Single-photon pulse propagation in and into a medium of two-level atoms: Microscopic Fresnel Equations - Berman, P.R.; Ooi, Chong Heng Raymond (American Physical Society, 2011)
The propagation of an off-resonant, single-photon pulse in and into a medium of two-level atoms is considered. When the pulse is launched from within the medium, there are two propagation speeds, neither of which is the normal group velocity. For densities as small as 10(11) atoms/cm(3) and detunings of order 10(11) s(-1), both propagation speeds approach one half the speed of light in vacuum. Moreover, rather remarkably, there are Rabi oscillations between the field and atomic excitation, even for this single-photon pulse. In contrast, for a pulse sent into the medium, the atom-field system remains adiabatically in a dressed state that propagates with the normal group velocity. In the limit that the index of refraction is approximately equal to unity, we obtain the Fresnel equations for the reflection and transmission coefficients based on this microscopic model. The transmission coefficient differs from the conventional result owing to the fact that we quantize the field in free space.