Superconducting qubit-oscillator circuit beyond the ultrastrong-coupling regime

Abstract: The interaction between an atom and the electromagnetic field inside a cavity has played a crucial role in the historical development of our understanding of light-matter interaction and is a central part of various quantum technologies, such as lasers and many quantum computing architectures. The emergence of superconducting qubits has allowed the realization of strong and ultrastrong coupling between artificial atoms and cavities. If the coupling strength $g$ becomes as large as the atomic and cavity frequencies ($\Delta$ and $\omega_{\rm o}$ respectively), the energy eigenstates including the ground state are predicted to be highly entangled. This qualitatively new regime can be called the deep strong-coupling regime, and there has been an ongoing debate over whether it is fundamentally possible to realize this regime in realistic physical systems. By inductively coupling a flux qubit and an LC oscillator via Josephson junctions, we have realized circuits with $g/\omega_{\rm o}$ ranging from 0.72 to 1.34 and $g/\Delta\gg 1$. Using spectroscopy measurements, we have observed unconventional transition spectra, with patterns resembling masquerade masks, that are characteristic of this new regime. Our results provide a basis for ground-state-based entangled-pair generation and open a new direction of research on strongly correlated light-matter states in circuit-quantum electrodynamics.