Microwave cavities with high quality factors enable coherent coupling of distant quantum systems. Virtual photons lead to a transverse exchange interaction between qubits, when they are non-resonant with the cavity but resonant with each other. We ex
perimentally probe the inverse scaling of the inter-qubit coupling with the detuning from a cavity mode and its proportionality to the qubit-cavity interaction strength. We demonstrate that the enhanced coupling at higher frequencies is mediated by multiple higher-harmonic cavity modes. Moreover, in the case of resonant qubits, the symmetry properties of the system lead to an allowed two-photon transition to the doubly excited qubit state and the formation of a dark state.
We have designed and fabricated superconducting coplanar waveguide resonators with fundamental frequencies from 2 to $9 rm{GHz}$ and loaded quality factors ranging from a few hundreds to a several hundred thousands reached at temperatures of $20 rm{m
K}$. The loaded quality factors are controlled by appropriately designed input and output coupling capacitors. The measured transmission spectra are analyzed using both a lumped element model and a distributed element transmission matrix method. The experimentally determined resonance frequencies, quality factors and insertion losses are fully and consistently characterized by the two models for all measured devices. Such resonators find prominent applications in quantum optics and quantum information processing with superconducting electronic circuits and in single photon detectors and parametric amplifiers.
