Tunable-cavity QED with phase qubits*

We describe a tunable-cavity QED architecture with an rf SQUID phase qubit inductively coupled to a single-mode, resonant cavity with a tunable frequency that allows for both tunneling and dispersive measurements. Dispersive measurement is well characterized by a three-level model, strongly dependent on qubit anharmonicity, qubit-cavity coupling and detuning. The tunable cavity frequency provides dynamic control over the coupling strength and qubit-cavity detuning helping to minimize Purcell losses and cavity-induced dephasing during qubit operation. The maximum decay time $T_1 = 1.5\,\mu\rm{s}$ is limited by dielectric losses from a design geometry similar to planar transmon qubits.