Theory of Thermal Motion in Electromagnetically Induced Transparency: Diffusion, Doppler, Dicke and Ramsey

We present a theoretical model for electromagnetically induced transparency (EIT) in vapor, that incorporates atomic motion and velocity-changing collisions into the dynamics of the density-matrix distribution. Within a unified formalism we demonstrate various motional effects, known for EIT in vapor: Doppler-broadening of the absorption spectrum; Dicke-narrowing and time-of-flight broadening of the transmission window for a finite-sized probe; Diffusion of atomic coherence during storage of light and diffusion of the light-matter excitation during slow-light propagation; and Ramsey-narrowing of the spectrum for a probe and pump beams of finite-size.