Large collective Lamb shift of two distant superconducting artificial atoms

Virtual photons can mediate interaction between atoms, resulting in an energy shift known as a collective Lamb shift. Observing the collective Lamb shift is challenging, since it can be obscured by radiative decay and direct atom-atom interactions. Here, we place two superconducting qubits in a transmission line terminated by a mirror, which suppresses decay. We measure a collective Lamb shift reaching 0.8% of the qubit transition frequency and exceeding the transition linewidth. We also show that the qubits can interact via the transmission line even if one of them does not decay into it.