the two-level model of emitters, this process with such a configuration of operating transitions may occur without population inversion in the whole, if the doublet is prepared at the initial instant in a superposition (coherent) state. In the ideal case of a Hamilton system, in which the cavity losses and relaxation in the radiator ensemble are disregarded, the conservation laws are derived, which allow a substantial reduction of the dimension of the phase space of the model (ℝ11 → ℝ5) and the application of methods of dynamics of nonlinear systems for analyzing the three-level superradiance under these conditions. The possibility of different (both quasiperiodic and chaotic) scenarios of the three-level superradiance is demonstrated on the basis of Poincaré’s mappings. Global bifurcation of the system upon a transition from the conventional superradiance regime to inversionless one is revealed. The effects of cavity losses, as well as homogeneous and inhomogeneous broadening in the system of radiators on the regularities found are also discussed.

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References

  1. R. H. Dicke, Phys. Rev. 93, 99 (1954).

    Article  ADS  Google Scholar 

  2. N. E. Rehler and J. H. Eberly, Phys. Rev. A 3, 1735 (1971).

    Article  ADS  Google Scholar 

  3. K. Bonifacio, P. Schwendimann, and F. Haake, Phys. Rev. A 4, 302 (1971), Phys. Rev. A 4, 854 (1971).

    Article  ADS  Google Scholar 

  4. I. V. Sokolov and E. D. Trifonov, Sov. Phys. JETP 38, 37 (1974).

    ADS  Google Scholar 

  5. R. Bonifacio and L. A. Lugiato, Phys. Rev. A 11, 1507 (1975); Phys. Rev. A 12, 587 (1975).

    Article  ADS  Google Scholar 

  6. J. C. MacGillivray and M. S. Feld, Phys. Rev. A 14, 1169 (1976); Phys. Rev. A 23, 1334 (1981).

    Article  ADS  Google Scholar 

  7. N. Scribanovich, I. P. Herman, J. C. MacGillevray, and M. S. Feld, Phys. Rev. Lett. 30, 309 (1973).

    Article  ADS  Google Scholar 

  8. H. M. Gibbs, Q. H. F. Vrehen, and H. M. J. Hikspoors, Phys. Rev. Lett. 39, 547 (1976).

    Article  ADS  Google Scholar 

  9. A. Flusberg, T. Mossberg, and S. R. Hartman, Phys. Lett. A 58, 373 (1976).

    Article  ADS  Google Scholar 

  10. R. Florian, L. O. Schwan, and D. Schmid, Solid State Commun. 42, 55 (1982); Phys. Rev. A 28, 2709 (1984).

    Article  ADS  Google Scholar 

  11. M. S. Malcuit, J. J. Maki, D. J. Simkin, and R. W. Boyd, Phys. Rev. Lett. 59, 1189 (1987).

    Article  ADS  Google Scholar 

  12. Yu. V. Nabokin, V. V. Samartsev, and N. B. Silaeva, Izv. Akad. Nauk SSSR, Ser. Fiz. 47, 74 (1983).

    Google Scholar 

  13. P. V. Zinov’ev, S. V. Lopina, Yu. V. Nabokin, N. B. Silaeva, V. V. Samartsev, and Yu. E. Sheibut, Sov. Phys. JETP 58, 1129 (1983).

    Google Scholar 

  14. F. Auzel, S. Hubert, and D. Meichenin, Europhys. Lett. 7, 459 (1988).

    Article  ADS  Google Scholar 

  15. C. Greiner, B. Boggs, and T. W. Mossberg, Phys. Rev. Lett. 85, 3793 (2000).

    Article  ADS  Google Scholar 

  16. Yu. F. Kiselev, A. F. Prudkoglyad, A. S. Shumovskii, and V. I. Yukalov, Sov. Phys. JETP 67, 413 (1988).

    Google Scholar 

  17. N. A. Bazhanov, D. S. Bulyanitsa, A. I. Zaitsev, A. I. Kovalev, V. A. Malyshev, and E. D. Trifonov, Sov. Phys. JETP 70, 1128 (1990).

    Google Scholar 

  18. V. I. Yukalov, Phys. Rev. Lett. 75, 3000 (1995).

    Article  ADS  Google Scholar 

  19. D. S. Druzhin, D. S. Bulyanitsa, and E. D. Trifonov, J. Exp. Theor. Phys. 91, 239 (2000).

    Article  ADS  Google Scholar 

  20. V. I. Yukalov and E. P. Yukalova, Phys. Part. Nucl. 35, 348 (2004).

    Google Scholar 

  21. J. Vanacken, S. Stroobants, M. Malfait, et al., Phys. Rev. B 70, 220401(R) (2004).

    Article  ADS  Google Scholar 

  22. M. G. Benedict, P. Foeldi, and F. M. Peeters, Phys. Rev. B 72, 214430 (2005).

    Article  ADS  Google Scholar 

  23. V. I. Yukalov and E. P. Yukalova, Laser Phys. Lett. 8, 804 (2011).

    Article  ADS  Google Scholar 

  24. C. Ohae, A. Fukumi, S. Kuma, et al., J. Phys. Soc. Jpn. 83, 044301 (2014).

    Article  ADS  Google Scholar 

  25. T. Brandes, Phys. Rep. 408, 315 (2005).

    Article  ADS  Google Scholar 

  26. V. N. Pustovit and T. V. Shahbazyan, Phys. Rev. Lett. 102, 077401 (2009); Phys. Rev. B 82, 075429 (2010).

    Article  ADS  Google Scholar 

  27. V. V. Popov, O. V. Polischuk, A. R. Davoyan, V. Ryzhii, T. Otsuji, and M. S. Shur, Phys. Rev. B 86, 195437 (2012).

    Article  ADS  Google Scholar 

  28. R. Fleury and A. Aluù, Phys. Rev. B 87, 201101(R) (2013).

    Article  ADS  Google Scholar 

  29. A. Fukumi, S. Kuma, Y. Miyamoto, et al., Prog. Theor. Exp. Phys. 2012, 04D002 (2012).

    Article  Google Scholar 

  30. S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, J. Stanger, D. E. Pritchard, and W. Ketterle, Science 285, 571 (1999).

    Article  Google Scholar 

  31. M. G. Moore and P. Meystre, Phys. Rev. Lett. 83, 5202 (1999).

    Article  ADS  Google Scholar 

  32. E. D. Trifonov, J. Exp. Theor. Phys. 93, 969 (2001)

    Article  ADS  Google Scholar 

  33. E. D. Trifonov, Laser Phys. 12, 211 (2002).

    Google Scholar 

  34. Y. A. Avetisyan and E. D. Trifonov, Laser Phys. Lett. 1, 373 (2004); Laser Phys. Lett. 2, 512 (2005); Phys. Rev. A 88, 025601-3 (2013).

    Article  ADS  Google Scholar 

  35. M. Gross and S. Haroche, Phys. Rep. 93, 301 (1982).

    Article  ADS  Google Scholar 

  36. A. V. Andreev, V. I. Emel’yanov, and Yu. A. Il’inskii, Sov. Phys. Usp. 23, 493 (1980).

    Article  ADS  Google Scholar 

  37. V. V. Zheleznyakov, V. V. Kocharovskii, and Vl. V. Kocharovskii, Sov. Phys. Usp. 32, 835 (1989).

    Article  ADS  Google Scholar 

  38. A. V. Andreev, V. I. Emel’yanov, and Yu. A. Il’inskii, Cooperative Effects in Optics (IOP, Bristol, Philadelphia, 1993).

    Google Scholar 

  39. M. G. Benedict, A. M. Ermolaev, V. A. Malyshev, I. V. Sokolov, and E. D. Trifonov, Super-Radiance: Multiatomic Coherent Emission (IOP, Bristol, Philadelphia, 1996).

    Google Scholar 

  40. A. A. Kalachev and V. V. Samartsev, Coherent Phenomena in Optics (Kazan Gos. Univ., Kazan, 2003) [in Russian].

    Google Scholar 

  41. V. A. Malyshev, I. V. Ryzhov, E. D. Trifonov, and A. I. Zaitsev, SPIE Proc. 3239, 129 (1997).

    Article  ADS  Google Scholar 

  42. V. A. Malyshev, I. V. Ryzhov, E. D. Trifonov, and A. I. Zaitsev, Laser Phys. 8, 494 (1998).

    Google Scholar 

  43. J. T. Manassah and B. Gross, Opt. Commun. 150, 189 (1998).

    Article  ADS  Google Scholar 

  44. A. I. Zaitsev, V. A. Malyshev, E. D. Trifonov, and I. V. Ryzhov, J. Exp. Theor. Phys. 88, 278 (1999); Opt. Spectrosc. 87, 755 (1999).

    Article  ADS  Google Scholar 

  45. V. Kozlov, O. Kocharovskaya, Yu. Rostovtsev, and M. Scully, Phys. Rev. A 60, 1598 (1999).

    Article  ADS  Google Scholar 

  46. I. V. Ryzhov, N. A. Vasil’ev, I. S. Kosova, M. D. Shtager, and V. A. Malyshev, Opt. Spectrosc. 120, 440 (2016).

    Article  ADS  Google Scholar 

  47. V. A. Malyshev, I. V. Ryzhov, E. D. Trifonov, and A. I. Zaitsev, Laser Phys. 9, 876 (1999).

    Google Scholar 

  48. A. I. Zaitsev, I. V. Ryzhov, E. D. Trifonov, and V. A. Malyshev, Opt. Spectrosc. 87, 956 (1999).

    ADS  Google Scholar 

  49. A. I. Zaitsev and I. V. Ryzhov, Opt. Spectrosc. 89, 601 (2000); Opt. Spectrosc. 91, 941 (2001).

    Article  ADS  Google Scholar 

  50. A. A. Bogdanov, A. I. Zaitsev, and I. V. Ryzhov, Opt. Spectrosc. 89, 935 (2000).

    Article  ADS  Google Scholar 

  51. I. V. Ryzhov, A. I. Zaitsev, and E. V. Shuval-Sergeeva, Opt. Spectrosc. 112, 604 (2012).

    Article  ADS  Google Scholar 

  52. O. A. Kocharovskaya and Ya. I. Khanin, JETP Lett. 48, 630 (1988).

    ADS  Google Scholar 

  53. Ya. I. Khanin and O. A. Kocharovskaya, J. Opt. Soc. Am. B 7, 2016 (1990).

    Article  ADS  Google Scholar 

  54. S. E. Harris, Phys. Rev. Lett. 62, 1033 (1989).

    Article  ADS  Google Scholar 

  55. O. Kocharovskaya, Phys. Rep. 219, 175 (1992).

    Article  ADS  Google Scholar 

  56. F. T. Arecchi and E. Courtens, Phys. Rev. A 2, 1730 (1970).

    Article  ADS  Google Scholar 

  57. A. M. Basharov, G. G. Grigoryan, N. V. Znamenskiy, E. A. Manykin, Yu. V. Orlov, A. Yu. Shashkov, and T. G. Yukina, J. Exp. Theor. Phys. 102, 206 (2006).

    Article  ADS  Google Scholar 

  58. F. Haake, H. King, G. Schröder, J. Haus, and R. Glauber, Phys. Rev. A 20, 2047 (1979); Phys. Rev. Lett. 45, 558 (1980).

    Article  ADS  Google Scholar 

  59. N. W. Carlson, D. J. Jackson, A. I. Shawlow, M. Gross, and S. Haroch, Opt. Commun. 32, 350 (1980).

    Article  ADS  Google Scholar 

  60. R. F. Malikov and E. D. Trifonov, Opt. Commun. 52, 74 (1984).

    Article  ADS  Google Scholar 

  61. S. P. Kuznetsov, Dynamical Chaos (Fizmatlit, Moscow, 2001) [in Russian].

    Google Scholar 

  62. G. Korn and T. Korn, Mathematical Handbook for Scientists and Engineers (Nauka, Moscow, 1974; McGraw- Hill, New York, 1961).

    MATH  Google Scholar 

  63. F. C. Moon, Chaotic Vibrations: An Introduction for Applied Scientists and Engineers (Wiley-VCH, Weinheim, 2004).

    Book  MATH  Google Scholar 

  64. G. Hacken, Synergetics (Springer, Berlin, 1978; Mir, Moscow, 1980).

    Google Scholar 

  65. Yu. I. Neimark and P. S. Landa, Stochastic and Chaotic Vibrations (Nauka, Moscow, 1987) [in Russian].

    MATH  Google Scholar 

  66. G. Duffing, Erzwungene Schwingungen bei Veränderlicher Eigenfrequenz und ihre Technische Bedeutung (Vieweg, Braunschweig, 1918) [in German].

    MATH  Google Scholar 

  67. A. P. Kuznetsov and S. P. Kuznetsov, Nonlinear Oscillations (Fizmatlit, Moscow, 2005) [in Russian].

    MATH  Google Scholar 

  68. R. F. Malikov, V. A. Malyshev, and E. D. Trifonov, Opt. Spectrosc. 53, 387 (1982).

    ADS  Google Scholar 

  69. A. I. Zaitsev, V. A. Malyshev, and E. D. Trifonov, Opt. Spectrosc. 65, 599 (1988).

    ADS  Google Scholar 

  70. L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, New York, 1987; Mir, Moscow, 1978).

    Google Scholar 

  71. C. W. Thiel, T. Böttger, and R. L. Cone, J. Lumin. 131, 353 (2011).

    Article  Google Scholar 

  72. T. Zhong, J. M. Kindem, E. Miyazono, and A. Faraon, Nat. Commun. 6, 8206 (2015).

    Article  ADS  Google Scholar 

  73. M. Zhong, M. P. Hedges, R. L. Ahlefeldt, J. G. Bartholomew, S. E. Beavan, S. M. Wittig, J. J. Longdell, and M. J. Sellars, Nature 517, 177 (2015).

    Article  ADS  Google Scholar 

  74. V. A. Zuikov, A. A. Kalachev, V. V. Samartsev, and A. M. Shegeda, Laser Phys. 9, 951 (1999); Laser Phys. 10, 364 (2000).

    Google Scholar 

  75. V. A. Zuikov, A. A. Kalachev, V. V. Samartsev, and A. M. Shegeda, Quantum Electron. 30, 629 (2000).

    Article  ADS  Google Scholar 

  76. A. A. Kalachev and V. V. Samartsev, Laser Phys. 12, 1114 (2002); J. Lumin. 98, 331 (2002).

    Google Scholar 

  77. G. G. Grigoryan, Yu. V. Orlov, E. A. Petrenko, A. Yu. Shashkov, and N. V. Znamenskiy, Laser Phys. 15, 602 (2005).

    Google Scholar 

  78. G. G. Grigoryan, Yu. V. Orlov, A. Yu. Shashkov, T. G. Yukina, and N. V. Znamenskiy, Laser Phys. 17, 511 (2007).

    Article  ADS  Google Scholar 

  79. A. M. Basharov, G. G. Grigoryan, N. V. Znamenskii, Yu. V. Orlov, A. Yu. Shashkov, and T. G. Yukina, Quantum Electron. 39, 251 (2009).

    Article  ADS  Google Scholar 

  80. A. M. Basharov, N. V. Znamenskii, and A. Yu. Shashkov, Opt. Spectrosc. 104, 241 (2008).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Herzen State Pedagogical University of Russia, St. Petersburg, 191186, Russia

    I. V. Ryzhov, N. A. Vasil’ev, I. S. Kosova & M. D. Shtager

  2. Fock Research Institute of Physics, St. Petersburg State University, St. Petersburg, 198504, Russia

    V. A. Malyshev

  3. Zernike Institute for Advanced Materials, University of Groningen, AG Groningen, 9747, The Netherlands

    V. A. Malyshev

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  1. I. V. Ryzhov
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  2. N. A. Vasil’ev
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Correspondence to I. V. Ryzhov.

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Original Russian Text © I.V. Ryzhov, N.A. Vasil’ev, I.S. Kosova, M.D. Shtager, V.A. Malyshev, 2017, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2017, Vol. 151, No. 5, pp. 803–822.

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Ryzhov, I.V., Vasil’ev, N.A., Kosova, I.S. et al. Cooperative emission from an ensemble of three-level Λ radiators in a cavity: An insight from the viewpoint of dynamics of nonlinear systems. J. Exp. Theor. Phys. 124, 683–700 (2017). https://doi.org/10.1134/S1063776117050053

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