Superconducting cavity QED: box modes for quantum control of qubits

Circuit QED uses two types of superconducting cavities: one-dimensional superconducting resonators that contain charge excitations, and two or three-dimensional regions of space between superconducting mirrors that contain photons. This latter type of cavity does not necessarily need to be enclosed. Any superconducting circuit acts as a cavity for the surrounding photonic modes with wavelengths on the order of the circuit geometry. Normally these are referred to as box modes, and treated primarily as a source of dissipation (except when a box mode frequency happens to be close to qubit frequencies). However, quantum transduction methods show that a system can be designed so that energy flows between modes at very different frequencies. We treat the problem of a superconducting qubit in a THz cavity by quantizing Maxwell’s equations, showing that the driven system is described by the linearized Hamiltonian of cavity optomechanical systems used for quantum transduction.