Exact Analytical Solution of the Driven Qutrit in an Open Quantum System: V and $\mathrm{\Lambda }$ Configurations

We obtain the exact analytical solution for the continuously driven qutrit in the V and $\mathrm{\Lambda }$ configurations governed by the Lindblad master equation. We calculate the linear susceptibility in each system, determining regimes of transient gain without inversion, and identify exact parameter values for superluminal, vanishing, and negative group velocity for the probe field.