Design of a Tunable 3D Microwave Cavity for Use in Coupling to Quantum Superconducting Circuits*

We have designed a tunable 3D cavity system for use with transmon qubits. We use an rf SQUID loop as a variable inductive element that perturbs the cavity modes and produces a shift in the cavity frequency that depends on the flux applied to the loop. Our 3D cavity is made of aluminum and has a lowest mode TE101 frequency of 6.2 GHz. Following a method developed by E. U. Condon, we estimate our cavity to have an effective inductance of 100 nH [1]. Our inductive SQUID loop is made of thermally deposited aluminum on a sapphire substrate, with dimensions 250$\mu$m x 250$\mu$m, which yields an expected geometric inductance of 0.9 nH. We use a single junction in our inductive loop with a critical current of approximately 1$\mu$A. We tune the effective inductance of the loop by using a modulation coil that is well isolated from the cavity at the resonance frequency. \\[4pt] [1] Condon, E. U. Reviews of Modern Physics. Volume 14, Number 4 (1942)