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Self-induced transparency and optical transients in atomic vapors

B. S. Cartwright, S. A. Wrathmall*, and R. M. Potvliege†

  • *Contact author: s.a.wrathmall@durham.ac.uk
  • †Contact author: r.m.potvliege@durham.ac.uk
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Phys. Rev. A 113, 033104 – Published 10 March, 2026

DOI: https://doi.org/10.1103/jslj-zzvc

Abstract

The rapid turn-on of a strong, resonant, continuous wave laser field may trigger the formation of a transient oscillation akin to a train of damped solitons, before the vapor-field system relaxes into a stationary state. We study this transient dynamic on theoretical models of a rubidium vapor. We also consider doubly resonant V systems, for which the transients take the form of trains of damped simultons. We compute the propagating field(s) by solving the Maxwell-Bloch equations, taking homogeneous broadening, Doppler broadening and the full hyperfine structure of the atoms into account. We also compare the actual fields to the stationary dnoidal fields predicted by the Maxwell-Bloch equations in conditions of self-induced transparency. A similar dynamics is expected to occur in any atomic vapor at the turn-on of a strong resonant continuous wave field provided the turn-on is sufficiently fast compared to relaxation.

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References (62)

  1. S. L. McCall and E. L. Hahn, Phys. Rev. Lett. 18, 908 (1967); Phys. Rev. 183, 457 (1969).
  2. M. D. Crisp, Phys. Rev. Lett. 22, 820 (1969).
  3. J. H. Eberly, Phys. Rev. Lett. 22, 760 (1969).
  4. G. L. Lamb Jr., Rev. Mod. Phys. 43, 99 (1971).
  5. L. A. Bol'shov and V. V. Likhanskiĭ, Kvant. Elektron. 12, 1339 (1985) [Sov. J. Quantum Electron. 15, 889 (1985)].
  6. A. I. Maimistov, A. M. Basharov, S. O. Elyutin, and Yu. M. Sklyarov, Phys. Rep. 191, 1 (1990); A. I. Maimistov and A. M. Basharov, Nonlinear Optical Waves (Kluwer, Dordrecht, 1999).
  7. For an introduction to the early work on SIT, see, e.g., L. Allen and J. H. Eberly, Optical Resonances and Two-level Atoms (Wiley, New York, 1975).
  8. T. P. Ogden, K. A. Whittaker, J. Keaveney, S. A. Wrathmall, C. S. Adams, and R. M. Potvliege, Phys. Rev. Lett. 123, 243604 (2019).
  9. M. V. Arkhipov, A. A. Shimko, N. N. Rosanov, I. Babushkin, and R. M. Arkhipov, Phys. Rev. A 101, 013803 (2020).
  10. Z. Bai, C. S. Adams, G. Huang, and W. Li, Phys. Rev. Lett. 125, 263605 (2020).
  11. See, e. g., C. Jirauschek, M. Riesch, P. Tzenov, Adv. Theory Simul. 2, 1900018 (2019); G. T. Adamashvili, Eur. Phys. J. D 74, 41 (2020); S. K. Hazra, P. K. Pathak, and T. N. Dey, Phys. Rev. B 107, 235409 (2023); M. S. Najafabadi, L. L. Sánchez-Soto, J. F. Corney, N. Kalinin, A. A. Sorokin, and G. Leuchs, Phys. Rev. Res. 6, 023142 (2024).
  12. See, e. g., S. Hughes, Phys. Rev. Lett. 81, 3363 (1998); D. V. Novitsky, Phys. Rev. A 84, 013817 (2011); H. Wu, J. Tang, M. Chen, M. Xiao, Y. Lu, K. Xia, and F. Nori, Opt. Express 32, 11010 (2024); A. Pakhomov, Phys. Rev. A 111, 013502 (2025).
  13. A. M. Alhasan, J. Fiutak, and W. Miklaszewski, Z. Phys. B 88, 349 (1992).
  14. W. Miklaszewski and J. Fiutak, Z. Phys. B 93, 491 (1994).
  15. M. J. Konopnicki and J. H. Eberly, Phys. Rev. A 24, 2567 (1981).
  16. See also M. J. Konopnicki, P. H. Drummond, and J. H. Eberly, Opt. Commun. 36, 313 (1981); C. R. Stroud, Jr. and D. A. Cardimona, ibid. 37, 221 (1981).
  17. Many-state V systems may also support many-color simultons — see, e. g., G. Huang and C. Hang, Phys. Lett. A 354, 406 (2006); G. Huang, C. Hang, and L. Deng, Eur. Phys. J. D 40, 437 (2006).
  18. F. T. Hioe and R. Grobe, Phys. Rev. Lett. 73, 2559 (1994).
  19. M. D. Crisp, Phys. Rev. A 5, 1365 (1972).
  20. B. Ségard, B. Macke, J. Zemmouri, and W. Sergent, Ann. Phys. (Paris) 15, 167 (1990).
  21. J. de Lamare, Ph. Kupecek, and M. Comte, Opt. Commun. 95, 305 (1993).
  22. M. D. Crisp, Phys. Rev. A 1, 1604 (1970); A. Z. Akcasu and J. J. Duderstadt, ibid. 2, 2172 (1970).
  23. J. E. Rothenberg, D. Grischkowsky, and A. C. Balant, Phys. Rev. Lett. 53, 552 (1984).
  24. O. Avenel, E. Varoquaux, and G. A. Williams, Phys. Rev. Lett. 53, 2058 (1984).
  25. E. M. Pessina, B. Ségard, and B. Macke, Opt. Commun. 81, 397 (1991).
  26. W. R. LeFew, S. Venakides, and D. J. Gauthier, Phys. Rev. A 79, 063842 (2009).
  27. D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. Lett. 103, 093602 (2009).
  28. B. Macke and B. Ségard, Phys. Rev. A 81, 015803 (2010).
  29. K. E. Oughstun, N. A. Cartwright, D. J. Gauthier, and H. Jeong, J. Opt. Soc. Am. B 27, 1664 (2010); B. Macke and B. Ségard, ibid. 28, 450 (2011); K. E. Oughstun, N. A. Cartwright, D. J. Gauthier, and H. Jeong, ibid. 28, 468 (2011).
  30. B. Horovitz and N. Rosenberg, Phys. Rev. A 26, 2799 (1982).
  31. D. J. Kaup, Phys. Rev. A 16, 704 (1977).
  32. M. A. Newbold and G. J. Salamo, Phys. Rev. Lett. 42, 887 (1979); J. L. Shultz and G. J. Salamo, ibid. 78, 855 (1997); M. O. Scully, G. S. Agarwal, O. Kocharovskaya, V. V. Kozlov, and A. B. Matsko, Opt. Express 8, 66 (2001); S. M. Saadeh, J. L. Shultz, and G. J. Salamo, ibid. 8, 153 (2001).
  33. B. S. Cartwright, Optical transients in atomic vapours, Durham thesis, Durham University, 2022, http://etheses.dur.ac.uk/14532/.
  34. See, e.g., P. Lambropoulos and D. Petrosyan, Fundamentals of Quantum Optics and Quantum Information (Springer, Berlin, 2007). No time-derivative of the polarization amplitude P(z,t) appears in Eq. (4) because the corresponding terms are negligible compared to the term in ωP(z,t) forming the right-hand side of this equation, For the systems considered in the present paper, the amplitudes E(z,t) and P(z,t) vary on a time scale roughly equivalent to 106 optical periods.
  35. These results are readily derived by particularizing the calculations outlined in the Appendix to the case of a single field. They only apply to systems for which the function g(Δ) appearing in Eq. (21) is an even function of Δ. They need to be supplemented by a dispersion relation in more general cases [1].
  36. We follow the NIST Digital Library of Mathematical Functions, (https://dlmf.nist.gov/) in the definition of this function: K(z)=∫0π/2dθ1−z2sin2θ.
  37. V. V. Kozlov and E. B. Kozlova, Opt. Spektrosk. 107, 129 (2009) [Opt. Spectrosc. 107, 129 (2009)].
  38. L. A. Bol'shov, N. N. Elkin, T. K. Kirichenko, V. V. Likhanskiĭ, and A. P. Napartovich, Kvant. Elektron. 9, 1476 (1982) [Sov. J. Quantum Electron. 12, 941 (1982)].
  39. L. A. Bol'shov, N. N. Elkin, T. K. Kirichenko, V. V. Likhanskiĭ, and M. I. Persiantsev, Preprint IAE-3732/16, Atomic Energy Inst., Moscow (1983) [in Russian].
  40. L. A. Bol'shov, N. N. Yelkin, V. V. Likhanskiĭ, and M. I. Persiantsev, Zh. Eks. Teor. Fiz. 94, 101 (1988) [Sov. Phys. JETP 67, 2013 (1988)].
  41. V. V. Kozlov and E. E. Fradkin, Pis. Zh. Eksp. Teor. Fiz. 68, 359 (1998) [JETP Lett. 68, 383 (1998)].
  42. N. V. Denisova, V. S. Egorov, V. V. Kozlov, N. M. Reutova, P. Yu. Serdobintsev, and E. E. Fradkin, Zh. Eksp. Teor. Fiz. 113, 71 (1998) [J. Exp. Theor. Phys. 86, 39 (1998)].
  43. V. V. Kozlov, P. G. Polynkin, and M. O. Scully, Phys. Rev. A 59, 3060 (1999).
  44. E. Paspalakis, N. J. Kylstra, and P. L. Knight, Phys. Rev. A 61, 045802 (2000).
  45. V. V. Kozlov and E. B. Kozlova, Opt. Spektrosk. 108, 824 (2010) [Opt. Spectrosc. 108, 780 (2010)].
  46. O. M. Fedotova, O. K. Khasanov, G. A. Rusetsky, J. Degert, and E. Freysz, Phys. Rev. A 90, 053843 (2014).
  47. R. M. Potvliege and S. A. Wrathmall, Comput. Phys. Commun. 306, 109374 (2025).
  48. D. A. Steck, Rubidium 85 D line data, available online at http://steck.us/alkalidata.
  49. H. P. Grieneisen, J. Goldhar, N. A. Kurnit, and A. Javan, Appl. Phys. Lett. 21, 559 (1972).
  50. S. M. Hamadani, J. Goldhar, N. A. Kurnit, and A. Javan, Appl. Phys. Lett. 25, 160 (1974).
  51. M. Matusovsky, B. Vaynberg, and M. Rosenbluh, J. Opt. Soc. Am. B 13, 1994 (1996).
  52. According to the Beer-Lambert law, the intensity of the probe field would decrease like Ipinexp(−αz) with α=(0.42mm)−1 in the case of Fig. 4 and α=(1.2mm)−1 in the case of Fig. 7, in the absence of the coupling field. See, e.g., Ref. [47] for the calculation of the absorption coefficient α with Doppler broadening.
  53. E.g., C. R. Higgins and I. G. Hughes, J. Phys. B 54, 165403 (2021).
  54. T. Y. Abi-Salloum, Phys. Rev. A 81, 053836 (2010).
  55. S. Khan, V. Bharti, and V. Natarajan, Phys. Lett. A 380, 4100 (2016).
  56. Quantum interference plays a role for weak coupling fields, though. See C. Zhu, C. Tan, and G. Huang, Phys. Rev. A 87, 043813 (2013).
  57. P. Siddons, J. Phys. B 47, 093001 (2014).
  58. Doubly dressed states have been considered previously for ladder systems, [see, e.g., R.-Y. Chang, W.-C. Fang, Z.-S. He, B.-C. Ke, P.-N. Chen, and C.-C. Tsai, Phys. Rev. A 76, 053420 (2007)] but, to our knowledge, not for V systems.
  59. It is known that SIT solitons and simultons undergo transverse reshaping upon propagation: see N. Wright and M. C. Newstein, Opt. Commun. 9, 8 (1973); H. M. Gibbs, B. Bölger, F. P. Mattar, M. C. Newstein, G. Forster, and P. E. Toschek, Phys. Rev. Lett. 37, 1743 (1976); L. A. Bol'shov, V. V. Likhanskiĭ, and A. P. Napartovich, Zh. Eksp. Teor. Fiz. 72, 1769 (1977) [Sov. Phys. JETP 45, 928 (1977)]; F. P. Mattar and M. C. Newstein, Comput. Phys. Comm. 20, 139 (1980); L. A. Bol'shov, T. K. Kirichenko, V. V. Likhanskiĭ, M. I. Persiantsev, and L. K. Sokolova, Zh. Eksp. Teor. Fiz. 86, 1240 (1984) [Sov. Phys. JETP 59, 724 (1984)]; P. D. Drummond, Opt. Commun. 49, 219 (1984); J. de Lamare, M. Comte, and Ph. Kupecek, Phys. Rev. A 50, 3366 (1994); J. de Lamare, Ph. Kupecek, and M. Comte, ibid. 51, 4289 (1995).
  60. The propagated fields and the corresponding input data for use with the open-source Maxwell-Bloch solver CoOMBE [47] can be found at https://doi.org/10.15128/r2jq085k062.
  61. A. Rahman, Phys. Rev. A 60, 4187 (1999); A. Rahman and J. H. Eberly, Opt. Express 4, 133 (1999).
  62. These equations take into the fact that the symbol Δ used in Ref. [2] denotes the negative of the detuning Δ defined in the present work.

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Phys. Rev. A 113, 033104– Published 10 March, 2026
  • Received 23 May 2025
  • Accepted 11 February 2026
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