previously in the literature. Our experimental results, along with numerical simulations, demonstrate that as the coupling strength increases, the spectrum of a circuit-QED system undergoes multiple qualitative transformations, such that several ranges are identified, each with its own unique spectral features. These results allow us to define characteristic features that distinguish several different regimes of coupling in circuit-QED systems.

is indispensable. Specifically, the coupling rate g must be larger than the decay rates. If g is increased further and becomes as large as the frequencies of light and matter excitations, the energy eigenstates including the ground state are predicted to be highly entangled. This qualitatively new coupling regime can be called the deep strong-coupling regime. One approach toward the deep strong-coupling regime is to use huge numbers of identical systems to take advantage of ensemble enhancement. With the emergence of so-called macroscopic artificial atoms, superconducting qubits for example, it has become possible for a single artificial atom to realize ultrastrong coupling, where ℏg exceeds ~10% of the energies of the qubit ℏωq and the harmonic oscillator ℏωo. By making use of the macroscopic magnetic dipole moment of a flux qubit, large zero-point-fluctuation current of an LC oscillator, and large Josephson inductance of a coupler junction, we have realized circuits in the deep strong-coupling regime, where g/ωo ranges from 0.72 to 1.34 and g/ωq >> 1. Using energy spectroscopy measurements, we have observed unconventional transition spectra between Schrodinger cat-like energy eigenstates. These states involve quantum superpositions of Fock states with phase-space displacements of ±g/ωo and remarkably survive with environmental noise. Our results provide a basis for ground-state-based entangled-pair generation and open a new direction in circuit-QED.