  We investigate three types of amplification processes for light fields
coupling to an atom near the end of a one-dimensional semi-infinite waveguide.
We consider two setups where a drive creates population inversion in the bare
or dressed basis of a three-level atom and one setup where the amplification is
due to higher-order processes in a driven two-level atom. In all cases, the end
of the waveguide acts as a mirror for the light. We find that this enhances the
amplification in two ways compared to the same setups in an open waveguide.
Firstly, the mirror forces all output from the atom to travel in one direction
instead of being split up into two output channels. Secondly, interference due
to the mirror enables tuning of the ratio of relaxation rates for different
transitions in the atom to increase population inversion. We quantify the
enhancement in amplification due to these factors and show that it can be
demonstrated for standard parameters in experiments with superconducting
quantum circuits.
