Quantum gates between superconducting and atomic qubits

We propose methods for performing entangling gate operations between superconducting phase qubits and neutral atom hyperfine qubits. The gate is mediated by mapping the superconducting qubit onto a microwave excitation of a coplanar waveguide resonator (CPW). The large transition dipole moments of atomic Rydberg states at microwave frequencies enable bidirectional entanglement between a single atom and a single CPW photon. Specific gate protocols and fidelity calculations are presented for experimentally realistic geometries.