We theoretically investigate the simulation of moving cavities in a superconducting circuit setup. In particular, we consider a recently proposed experimental scenario where the phaseof the cavity field is used as a moving clock. By computing the error made when simulating the cavity trajectory with SQUIDs, we identify parameter regimes where the correspondence holds, and where time dilation, as well as corrections due to clock size and particle creation coefficients, are observable. These findings may serve as a guideline when performing experiments on simulation of moving cavities in superconducting circuits.

We show that motion and gravity affect the precision of quantum clocks. We consider a localised quantum field as a fundamental model of a quantum clock moving in spacetime and showthat its state is modified due to changes in acceleration. By computing the quantum Fisher information we determine how relativistic motion modifies the ultimate bound in the precision of the measurement of time. While in the absence of motion the squeezed vacuum is the ideal state for time estimation, we find that it is highly sensitive to the motion-induced degradation of the quantum Fisher information. We show that coherent states are generally more resilient to this degradation and that in the case of very low initial number of photons, the optimal precision can be even increased by motion. These results can be tested with current technology by using superconducting resonators with tunable boundary conditions.

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.