Coupling ultracold atoms to a superconducting coplanar waveguide resonator

We demonstrate coupling of magnetically trapped ultracold $^87$Rb ground state atoms to a coherently driven superconducting coplanar resonator on an integrated atom chip. We measure the microwave field strength in the cavity through observation of the AC shift of the hyperfine transition frequency when the cavity is driven off-resonance from the atomic transition. The measured shifts are used to reconstruct the field in the resonator, in close agreement with transmission measurements of the cavity, giving proof of the coupling between atoms and resonator. When driving the cavity in resonance with the atoms, we observe Rabi oscillations between atomic hyperfine states, demonstrating coherent control of the atomic states through the cavity field. The observation of two-photon Rabi oscillations using an additional external radio frequency enables the preparation of magnetically trapped coherent superposition states near the superconducting cavity, which are required for the implementation of an atomic quantum memory.