  Quantum technologies are built on the power of coherent superposition. Atomic
coherence is typically generated from optical coherence, most often via Rabi
oscillations. However, canonical coherent states of light create imperfect
resources; a fully-quantized description of "$\tfrac{\pi}{2}$ pulses" shows
that the atomic superpositions generated remain entangled with the light. We
show that there are quantum states of light that generate coherent atomic
states perfectly, with no residual atom-field entanglement. These states can be
found for arbitrarily short times and approach slightly-number-squeezed
$\tfrac{\pi}{2}$ pulses in the limit of large intensities; similar ideal states
can be found for any $(2k+1)\tfrac{\pi}{2}$ pulses, requiring more number
squeezing with increasing $k$. Moreover, these states can be repeatedly used as
"quantum catalysts" to successfully generate coherent atomic states with high
probability. From this perspective we have identified states that are "more
coherent" than coherent states.
