Fossil fuels have been critical to the development of modern society, but concerns over pollution, environmental degradation and climate change demand humans transition to renewable sources of energy. Solar energy is, among renewables, by far the largest exploitable resource, providing more energy in 1 hour to the earth than all of the energy consumed by humans in an entire year. The principal problem related to solar energy use is its intermittency. Collecting and storing solar energy in chemical bonds (solar fuel), as nature accomplishes through photosynthesis, is possible through photo-electrochemical water splitting, a clean and sustainable way for hydrogen production. The materials used as photo-electrodes in a photo-electrochemical cell must fulfil a variety of thermodynamic and kinetic requirements to ensure good efficiency and durability. Since there is no material in nature satisfying all these requirements, tailoring the optical, electrical, and morphological properties of the existing materials to construct photo-electrodes with the desired performance is a big task for materials scientists. In this thesis, we study TiO2 based photo-catalysts and Fe2O3 based water oxidation catalysts. TiO2 thin films were deposited by radio frequency magnetron sputtering technique and their optical, electrical and morphological properties were changed to enhance the visible light absorption and/or limit the recombination rate of charge carriers. More specifically, the effect of compensated (V and N) and non compensated (Cu and N) n-p codoping of TiO2 was studied. The role of coupling TiO2 thin films with indium tin oxide films in single and multilayer structures, compact and porous morphologies was underlined. The effect of hydrogen doping in passivating dangling bonds in TiO2 was demonstrated. Fe2O3 nanoparticles assembled coatings were synthesized by pulsed laser deposition and studied for the functionalization of electrodes and absorbers surfaces as water oxidation catalysts. The response of the optical and electrochemical properties of the coating to the tuning of film morphology was studied, ranging from a low-transmittance compact layer to a porous nanoparticle-assembled coating, which resulted to be highly transparent. Materials properties were characterized by various techniques such as Raman spectroscopy, x-ray diffraction, UV-vis spectroscopy, x-ray photoelectron spectroscopy, energy dispersive x-ray spectroscopy, and scanning electron microscopy. Electrochemical and photo-electrochemical properties of the samples were studied by testing them as electrodes in a photoelectrochemical cell. Both materials were chosen because they are widespread, non-hazardous, biocompatible and scalable. This enables the large-scale application of photo-electrochemical water splitting and the full exploitation of the green potential of this technology.

To gain a deeper insight on the local origin of NTE in zincblende crystals, EXAFS measurements have been performed on CdTe, which has NTE properties intermediate between Ge and CuCl. In this work an accurate evaluation of the bond thermal expansion, parallel and perpendicular MSRDs and distribution asymmetry of the first shell of CdTe has been made, obtaining a good agreement between two different procedures of the data analysis (i) ratio method (ii) FEFF6-FEFFIT method. The values of the relevant parameters of CdTe were found intermediate between the corresponding values previously found for Ge and CuCl. The positive contribution to thermal expansion due to the bond stretching and the negative contribution due to the tension effects are disentangled and quatified in terms of the bond thermal expansion and the perpendicular MSRD, respectively, determined by the EXAFS analysis. A critical comparison of EXAFS and Bragg diffraction results; thermal expansion, thermal factors and correlation of atomic vibration, for the iso-structural crystals Ge, CdTe and CuCl has been performed. The correlation between several quantities measured by EXAFS and NTE properties is confirmed.

Matter at the nanoscale exhibits peculiar properties, often not shown by the bulk counterpart, and strongly coupled to the specific size, shape and structure of the atomic aggregate. Particularly, the enormous surface-to-volume ratio implies boosted reactivity with respect to the environment, while the electronic confinement might cause quantum effects to dominate physical properties. Characterization techniques are of course essential to investigate properties at the atomic scale. Scattering techniques have tremendously evolved in the recent past benefiting from third and fourth generation light sources, producing beams with unprecedented spatial and temporal resolution. In a different realm, atomistic simulations have also greatly evolved deriving advantages from both recent theories and modern computing units. In this framework, a detailed description of the system in a spatial and temporal range compatible with lengths probed by scattering techniques is provided. In a single sentence, the subject of this Thesis is the effort of tying atomistic methods and scattering techniques so to increase the comprehension around size, shape and structure of nanostructured particles.

When a second-order phase transition is crossed at finite speed, domains with independent order parameters can appear in the system, with the consequent formation of defects at the domain boundaries. The Kibble-Zurek theory provides a description for this universal phenomenon, which applies to many different systems in nature, and it predicts a power-law dependence of the defect density on the quench rate. This thesis reports on the results of the experimental study of the Kibble-Zurek mechanism in elongated Bose-Einstein condensates of atomic sodium gases, following the observations on the spontaneous formation of defects after temperature quenches across the BEC transition. The power-law scaling of the defect number with the quench speed was observed and characterized for the first time in ultracold gases. The characterization of the density and phase profiles of the defects allowed their identification as solitonic vortices, representing the first direct experimental evidence for this kind of long living excitation, which sets a link between solitons and vortices. The measurements reported in this thesis provide a novel approach to the study of the critical phenomena happening at phase transitions, and introduce to the possibility of exploring the turbulent dynamics of quenched systems through the spontaneous production of solitonic vortices.

The experimental achievement of Bose-Einstein condensation and Fermi degeneracy with ultracold gases boosted tremendous progresses both in theoretical methods and in the development of new experimental tools. Among them, intriguing possibilities have been opened by the implementation of optical lattices: periodic potentials for neutral atoms created by interfering laser beams. Degenerate gases in optical lattices can be forced in highly anisotropic traps, reducing the effective dimensionality of the system. From a fundamental point of view, the behavior of matter waves in reduced dimensions sheds light on the intimate properties of interparticle interactions. Furthermore, such reduced-dimensional systems can be engineered to quantum-simulate fasci- nating solid state systems, like bidimensional crystals, in a clean and controllable environment. Motivated by the exciting perspectives of this field, we devote this Thesis to the theoretical study of two systems where matter waves propagate in reduced dimensions. The long-range and anisotropic character of the dipole-dipole interaction critically affects the behavior of dipolar quantum gases. The continuous experimental progresses in this flourishing field might lead very soon to the creation of degenerate dipolar gases in optical potentials. In the first part of this Thesis, we investigate the emergence of a single dipolar-induced resonance in the two-body scattering process in quasi-one dimensional geometries. We develop a two-channel approach to describe such a resonance in a highly elongated cigar-shaped harmonic trap, which approximates the single site of a quasi-one-dimensional optical lattice. At this stage, we develop a novel atom-dimer extended Bose-Hubbard model for dipolar bosons in this quasi-one-dimensional optical lattice. Hence we investigate the T = 0 phase diagram of the model by exact diagonalization of a small-sized system, highlighting the effects of the dipolar-induced resonance on the many-body behavior in the lattice. In the second part of the Thesis, we present a general scheme to realize cold-atom quantum simulators of bidimensional atomic crystals, based on the possibility to independently trap two different atomic species. The first one constitutes a two-dimensional matter wave which interacts only with the atoms of the second species, deeply trapped around the nodes of a two-dimensional optical lattice. By introducing a general analytic approach, we investigate the matter-wave transport properties. We propose some illustrative applications to both Bravais (square, triangular) and non-Bravais (graphene, kagomeÌ ) lattices, studying both ideal periodic systems and experimental- sized, eventually disordered, ones. The features of the artificial atomic crystal critically depend on the two-body interspecies interaction strength, which is shown to be widely tunable via 0D-2D mixed-dimensional resonances. Keywords: matter waves, reduced dimensions, dipolar-induced resonances, mixed-dimensional resonances, extended Bose-Hubbard model, atomic artificial crystals.

The optomechanics field of research has been gathering a lot of momentum during the last couple of years. Recent experimental results show that the field is finally entering the quantum era. In this context, we have worked to develop new and competitive optomechanical devices. We have also worked towards the generation and observation of ponderomotive squeezing and we have identified, and experimentally demonstrated, an optomechanical effect that can ease the achievement of this goal. Finally, we have developed a stabilization technique that have been instrumental for the success of two experiments: the implementation of the Wiener-Kolmogorov data analysis and the squeezing of a mechanical thermal oscillator.

In this thesis we investigate the properties of mixtures of Bose gases in one dimensions at zero temperature using quantum Monte-Carlo methods. First we investigate the limiting case of an impurity interacting with an atomic bath. We characterize the impurity, by calculating its effective mass, binding energy as well as the contact parameter between the impurity and the bath. In particular, we find that the effective mass rapidly increases to very large values when the impurity gets strongly coupled to an otherwise weakly repulsive bath. Then we describe uniform balanced mixtures with repulsive interactions. We investigate the miscibility phase diagram of the two components and find that correlations do not alter the phase diagram predicted by mean-field theories. We investigate the Andreev-Bashkin effect , a non-dissipative drag between the the two components of the gas and find that the drag becomes very large in the strongly interacting regime. In non-homogeneous systems we also investigate the frequency of the spin-dipole mode. Finally we describe mixtures with attractive inter-species interactions, where one can obtain a liquid ground state because of the competition between the inter-species attraction and intra-species repulsion. We characterize the the liquid and we find that the liquid state can be formed if the ratio of coupling strengths between inter-species attractive and intra-species repulsive interactions exceeds a critical value.

The behavior of surface tension within the random first-order theory (RFOT) of glass transition is studied in a glass-forming liquid model by means of ad-hoc numerical methods. The spinodal point for RFOT excitations turns out to be well defined as a function of the energy of inherent structures (IS), i.e. the minima of potential energy which underlie the equilibrium configurations. The corresponding spinodal temperature, although not sharply defined, lies definitely above the mode coupling one. The role played by surface tension within the context of dynamical heterogeneities is also studied by means of a dynamic algorithm in which the overlap with the initial configuration is constrained along equilibrium dynamics. Indications are found that, in the proximity of the mode coupling temperature, a phase-separation between high and low overlap regions occurs, driven by surface tension. The existence of a positive surface tension between amorphous excitations, in the proximity of the mode-coupling temperature, is therefore observed for both static and dynamic excitations.

In this thesis I theoretically study the dynamic and ground state properties of ultracold dipolar Fermi gases. The mean-field approach based on the Thomas-Fermi energy functional is applied to consider the dynamic properties of bilayer harmonically trapped dipolar Fermi gases. The fixed-node Diffusion Monte Carlo method (FNDMC) is used instead to investigate the ground-state properties of two dimensional dipolar Fermi gases. This technique is also applied to the problem of one impurity in a bilayer configuration with dipolar fermions.

The recent realization of synthetic spin-orbit coupling represents an outstanding achievement in the physics of ultracold quantum gases. In this thesis we explore the properties of spin-orbit-coupled Bose-Einstein condensates with equal Rashba and Dresselhaus strengths. These systems present a rich phase diagram, which exhibits a tricritical point separating a single-minimum phase, a spin-polarized plane-wave phase, and a stripe phase. In the stripe phase translational invariance is spontaneously broken, in analogy with supersolids. Spin-orbit coupling also strongly affects the dynamics of the system. In particular, the excitation spectrum exhibits intriguing features, including the suppression of the sound velocity, the emergence of a roton minimum in the plane-wave phase, and the appearance of a double gapless band structure in the stripe phase. Finally, we discuss a combined procedure to make the stripes visible and stable, thus allowing for a direct experimental detection.