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 adrive 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.

We theoretically investigate resonant dipole-dipole interaction (RDDI) between artificial atoms in a 1D geometry, implemented by N transmon qubits coupled through a transmission line.Similarly to the atomic cases, RDDI comes from exchange of virtual photons of the unexcited modes, and causes the so-called collective Lamb shift (CLS). To probe the shift, we effectively set one end of the transmission line as a mirror, and examine the reflection spectrum of the probe field from the other end. Our calculation shows that when a qubit is placed at the node of the standing wave formed by the incident and reflected waves, even though it is considered to be decoupled from the field, it results in large energy splitting in the spectral profile of a resonant qubit located elsewhere. This directly signals the interplay of virtual photon processes and explicitly demonstrates the CLS. We further derive a master equation to describe the system, which can take into account mismatch of participating qubits and dephasing effects. Our calculation also demonstrates the superradiant and subradiant nature of the atomic states, and how the CLS scales when more qubits are involved.

We address the recent advances on microwave quantum optics with artificial
atoms. This field relies on the fact that the coupling between a
superconducting artificial atom and propagatingmicrowave photons in a 1D open
transmission line can be made strong enough to observe quantum coherent
effects, without using any cavity to confine the microwave photons. We
investigate the scattering properties in such a system with resonant coherent
microwaves. We observe the strong nonlinearity of the artificial atom and under
strong driving we observe the Mollow triplet. By applying two resonant tones,
we also observe the Autler-Townes splitting. By exploiting these effects, we
demonstrate two quantum devices at the single-photon level in the microwave
regime: the single-photon router and the photon-number filter. These devices
provide essential steps towards the realization of an on-chip quantum network.

We show, in the context of single photon detection, that an atomic
three-level model for a transmon in a transmission line does not support the
predictions of the nonlinear polarisabilitymodel known as the cross-Kerr
effect. We show that the induced displacement of a probe in the presence or
absence of a single photon in the signal field, cannot be resolved above the
quantum noise in the probe. This strongly suggests that cross-Kerr media are
not suitable for photon counting or related single photon applications. Our
results are presented in the context of a transmon in a one dimensional
microwave waveguide, but the conclusions also apply to optical systems.