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.

The thesis is devoted to my Ph.D. research activities during last three years within the CMS collaboration. My primary field of interest was the investigation of the Higgs sector of the Standard Model and in connection with Beyond-Standard-Model New Physics searches.

This work is mainly divided in two parts and deals with some aspects of quantum field theory in curved space-time and some open problems related with the cosmological history of our Universe.

The R&D program reported in this thesis (develop of cryogenic setups, analysis software and characterizations) has delivered the NUV HD Cryo technology of Silicon Photomultipliers (SiPM) developed in FBK to the DS-20k experiment for the research of Dark Matter. NUV HD Cryo technology currently represents the best cryogenic SiPM performance and fully satisfies the experiment requirements. These developments are relevant also to nEXO experiment and have attracted the attention of other large experiments, such as DUNE, which require large active areas of SiPMs operated in cryogenic noble liquids

In this thesis, we used CMOS-like technologies to produce improved, hierarchical multifunctional bioinspired surfaces. Different natural surfaces have been surveyed including well-known lotus leaf, sharkskin, back of the Namib Desert beetle, butterfly wings, and legs of water-walking insects. The lotus leaf features superhydrophobicity, which leads to low adhesion and self-cleaning. Sharkskin is composed of ripples that manage to reduce skin-friction and thus drag resistance. The Namib Desert beetle, harvests water from the heterogeneous pattern having hydrophilic/hydrophobic bumps on his back. Butterfly wings have re-entrant structures that manage to reach superhydrophobicity from a hydrophilic substrate. Hairy legs of water-walking insects are superhydrophobic with low adhesion that allows them to fight and jump on water. In chapter 1, we have undertaken a review of bioinspired surfaces that emulate the abilities of such natural surfaces. Then, in chapter 2 we have described the innovative CMOS-like techniques used for generating several hierarchical and re-entrant microstructures. Chapter 3 depicts the analysis of surfaces with hierarchical structures generated with a fast and easy process; this latter forms a second hierarchical level composed of random pyramidal elements using wet etching. Surfaces realized with this process manage to reach remarkably high contact angle and low contact angle hysteresis. Additionally, in this chapter we have introduced an analytical model to study the stability of Cassie-Baxter state over Wenzel state for these hierarchical surfaces. In chapter 4 the fabrication and analysis of surfaces composed of controlled hierarchical levels, which combine sharkskin with single-level lotus leaf-inspired pillared structures are reported. These particular hierarchical surfaces are demonstrated to hold high superhydrophobic properties along with low skin-friction. The superhydrophobicity of these surfaces has been characterized in a series of tests on an inclined plane. The data extrapolated from this measurement was used to evaluate the total dissipated energy of the sliding drop. Combining the data collected during this experiment with contact angle and contact angle hysteresis measurements we propose a global parameter that evaluates the superhydrophobic “level†of a surface. Furthermore, in chapter 5 similar hierarchical surfaces have also been tested for water harvesting together with single-level pillared surfaces that feature heterogeneous chemistry with hydrophilic/hydrophobic spot on every single pillar. In chapter 6 a series of tests have also been performed on butterfly-inspired surfaces. Although the substrate of such surfaces is hydrophilic, thanks to the re-entrant structures the surfaces reach high level of hydrophobicity. An implemented mathematical model and experimental test confirm the stability of this hydrophobic state. In chapter 7, we describe two sets of surfaces inspired by the hairy legs of water walking insect the first is composed of stretchable pyramidal-pillars and the second of truncated-conical silicon pillars. The ability of sharp structures to easily detach from water surfaces is exploited to change the contact angle value of a water drop deposed on this fast type of stretchable micropatterned surface. A mathematical model has been implemented and experimental tests have been carried out to evaluate the stability of the water-air composite interface on both types of microstructured surfaces. In particular, in the polymeric surfaces elasto-capillarity seams to influence the metastability of the Cassie-Baxter state.

The AEgIS experiment pursues the ambitious goal of measuring for the first time the gravitational pull on neutral antimatter. The envisioned method consists in producing a beam of cold anti-hydrogen and measuring the deflection of its free fall by means of a Moiré deflectometer. To do so the pulsed production of abundant cold anti-hydrogen is paramount, therefore the charge exchange production mechanism has been elected as the most promising candidate production method. Performing the charge exchange anti-hydrogen production requires access to an abundant source of cold positronium which can be achieved by the employment of oxide-coated nanochanneled silica plates (NCPs). We spend chapter 1 formulating a classical model of positronium production and thermalisation in NCPs and validating it by testing it against the available experimental data. In chapter 2 we describe the measurement of the energy spectrum of positronium produced by nanochanneled plates using the beam produced by the SURF machine. We then compare the measured energy spectra with the model proposed in chapter 1 showing, in the comparison, the indication of a transition during thermalisation process to a regime where quantum phenomena become significant. We describe in detail in chapter 3 several positronium spectroscopy measurements that we performed during the course of the last three years by employing the positron beam line of the experiment AEgIS. We will the proceed to illustrate an improved version of the detrending technique commonly employed in signal analysis which, applied to the analysis of SSPALS spectra, improves the achievable precision on the experimental results. In chapter 4 we describe an innovative approach that we are currently pursuing to employ the detector FACT, part of the AEgIS apparatus, to confirm the successful production of anti-hydrogen.

This thesis work covers scientific and technological advancements in integrated silicon photonics circuits aimed at developing an All-On-Chip device for quantum photonics experiments. The work has been carried out within the framework of project SiQuro, where the Silicon-On-Insulator platform is chosen to integrate all the components of an optical bench necessary for a quantum experiment into a single chip. The problem of generating photon pairs have been addressed by studying second order polarisation effects in strained silicon with the aim to realize a bright photon pairs source based on Spontaneous Down Conversion. The study revealed that processes other than the Pockels effect are responsible for the non-linearity coefficients previously measured, suggesting to look for other candidate processes for the generation of photon pairs, as third order non-linear processes. To provide with the bright coherent source necessary to enable non-linear processes the integration of a hybrid III-V-silicon mode-locked laser has also been studied. During this study, technological novelties have also been developed by modelling the wedge profile obtained during the wet etching of silicon glass materials to engineer 3D structures. In parallel, the physics of whispering gallery mode resonators, both in silicon and in silicon glass materials, have been addressed. Silicon nitride Ultra High-Quality resonators have been demonstrated by using a strip-loaded configuration, while relative tuning of resonant modes has been demonstrated in an all-optical experiment exploiting the thermo-optic effect. This work represents a step forward in the study of the physics and applications of silicon-based lightwave circuits for integrated photonics.

Simulating rare structural rearrangements of macromolecules with classical computational methods, such as Molecular Dynamics (MD), is an outstanding challenge. A multitude of technological advancements, from development of petaFLOPS supercomputers to advent of various enhance sampling methods, has granted access to time intervals of microseconds and even milliseconds in recent years. Yet, many key events occur on exponentially longer timescales. Here, path sampling techniques have the advantage of focusing the computational power on barrier-crossing trajectories, but generating uncorrelated transition paths that explore significantly different conformational regions remains a problem. To address this issue, we devised a hybrid path-sampling scheme, graph-Transition Path Sampling (gTPS), that generates the trial transition pathways using a quantum annealer. We first employ a classical computer to perform an uncharted exploration of the conformational space using a data-driven MD method. The dataset is then post-processed using a path-integral-based method to obtain a coarse-grained network representation of reactive pathways. By resorting to quantum annealing, the entire ensemble of these pathways can be encoded into a superposition in the initial quantum state of the annealer. Finally, by performing the quantum adiabatic transition on the state of the annealer, one can potentially generate/sample uncorrelated paths while they retain a high statistical probability (follow low free energy regions). We have first validated this scheme on a prototypically simple transition (α_R↔C_5 of alanine dipeptide) which could be extensively characterized on a desktop computer. Subsequently, we scaled up in complexity by generating a protein conformational transition (Bovine Pancreatic Trypsin Inhibitor - BPTI) that occurs on the millisecond timescale, obtaining results that match those of the Anton special-purpose supercomputer. Finally, we dicuss our current investigations on the application of gTPS to the unfolding process of headpiece subdomain of Villin and BPTI. Despite limitations due to the available quantum hardware, our study highlights how realistic biomolecular simulations provide a potentially impactful new ground for applying, testing, and advancing quantum technologies.

We analyze ground state properties of few-nucleons systems and $^{16}$O using \eftnopi (Pionless Effective Field Theory) at \ac{LO}. This is the first time the theory is extended to many-body nuclear systems. The free constants of the interaction are fitted using both experimental data and \ac{LQCD} results. The nuclear many-body Schr\"odinger equation is solved by means of the Auxiliary Field Diffusion Monte Carlo method. A linear optimization procedure has been used to recover the correct structure of the ground state wavefunction. {\eftnopi} as revealed to be an appropriate theory to describe light nuclei both in nature, and in the case where heavier quarks are used in order to make \ac{LQCD} calculation feasible. Our results are in good agreement with experiments and \ac{LQCD} predictions. In our \ac{LO} calculation, $^{16}$O appears to be unstable against breakup into four $^4$He for the quark masses considered.

One of the main reasons which makes Bose-Einstein condensates a successful topic of research is their flexibility for creating systems whose Hamiltonian can be engineered almost at will. A particularly relevant research topic in the field of Bose–Einstein condensation concerns the realization of binary mixtures in the presence of coherent coupling Ω. These systems show properties having analogies with the formation of stripe phases, which are related to supersolidity, or with the formation of domain walls, which are related to quark confinement in quantum chromodynamics. Technically, the realization of coherently coupled binary mixtures requires a deep knowledge of the system properties, even in absence of coherent coupling between the two states, and a highly precise control of the magnetic field. Both these topics are treated in this research work, which aims to lay the foundation for experimental studies in resonantly-coupled spinor BECs. More in detail, the simplest collective oscillation, i.e., the spin-dipole (SD) oscillation and the static SD polarizability are studied to test the miscibility properties of the system and its response to external perturbation of the trapping potentials, both at zero and at finite temperature in order to characterize the behaviour of the system at Ω = 0. This work also reports the theoretical study done to design a magnetic shield able to guarantee a precise control of the environmental magnetic field and suitable to be used to study the binary mixture in the presence of coherent coupling.