Pulsed single-photon magnetometry with a $Λ$-type three-level system: near-optimal frequency-resolved photon counting

We investigate pulsed single-photon magnetometry with a Zeeman-sensitive $Λ$-type three-level system driven by a classical control field. We derive the asymptotic output state and decompose its quantum Fisher information into photon-loss, spectral-intensity, and spectral-phase contributions. Environmental coupling reshapes the scattering response and can increase magnetic-field information. At critical coupling, real-frequency zeros of the scattering amplitude redistribute information toward measurable spectral intensity, allowing frequency-resolved photon counting to capture nearly all of the magnetic-field information encoded in the output state when the zeros lie within the pulse bandwidth. For long Gaussian pulses with a smooth, nonzero central-frequency scattering amplitude, the additional spectral-intensity contribution and residual spectral-phase information gap decrease as $T^{-2}$ or faster.