Zeeman-tunable slow–fast light and group-delay control via effective cross-damping in Doppler-broadened Rb vapor

Abstract We examine how thermal averaging changes the local linear dispersion of a Zeeman-resolved three-level medium with effective cross-damping. The probe-free steady state is determined self-consistently, and the susceptibility is constructed solely from the first-order probe-induced coherence. Within the same response calculation, the magnetic field shifts the Raman resonance, the effective cross-damping magnitude and relative optical phase reshape its amplitude and quadratures, and incoherent pumping changes populations and coherence linewidths. For co-propagating fields, the calculated magnetic reversal of the group-index sign survives Maxwell-Boltzmann averaging. Thermal averaging also changes the local dispersive branch at selected fixed detunings, rather than merely reducing its magnitude: one cross-damping scan gives a positive Doppler-free group index but a negative thermally averaged value. The reported group indices and derived delay parameters characterize local steady-state dispersion; they do not establish transmitted-pulse delays. The rubidium-85 mapping supplies illustrative atomic scales, while finite cross damping is a phenomenological assumption whose experimental realization is not established here. The results identify distinct control mechanisms and geometry-dependent thermal effects within this reduced model.