## Bose-Hubbard Models with Photon Pairing in Circuit-QED.

In this work we study a family of bosonic lattice models that combine an on-site repulsion term with a nearest-neighbor pairing term, ∑<i,j>a_i^†a_j^†+H.c. Like the original Bose-Hubbard model, the nearest-neighbor term is responsible for the mobility of bosons and it competes with the local interaction, inducing two-mode squeezing. However, unlike a trivial hopping, the counter-rotating terms form pairing cannot be studied with a simple mean-field theory and does not present a quantum phase transition in phase space. Instead, we show that there is a cross-over from a pure insulator to long-range correlations that start up as soon as the two-mode squeezing is switched on. We also show how this model can be naturally implemented using coupled microwave resonators and superconducting qubits.

## Circuit QED bright source for chiral entangled light based on dissipation.

We present a scalable and tunable framework for the quantum simulation of critical dissipative models based on a circuit QED cavity array interacting with driven superconducting qubits. We will show that the strongly correlated many-body state of the cavities can be mapped into the state of propagating photons in a transmission line. This allows not only for an efficient way of accessing the correlations in the many-body system, but also provides a bright source of chiral entangled light where directionality and entanglement are assisted by collective phenomena and breaking of reflection symmetry.

## Coupling Single-Molecule Magnets to Quantum Circuits.

In this work we study theoretically the coupling of single-molecule magnets (SMMs) to a variety of quantum circuits, including microwave resonators with and without constrictions and flux qubits. The main result of this study is that it is possible to achieve strong and ultrastrong coupling regimes between SMM crystals and the superconducting circuit, with strong hints that such a coupling could also be reached for individual molecules close to constrictions. Building on the resulting coupling strengths and the typical coherence times of these molecules (~ μs), we conclude that SMMs can be used for coherent storage and manipulation of quantum information, either in the context of quantum computing or in quantum simulations. Throughout the work we also discuss in detail the family of molecules that are most suitable for such operations, based not only on the coupling strength, but also on the typical energy gaps and the simplicity with which they can be tuned and oriented. Finally, we also discuss practical advantages of SMMs, such as the possibility to fabricate the SMMs ensembles on the chip through the deposition of small droplets.

## Entanglement, Fractional Magnetization and Long-Range Interactions.

Based on the theory of matrix product states, we give precise statements and complete analytical proofs of the following claim: A large fractionalization in the magnetization or the need of long-range interactions imply large entanglement in the state of a quantum spin chain.

## Exploiting Structured Environments for Efficient Energy Transfer: The Phonon Antenna Mechanism.

A non-trivial interplay between quantum coherence and dissipative environment-driven dynamics is becoming increasingly recognised as key for efficient energy transport in photosynthetic pigment-protein complexes, and converting these biologically-inspired insights into a set of design principles that can be implemented in artificial light-harvesting systems has become an active research field. Here we identify a specific design principle - the phonon antenna - that demonstrates how inter-pigment coherence is able to modify and optimize the way that excitations spectrally sample their local environmental fluctuations. We place this principle into a broader context and furthermore we provide evidence that the Fenna-Matthews-Olson complex of green sulphur bacteria has an excitonic structure that is close to such an optimal operating point, and suggest that this general design principle might well be exploited in other biomolecular systems.

## From Josephson Junction Metamaterials to Tunable Pseudo-Cavities.

The scattering through a Josephson junction (JJ) interrupting a superconducting line is revisited including power leakage. We also discuss how to make tunable and broadband resonant mirrors by concatenating junctions. As an application, we show how to construct cavities using these mirrors, thus connecting two research fields: JJ quantum metamaterials and coupled-cavity arrays. We finish by discussing the first nonlinear corrections to the scattering and their measurable effects.

## Generating and Verifying Graph States for Fault-Tolerant Topological Measurement-Based Quantum Computing in Two-Dimensional Optical Lattices.

We propose two schemes for implementing graph states useful for fault-tolerant topological measurement-based quantum computation in two-dimensional (2D) optical lattices. We show that bilayer cluster and surface-code states can be created by global single-row and controlled-Z operations. The schemes benefit from the accessibility of atom addressing on 2D optical lattices and the existence of an efficient verification protocol which allows us to ensure the experimental feasibility of measuring the fidelity of the system against the ideal graph state. The simulation results show potential for a physical realization toward fault-tolerant measurement-based quantum computation against dephasing and unitary phase errors in optical lattices.

## Hall Response of Interacting Bosonic Atoms in Strong Gauge Fields: From Condensed to Fractional-Quantum-Hall States.

Interacting bosonic atoms under strong gauge fields undergo a series of phase transitions that take the cloud from a simple Bose-Einstein condensate all the way to a family of fractional-quantum-Hall-type states [M. Popp, B. Paredes, and J. I. Cirac, Phys. Rev. A 70, 053612 (2004)]. In this work we demonstrate that the Hall response of the atoms can be used to locate the phase transitions and characterize the ground state of the many-body state. Moreover, the same response function reveals within some regions of the parameter space, the structure of the spectrum and the allowed transitions to excited states. We verify numerically these ideas using exact diagonalization for a small number of atoms, and provide an experimental protocol to implement the gauge fields and probe the linear response using a periodically driven optical lattice. Finally, we discuss our theoretical results in relation to recent experiments with condensates in artificial magnetic fields [L. J. LeBlanc, K. Jimenez-Garcia, R. A. Williams, M. C. Beeler, A. R. Perry, W. D. Phillips, and I. B. Spielman, Proc. Natl. Acad. Sci. USA 109, 10811 (2012)] and we analyze the role played by vortex states in the Hall response.

## Lieb-Robinson Bounds for Spin-Boson Lattice Models and Trapped Ions.

We derive a Lieb-Robinson bound for the propagation of spin correlations in a model of spins interacting through a bosonic lattice field, which satisfies a Lieb-Robinson bound in the absence of spin-boson couplings. We apply these bounds to a system of trapped ions and find that the propagation of spin correlations, as mediated by the phonons of the ion crystal, can be faster than the regimes currently explored in experiments. We propose a scheme to test the bounds by measuring retarded correlation functions via the crystal fluorescence.

## Nonequilibrium and Nonperturbative Dynamics of Ultrastrong Coupling in Open Lines.

The time and space resolved dynamics of a qubit with an Ohmic coupling to propagating 1D photons is studied, from weak coupling to the ultrastrong coupling regime. A nonperturbative study based on matrix product states shows the following results: (i) The ground state of the combined systems contains excitations of both the qubit and the surrounding bosonic field. (ii) An initially excited qubit equilibrates through spontaneous emission to a state, which under certain conditions is locally close to that ground state, both in the qubit and the field. (iii) The resonances of the combined qubit-photon system match those of the spontaneous emission process and also the predictions of the adiabatic renormalization [A. J. Leggett et al., Rev. Mod. Phys. 59, 1 (1987)]. Finally, nonperturbative ab initio calculations show that this physics can be studied using a flux qubit galvanically coupled to a superconducting transmission line.

## Relativistic Quantum Teleportation with Superconducting Circuits.

We study the effects of relativistic motion on quantum teleportation and propose a realizable experiment where our results can be tested. We compute bounds on the optimal fidelity of teleportation when one of the observers undergoes nonuniform motion for a finite time. The upper bound to the optimal fidelity is degraded due to the observer’s motion. However, we discuss how this degradation can be corrected. These effects are observable for experimental parameters that are within reach of cutting-edge superconducting technology.

## Scattering of Coherent States on a Single Artificial Atom.

In this work, we theoretically analyze a circuit quantum electrodynamics design where propagating quantum microwaves interact with a single artificial atom, a single Cooper-pair box. In particular, we derive a master equation in the so-called transmon regime, including coherent drives. Inspired by recent experiments, we then apply the master equation to describe the dynamics in both a two-level and a three-level approximation of the atom. In the two-level case, we also discuss how to measure photon antibunching in the reflected field and how it is affected by finite temperature and finite detection bandwidth.

## Seeing Majorana Fermions in Time-of-Flight Images of Staggered Spinless Fermions Coupled by S-Wave Pairing.

The Chern number ν, as a topological invariant that identifies the winding of the ground state in the particle-hole space, is a definitive theoretical signature that determines whether a given superconducting system can support Majorana zero modes. Here we show that such a winding can be faithfully identified for any superconducting system (p wave or s wave with spin-orbit coupling) through a set of time-of-flight measurements, making it a diagnostic tool also in actual cold-atom experiments. As an application, we customize the measurement scheme for a chiral topological model of spinless fermions. The proposed model only requires the experimentally accessible s-wave pairing and staggered tunneling that mimics spin-orbit coupling. By adiabatically connecting this model to Kitaev's honeycomb lattice model, we show that it gives rise to ν=±1 phases, where vortices bind Majorana fermions, and ν=±2 phases that emerge as the unique collective state of such vortices. Hence, the preparation of these phases and the detection of their Chern numbers provide an unambiguous signature for the presence of Majorana modes. Finally, we demonstrate that our detection procedure is resilient against most inaccuracies in experimental control parameters as well as finite temperature.

## Simulating Dirac Fermions with Abelian and Non-Abelian Gauge Fields in Optical Lattices.

In this work we present an optical lattice setup to realize a full Dirac Hamiltonian in 2+1 dimensions. We show how all possible external potentials coupled to the Dirac field can arise from perturbations of the existing couplings of the honeycomb lattice pattern. This greatly simplifies the proposed implementations, requiring only spatial modulations of the intensity of the laser beams to induce complex non-Abelian potentials. We finally suggest several experiments to observe the properties of the quantum field theory in the setup.

## Topological Phase Transitions Driven by Non-Abelian Gauge Potentials in Optical Square Lattices.

We analyze a tight-binding model of ultracold fermions loaded in an optical square lattice and subjected to a synthetic non-Abelian gauge potential featuring both a magnetic field and a translationally invariant SU(2) term. We consider in particular the effect of broken time-reversal symmetry and its role in driving nontrivial topological phase transitions. By varying the spin-orbit coupling parameters, we find both a semimetal-insulator phase transition and a topological phase transition between insulating phases with different numbers of edge states. The spin is not a conserved quantity of the system, and the topological phase transitions can be detected by analyzing its polarization in time-of-flight images, providing a clear diagnostic for the characterization of the topological phases through the partial entanglement between spin and lattice degrees of freedom.

## Tunable Coupling Engineering Between Superconducting Resonators: From Sidebands to Effective Gauge Fields.

In this work we show that a tunable coupling between microwave resonators can be engineered by means of simple Josephson junctions circuits, such as dc and rf superconducting quantum interference devices. We show that by controlling the time dependence of the coupling it is possible to switch on and off and modulate the cross-talk and boost the interaction towards the ultrastrong regime, as well as to engineer red and blue sideband couplings, nonlinear photon hopping, and classical gauge fields. We discuss how these dynamically tunable superconducting circuits enable key applications in the fields of all-optical quantum computing, continuous-variable quantum information, and quantum simulation—all within the reach of the state of the art in circuit-QED experiments.

## Wavepacket Detection with the Unruh-DeWitt Model.

In this paper we deal with several issues regarding the localization properties of the Unruh-DeWitt (UdW) detector model. Since its original formulation as a pointlike detector, the UdW model has been used to study extensively the physics of quantum fields in presence of accelerations or curved backgrounds. Natural extensions of it have tried to take into account the spatial profile of such detectors, but all of them have met a series of problems in their spectral response which render them useless to study some of the most interesting physical scenarios. In this paper we provide a derivation of the smeared UdW interaction from QED first principles, then we analyze the spectral response of spatially smeared UdW detectors, and discuss the kind of spatial profiles which are useful for the study of relevant cases.