# Ultrastrong coupling circuit QED in the radio-frequency regime

## TL;DR

This paper explores ultrastrong coupling in circuit QED with multiple qubits and a radio-frequency resonator, revealing novel symmetry-breaking transitions and particle-like quantum phenomena accessible through spectroscopic and Ramsey measurements.

## Contribution

It demonstrates how ultrastrong coupling leads to new symmetry-breaking transitions and effective particle dynamics in circuit QED, expanding the understanding of quantum phenomena in these systems.

## Key findings

- Observation of symmetry-breaking transitions in ground and excited states.
- Probing wave packet dynamics via GHz spectroscopy and Ramsey measurements.
- Identification of effective particle behavior in ultrastrong coupling regimes.

## Abstract

We study a circuit QED setup where multiple superconducting qubits are ultrastrongly coupled to a single radio-frequency resonator. In this extreme parameter regime of cavity QED the dynamics of the electromagnetic mode is very slow compared to all other relevant timescales and can be described as an effective particle moving in an adiabatic energy landscape defined by the qubits. The focus of this work is placed on settings with two or multiple qubits, where different types of symmetry-breaking transitions in the ground- and excited-state potentials can occur. Specifically, we show how the change in the level structure and the wave packet dynamics associated with these transition points can be probed via conventional excitation spectra and Ramsey measurements performed at GHz frequencies. More generally, this analysis demonstrates that state-of-the-art circuit QED systems can be used to access a whole range of particle-like quantum mechanical phenomena beyond the usual paradigm of coupled qubits and oscillators.