Slow-light dynamics from electromagnetically-induced-transparency spectra

Slow light from electromagnetically-induced transparency EIT has many potential applications, including photonic delay lines 1, interferometry 2,3, quantum memories 4, and atomic spectroscopy 5. These applications benefit from long pulse delay times, which arise from a reduced group velocity associated with steep dispersion from an atomic 4,6-10 or optical 11-16 resonance. Characterization of slow light for a particular medium often begins with the underlying static absorption resonance e.g., Refs. 4,7,10,11,17. However, extracting dispersive slow-light behavior from the associated absorption resonance via the Kramers-Kronig relations is often difficult. While these rela- tions provide a direct connection between absorption and dispersion spectra, they can be solved analytically only for a very limited range of absorption functions and numerical so- lutions often diverge 18. Other work 19 has taken a phe- nomenological Lorentzian absorption spectrum and calcu- lated the resulting group velocity reduction. Here, we show that a simple realistic model of EIT spectra allows accurate prediction of slow-light pulse delay from two easily measur- able parameters: the linewidth and off-resonant transmission level on a logarithmic scale. We find good agreement be- tween the predictions of this model and experimental mea- surements of EIT and slow light in warm rubidium vapor. This technique should be applicable to a wide range of slow- light media. EIT is a two-optical-field phenomenon in which a strong control field renders an otherwise absorbing medium trans- parent to a weak signal field via quantum interference be- tween two alternate excitation paths from the ground to ex- cited state 20. Both static line shapes 21 and dynamic behavior 22,23 may be straightforwardly calculated. Here, we extract model parameters from the three-level-atom ab- sorption resonance and determine the group velocity and ef- fective optical depth, which together determine the absolute pulse delay. We calculate steady-state signal absorption in EIT from the imaginary component of the susceptibility. For a three- level system, the susceptibility as a function of two-photon Raman detuning, ,i s21 = n 2