Ultimate quantum limit for amplification: a single atom in front of a mirror

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.