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This work explores temporal and spatial aspects of coherent population transfer in a three-level atom through a synergic combination of experimental measurements and theoretical calculations. Experimental measurements exploit the broad bandwidth of a femtosecond laser pulse to initiate simultaneous excitation of the $5p{}^{2}{P}_{1/2}\ensuremath{\leftarrow}5s{}^{2}{S}_{1/2}$ and $5p{}^{2}{P}_{3/2}\ensuremath{\leftarrow}5s{}^{2}{S}_{1/2}$ components of the doublet line of atomic rubidium. By adjusting positive or negative frequency sweeps the pump pulse favors either one of the two transitions and eventually even decouples the two excited states. The population of the excited spin-orbit levels is monitored in real time by stimulated emission probing under conditions of different intensity, chirp, and pulse width of the driving field, giving detailed information on the coupling between the three levels and their interactions with the driving and probe fields at different points in spacetime. Both pump and probe pulses are carefully characterized after the interaction region by frequency-resolved optical gating. In order to interpret and understand the experimental results it is essential to consider the close relationship between pulse propagation and time evolution of the atomic system via the coupled Maxwell-Bloch equations. This analysis highlights the importance of spatial propagation of the light fields, as well as their temporal dependence, in understanding the dynamical population evolution, and quantitatively reproduces all aspects of the experimental measurements.

We present a contribution to the discussion of how best to minimize time-evolving wave functions near the edge of a space-time grid. Our suggestion builds on the work of several groups and adopts an optical potential with real and imaginary parts separated in space (though not necessarily in time) to bring about an artificial acceleration and subsequent suppression of the wave-function amplitude as it approaches the boundary of discretized space-time. The emphasis of the proposal is on the absorption of incident wave functions characterized by low kinetic energy (long de Broglie wavelength) and/or a broad spread of momenta. The action of the optical potential is quantified by calculations of transmission and reflection as a function of incident wave-function kinetic energy, relative bandwidth, and de Broglie wavelength. Numerical constraints on the maximum by which a wave packet may be accelerated and the time and space over which the accelerating potential may act are discussed within the terms of the split-operator method for wave-function propagation. The perceived advantages of spatially overlapping real and imaginary potentials with respect to the minimization of broad-bandwidth wave functions are investigated. It is found that the addition of a simple, though not totally arbitrary, energy shift applied in space prior to absorption by a negative imaginary potential greatly enhances the absorption of wave packets constructed from multiple momentum components.