# Optimal gauge for the multimode Rabi model in circuit QED

## TL;DR

This paper identifies an optimal gauge choice in circuit QED's multimode Rabi model to minimize discrepancies caused by Hilbert space truncation, based on qubit anharmonicity and environmental frequency.

## Contribution

It introduces a simple criterion for selecting the optimal gauge in the multimode Rabi model, improving the accuracy of truncated Hamiltonians in circuit QED.

## Key findings

- Optimal gauge depends on anharmonicity and environmental frequency ratio.
- Standard flux and charge gauges may not be optimal in multimode scenarios.
- The proposed criterion reduces discrepancies between truncated and full Hamiltonians.

## Abstract

In circuit QED, a Rabi model can be derived by truncating the Hilbert space of the anharmonic qubit coupled to a linear, reactive environment. This truncation breaks the gauge invariance present in the full Hamiltonian. We analyze the determination of an optimal gauge such that the differences between the truncated and the full Hamiltonian are minimized. Here, we derive a simple criterion for the optimal gauge. We find that it is determined by the ratio of the anharmonicity of the qubit to an averaged environmental frequency. We demonstrate that the usual choices of flux and charge gauge are not necessarily the preferred options in the case of multiple resonator modes.