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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 20, Iss. 11 — Nov. 1, 2003
  • pp: 2368–2376

Quantum-jump statistical analysis of three-level systems with arbitrary coupling laser intensities and detunings

Jordi Mompart and Ramón Corbalán  »View Author Affiliations

JOSA B, Vol. 20, Issue 11, pp. 2368-2376 (2003)

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We develop the quantum-jump statistical tools required to analyze the probe response in three-level systems where the probe and driving lasers have arbitrary intensities and detunings. We apply these tools to investigate the appearance of two inversionless amplification sidebands in the probe spectrum as the driving laser intensity increases.

© 2003 Optical Society of America

OCIS Codes
(270.1670) Quantum optics : Coherent optical effects
(270.3430) Quantum optics : Laser theory
(270.4180) Quantum optics : Multiphoton processes

Jordi Mompart and Ramón Corbalán, "Quantum-jump statistical analysis of three-level systems with arbitrary coupling laser intensities and detunings," J. Opt. Soc. Am. B 20, 2368-2376 (2003)

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  1. E. Arimondo, “Coherent population trapping in laser spectroscopy,” in Progress in Optics, Vol. XXXV, E. Wolf, ed. (Elsevier, Amsterdam, 1996).
  2. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36–42 (1997).
  3. O. Kocharovskaya, “Amplification and lasing without inversion,” Phys. Rep. 219, 175–190 (1992).
  4. M. O. Scully, “From lasers and masers to phaseounium and phasers,” Phys. Rep. 219, 191–201 (1992).
  5. P. Mandel, “Lasing without inversion: a useful concept?” Contemp. Phys. 34, 235–246 (1993).
  6. J. Mompart and R. Corbalán, “Lasing without inversion,” J. Opt. B: Quantum Semiclassical Opt. 2, R7-R24 (2000).
  7. C. Peters and W. Lange, “Laser action below threshold inversion due to coherent population trapping,” Appl. Phys. B 62, 221–224 (1996).
  8. J. Mompart, R. Corbalán, and R. Vilaseca, “Giant pulse lasing in three-level systems,” Phys. Rev. A 59, 3038–3043 (1999).
  9. G. S. Agarwal, “Origin of gain in systems without inversion in bare or dressed states,” Phys. Rev. A 44, R28-R30 (1991).
  10. J. Mompart and R. Corbalán, “Inversionless amplification in three-level systems: dressed-states quantum interference and quantum-jump analyses,” Opt. Commun. 156, 133–144 (1998).
  11. P. Mandel and O. Kocharovskaya, “Inversionless amplification of a monochromatic field by a three-level medium,” Phys. Rev. A 46, 2700–2706 (1992).
  12. These results hold for the usual case in which the driven transition is not inverted; see Ref. 10.
  13. J. Kitching and L. Hollberg, “Interference-induced optical gain without population inversion in cold, trapped atoms,” Phys. Rev. A 59, 4685–4689 (1999).
  14. A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, “Experimental demonstration of laser oscillation without population inversion via quantum interference in Rb,” Phys. Rev. Lett. 75, 1499–1502 (1995).
  15. H. J. Carmichael, “An open-systems approach to quantum optics,” Lect. Notes Phys. 18 (1993).
  16. J. Dalibard, Y. Castin, and K. Mølmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68, 580–583 (1992).
  17. R. Dum, P. Zoller, and H. Ritsch, “Monte Carlo simulation of the atomic master equation for spontaneous emission,” Phys. Rev. A 45, 4879–4887 (1992).
  18. K. Mølmer, Y. Castin, and J. Dalibard, “Monte Carlo wave-function method in quantum optics,” J. Opt. Soc. Am. B 10, 524–538 (1993).
  19. E. Arimondo, “Mechanism in laser without inversion,” in Shangai International Symposium on Quantum Optics, D.-H. Wabg and Z. Wang, eds., Proc. SPIE 1726, 484–489 (1992).
  20. C. Cohen-Tannoudji, B. Zambon, and E. Arimondo, “Quantum-jump approach to dissipative processes: application to amplification without inversion,” J. Opt. Soc. Am. B 10, 2107–2120 (1993).
  21. H. J. Carmichael, “Coherence and decoherence in the interaction of lights with atoms,” Phys. Rev. A 56, 5065–5099 (1997).
  22. J. Mompart and R. Corbalán, “Quantum-jump approach to dipole dephasing: application to inversionless amplification,” Eur. Phys. J. D 5, 351–356 (1999).
  23. J. Mompart and R. Corbalán, “Generalized Einstein B coefficients for coherently driven three-level systems,” Phys. Rev. A 63, 063810 (2001).
  24. Note that it is straightforward to use these Rij with i≠j to describe bidirectional pumping. For instance, let us denote by Λ the rate of a bidirectional pumping process coupled to transition |a〉–|b〉; then Rab=Λ+γab and Rba=Λ with γab being the spontaneous emission rate from |a〉 to |b〉.
  25. As a general feature, dissipative processes associated with Rij with i≠j correspond to quantum jumps connecting different manifolds, while those associated with Rij with i=j yield a new coherent evolution period in the same manifold as the previous one; see Ref. 22.
  26. The mean change of the probe photon number per unit time relates to the mean change per period as 〈dNα/dt〉=〈ΔNα〉/T where T is the average time between two consecutive quantum jumps; see Eqs. (4.11) and (4.16) in Ref. 20.
  27. Note that as a result of the presence of dissipation, xij(τ), yij(τ)→0 in an exponential way, which guarantees the convergence of ∫0|cij(τ)|2dτ.

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