Microwave amplification via interfering multi-photon processes in a half-waveguide quantum electrodynamics system

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.