Competing Orders and Ultrafast Energy Transfer at the Quantum Limit in a Nb$_3$Sn Superconductor Probed by Terahertz Electrodynamics

We report the low-energy electrodynamics of a moderately clean A15 superconductor (SC) following ultrafast excitation to understand and manipulate terahertz (THz) quasi--particle (QP) transport by tuning pump photoexcitation of from competing orders. Using 35-fs optical pulses, we observe a non-thermal enhancement in the low frequency conductivity, opposite to that observed for THz pump, which persists up to an additional critical temperature, above the SC one, from an electronic order in the Martensitic normal state. In the SC state, the fluence dependence of pair breaking kinetics together with an analytic model provides evidence for a `one photon-to-one pair non-resonant energy transfer during the laser pulse. Such initial transfer of photon energy $hbaromega$ to QPs at the {em quantum} limit, set by $2Delta_{SC}/hbaromega$=0.33$%$, is more than one order of magnitude smaller than in previously studied BCS SCs, which we attribute to strong electron--phonon coupling and possible influence of phonon condensation in A15 SCs.