Quantitative analysis of the transient response of the refractive index to conditions of electromagnetically induced transparency

For the example of the D{}₁$ line of ${}⁸⁷$Rb we analyze the experimental parameters that control the transient response of electromagnetically induced transparency. Quantum coherent free-induction decay is observed on time scales exceeding several milliseconds in a buffer-gas vapor cell. Numerical solutions of the quantum master equation and approximate analytical solutions are tested and absolute comparisons of the transient time scales, power broadening, resonance contrast, and frequency shifts are made. Two actively-phase-locked lasers are employed. The effects of laser phase noise that is not fully correlated are studied.