  Semiclassically, laser pulses can be used to implement arbitrary
transformations on atomic systems; quantum mechanically, residual atom-field
entanglement spoils this promise. Transcoherent states are field states that
fix this problem in the fully quantized regime by generating perfect coherence
in an atom initially in its ground or excited state. We extend this fully
quantized paradigm in four directions: First, we introduce field states that
transform an atom from its ground or excited state to any point on the Bloch
sphere without residual atom-field entanglement. The best strong pulses for
carrying out rotations by angle $\theta$ are are squeezed in photon-number
variance by a factor of $\rm{sinc}\theta$. Next, we investigate implementing
rotation gates, showing that the optimal Gaussian field state for enacting a
$\theta$ pulse on an atom in an arbitrary, unknown initial state is number
squeezed by less: $\rm{sinc}\tfrac{\theta}{2}$. Third, we extend these
investigations to fields interacting with multiple atoms simultaneously,
discovering once again that number squeezing by $\tfrac{\pi}{2}$ is optimal for
enacting $\tfrac{\pi}{2}$ pulses on all of the atoms simultaneously, with small
corrections on the order of the ratio of the number of atoms to the average
number of photons. Finally, we find field states that best perform arbitrary
rotations by $\theta$ through nonlinear interactions involving $m$-photon
absorption, where the same optimal squeezing factor is found to be
$\rm{sinc}\theta$. Backaction in a wide variety of atom-field interactions can
thus be mitigated by squeezing the control fields by optimal amounts.
