We revisit the derivation of Rabi-and Dicke-type models, which are commonly used for the study of quantum light-matter interactions in cavity and circuit QED. We demonstrate that the validity of the two-level approximation, which is an essential step in this derivation, depends explicitly on the choice of gauge once the system enters the ultrastrong coupling regime. In particular, while in the electric dipole gauge the two-level approximation can be performed as long as the Rabi frequency remains much smaller than the energies of all higher-lying levels, it can dramatically fail in the Coulomb gauge, even for systems with an extremely anharmonic spectrum. We extensively investigate this phenomenon both in the single-dipole (Rabi) and multi-dipole (Dicke) case, and considering the specific examples of dipoles confined by double-well and by square-well potentials, and of circuit QED systems with flux qubits coupled to an LC resonator. arXiv:1805.05339v4 [quant-ph]

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Modulational instabilities play a key role in a wide range of nonlinear optical phenomena, leading e.g. to the formation of spatial and temporal solitons, rogue waves and chaotic dynamics. Here we experimentally demonstrate the existence of a modulational instability in condensates of cavity polaritons, arising from the strong coupling of cavity photons with quantum well excitons. For this purpose we investigate the spatiotemporal coherence properties of polariton condensates in GaAs-based microcavities under continuous-wave pumping. The chaotic behavior of the instability results in a strongly reduced spatial and temporal coherence and a significantly inhomogeneous density. Additionally we show how the instability can be tamed by introducing a periodic potential so that condensation occurs into negative mass states, leading to largely improved coherence and homogeneity. These results pave the way to the exploration of long-range order in dissipative quantum fluids of light within a controlled platform. arXiv:1707.05798v3 [cond-mat.mes-hall]