Simulation and Measurement of the Vacuum Rabi Coupling g in a 3D Transmon System

A transmon qubit in the 3-dimensional microwave cavity is a versatile system for various circuit QED experiments. We have performed numerical calculations of the vacuum Rabi coupling $g$ in 3D transmon circuit QED system, and compared the values with the experimental measurements. We used COMSOL Multiphysics RF package with an appropriate model to efficiently calculate the coupling strength. The calculation agrees with the measurement within a few percents in simple cases. Depending on the position of the qubit in the cavity, we calculated the coupling strengths to different eigenmodes. We compared our result for the fundamental mode (TE101) and a higher mode (TE201) with the experiment by changing the qubit position, as shown in Fig. 2. This simulation and characterization enable efficient design methods for future 3D circuit QED experiments. We confirm that we can design and predict the qubit coupling to the cavity modes with enough accuracy in 3D circuit QED system.