resonator, which is coupled symmetrically to multiple superconducting qubits. Starting from a minimal circuit model, we demonstrate that, in addition to the usual collective qubit-photon coupling, the resulting Hamiltonian contains direct qubit-qubit interactions, which have a drastic effect on the ground- and excited-state properties of such circuits in the ultrastrong-coupling regime. In contrast to the superradiant phase transition expected from the standard Dicke model, we find an opposite mechanism, which at very strong interactions completely decouples the photon mode and projects the qubits into a highly entangled ground state. These findings resolve previous controversies over the existence of superradiant phases in circuit QED, but they more generally show that the physics of two- or multiatom cavity QED settings can differ significantly from what is commonly assumed.

DOI: 10.1103/physreva.94.033850

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We study effective light-matter interactions in a circuit QED system consisting of a single

LC

We study effective light-matter interactions in a circuit QED system consisting of a single

LC

resonator, which is coupled symmetrically to multiple superconducting qubits. Starting from a minimal circuit model, we demonstrate that in addition to the usual collective qubit-photon coupling the resulting Hamiltonian contains direct qubit-qubit interactions, which prevent the otherwise expected superradiant phase transition in the ground state of this system. Moreover, these qubit-qubit interactions are responsible for an opposite mechanism, which at very strong couplings completely decouples the photon mode and projects the qubits into a highly entangled ground state. These findings shed new light on the controversy over the existence of superradiant phase transitions in cavity and circuit QED systems, and show that the physics of ultrastrong light-matter interactions in two- or multi-qubit settings differ drastically from the more familiar one qubit case.

We study a generic cavity-QED system where a set of (artificial) two-level dipoles is coupled to the electric field of a single-mode

LC

resonator. This setup is used to derive a minimal quantum mechanical model for cavity QED, which accounts for both dipole-field and direct dipole-dipole interactions. The model is applicable for arbitrary coupling strengths and allows us to extend the usual Dicke model into the nonperturbative regime of QED, where the dipole-field interaction can be associated with an effective fine-structure constant of order unity. In this regime, we identify three distinct classes of normal, superradiant, and subradiant vacuum states and discuss their characteristic properties and the transitions between them. Our findings reconcile many of the previous, often contradictory predictions in this field and establish a common theoretical framework to describe ultrastrong-coupling phenomena in a diverse range of cavity-QED platforms.

N

-qubit model with

U(1)

symmetry is studied and we find that the superradiant phase transition is inhibited or restored with the qubit-number parity.