We investigate the amplification of a microwave probe signal by a
superconducting artificial atom, a transmon, strongly coupled to the end of a
one-dimensional semi-infinite transmission line. The end of the transmission
line acts as a mirror for microwave fields. Due to the weak anharmonicity of
the artificial atom, a strong pump field creates multi-photon excitations among
the dressed states. Transitions between these dressed states, Rabi sidebands,
give rise to either amplification or attenuation of the weak probe. We obtain a
maximum amplitude amplification of about 18 %, higher than in any previous
experiment with a single artificial atom, due to constructive interference
between Rabi sidebands. We also characterize the noise properties of the system
by measuring the spectrum of spontaneous emission