Quantum circuits rely on advanced nano-fabrication techniques to craft a great variety of model Hamiltonians, allowing to address remarkable physical effects in a more controllable way than in the solid state. This approach provides new vista into fundamental questions relative not only to out-of-equilibrium transport in electronic systems, but also to the many–body problem, to engineered topology, and to multi-particle entanglement. Our theoretical work bridges from the elaboration of new concepts in quantum mechanics, to the modeling of state-of-the-art experiments, based on analytical and numerical tools.

Denis FEINBERG, Serge FLORENS (coordinator), Régis MELIN

Large-scale superconducting circuits have been proposed recently as a new platform for quantum optics in the non-perturbative regime. Understanding the nature of the bosonic environmental states realized beyond the usual paradigm of open quantum system has led us to harness the superposition principle into the many-body domain, allowing to describe non-linear physical processes out of massively entangled states. This general concept is presently extended to tackle strongly correlated fermionic states of matter as well.

**Probing a transmon qubit via the ultra-strong coupling to a Josephson waveguide**
J. Puertas Martínez, S. Léger, N. Gheereart, R. Dassonneville, L. Planat, F. Foroughi, Y. Krupko, O. Buisson, C. Naud, W. Guichard, S. Florens, I. Snyman, and N. Roch, NPJ Quantum Information (2018, in press).

**Particle production in ultra-strongly coupled quantum waveguides**
N. Gheeraert, X. Zhang, T. Sépulcre, S. Bera, N. Roch, H. U. Baranger, and S. Florens, Phys. Rev. A 98, 043816 (2018).

**Microscopic bosonization of band structures: X-ray processes beyond the Fermi edge **I. Snyman and S. Florens, New J. Phys. 19, 113031 (2017).

Since the early 1960’s, the Josephson effect has attracted continuous interest and its development over the years has led to major applications in quantum information and technologies. It occurs when two superconductors connect a non-superconducting material and its physical mechanism can be described via the notion of Andreev bound states. Many physical properties of the Josephson junctions, such as the value of the Josephson current, depend on the energy-phase relation of the Andreev bound states at zero bias voltage and finite phase drop across the junction. What is the fate of Andreev bound states in the presence of voltage biasing? An analogy between the Josephson effect and basic notions of band theory can be developed. Indeed, the nonequilibrium Andreev bound states resemble to the so-called “ladders of Wannier-Stark resonances” in semiconducting superlattices which were observed by optical spectroscopy in the 1980s.

**Simple Floquet-Wannier-Stark-Andreev viewpoint and emergence of low-energy scales in a voltage-biased three-terminal Josephson junction, **R. Mélin, J.-G. Caputo, K. Yang and B. Douçot, Phys. Rev. B 95, 085415 (2017).

Multiterminal Josephson junctions provide new transport regimes, among them multi-Cooper pair modes (as electron quartets) when biased with commensurate voltages. The Andreev states of such junctions also emulate the band structure of various lattices, for instance graphene and its generalisations. Irradiating such junctions with microwave can be used as a probe of the topology of those states, and even create topological phases.

**Multipair dc Josephson resonances in a biased all-superconducting bijunction, **T. Jonckheere, J. Rech, T. Martin, D. Feinberg and R. Mélin, Phys. Rev. B 87, 214501 (2013).

**Berry curvature tomography and realisation of topological Haldane model in driven three-terminal Josephson junctions**, L. Peralta Gavensky, G. Usaj, C. Balseiro, D. Feinberg, Phys. Rev. B (Rapid. Comm.) 97,0220505 (2018).