From superradiance to collective EIT in three-level ensembles

We investigate the collective dynamics of a three-level ensemble under the Dicke limit, revealing a unified connection between superradiant emission and electromagnetically induced transparency (EIT). Our results show that the transient superradiant burst exhibits the expected peak intensity scaling I_maxsim N², with a universal finite-size correction |ξ(N)-2|sim 1/ln N that governs the apparent scaling exponent in realistic ensembles. In the stationary regime, collective broadening modifies the EIT response: although it typically enhances absorption, it counterintuitively increases the group velocity, leading to a relative scaling v_gpropto N², even while v_gll c. This effect suggests that cooperative interactions fundamentally limit the achievable slow-light delay in dense media. To achieve these results, we derive a representative-atom master equation that quantitatively reproduces both the superradiant and EIT regimes, in excellent agreement with the exact symmetric-subspace dynamics and correctly incorporating collective feedback and N-dependent broadening. This unified framework bridges transient superradiant emission and steady-state quantum interference, with direct implications for slow light, quantum memories, and precision metrology.