lowest two energy eigenstates are utilized for quantum information science applications, the energy spectrum indeed extends to higher-energy levels corresponding to higher-excited states of the circuit. The separation between pairs of energy levels typically falls in the radio frequency and microwave regimes, and resonantly driving the artificial atom with a harmonic field can couple and induce quantum-state transitions.

Due to their relatively large size, superconducting artificial atoms can be strongly coupled to their external control fields. It is this feature, along with their quantum coherence, that we utilize in the present article. A large-amplitude harmonic control field can drive an artificial atom throughout its energy-level spectrum. When driven through an avoided level crossing, a Landau-Zener-Stückelberg (LZS) transition occurs. This is a coherent process akin to a beamsplitter for photons, taking an input state of the atom and outputting a superposition of states. Repeated passages through an avoided crossing act as an atom interferometer, causing the atomic superposition state to interfere quantum mechanically with itself. Since the weighting of the superposition state depends sensitively on the size of the avoided crossing and the velocity (change in relative energy between levels per unit time) with which it is traversed, the quantum interference 