Multimode mediated qubit-qubit coupling and dark-state symmetries in circuit quantum electrodynamics

Microwave cavities with high quality factors enable coherent coupling of distant quantum systems. Virtual photons lead to a transverse interaction between qubits when they are nonresonant with the cavity but resonant with each other. We experimentally investigate the inverse scaling of the interqubit 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, we observe dark states of the coupled qubit-qubit system and analyze their relation to the symmetry of the applied driving field at different frequencies.