The fully quantum mechanical treatment of superfluorescence buildup in the linearized regime of superfluorescence is presented for coherently, optically pumped three-level systems. It is shown that to order $\frac{{\ensuremath{\tau}}_{p}}{{\ensuremath{\tau}}_{R}}$, where ${\ensuremath{\tau}}_{p}$ is the pump time duration and ${\ensuremath{\tau}}_{R}$ the characteristic superfluorescence time, fluorescence buildup during the dynamical pumping process contributes significantly to quantum initiation of superfluorescence.
We have studied superfluorescence (SF) under highly unfavorable conditions of rapid collisional and radiative distribution in a Doppler-broadened medium. Nanosecond SF pulses at 5.5 \ensuremath{\mu}m were generated on the Ca
4s4p1P1−−3d4s1D2 transition from a column of calcium vapor buffered with Ar by optically pumping the
4s21S0−−4s4p1P1 transition. The Rabi frequency associated with the intense pump pulse prevents the occurrence of SF while the pump laser is on. As a result, the predicted scaling laws that describe the properties of SF in a transversely excited system, such as peak heights, pulse widths, and delay times, are shown to apply in our situation in which the conditions resemble swept excitation. The delay times were found to be in agreement with a fully quantum mechanical calculation which describes the initiation of SF. Measurements of the densities of the three levels, the absolute SF photon yield, and the spatial distribution of the excited states indicate that the system has a quantum yield of unity. The SF intensity increases with an increase in Ar pressure due to collisional redistribution until the collisional dephasing rate inhibits SF. The conditions describing the transition of SF to amplified spontaneous emission allow us to measure the collisional broadening rate for the SF transition.