The experimental work presented in this thesis is done to develop an innovative procedure to create a protective nanostructured coating inside the X-band radio frequency cavity, a key component in future particle accelerator. The scope of the multilayer coating is to prevent the breakdown due to high electric and magnetic field. In fact the electrical discharges damage, in irreversible way, the internal surface of the cavity and compromise the final operation of the device. The keen interest on the topic is due to decrease the length and the cost of the next generation linear accelerator. To do this it is essential to enhance the performance of X-band Linacs up to 100MV/m accelerating gradient and to maintain, high as possible, the electrical breakdown reliability. Several studies are made on different materials in order to develop these cavities [1] [2], but the use of physical vapor deposition technique (PVD), to obtain nanostructured coating directly on internal wall of these small sized cavities is not reported in literature. The size of the cavities is of order of few millimeters and the iris aperture ranges from 2 to 6mm: for this reason the direct PVD coating is not possible. Hence a mandrel, that is the negative shape of the cavity, is first coated using PVD technique and finally chemically dissolved after copper electroforming[3]. The novel nanostructured coating is a multilayer composed by two high purity and immiscible metals. One is Copper to guarantee electrical conductivity of the cavity and the second is Molybdenum because it is a refractory metal. Moreover the choice of immiscible materials is important, because these materials do not form alloy during the deposition phase. Keeping a well-defined interface is important to guarantee a barrier effect to the motion of the defects inside the cavity’s material[4][5]. The experimental part of the thesis is divided in three different parts: design and setup of the PVD deposition system, plasma discharge analysis and, finally, the characterization of the coatings. This work is a collaboration between Industrial Engineering Department (University of Trento) and the National Laboratory of Legnaro (National Institute of Nuclear Physics LNL-INFN), but this research involves several institutes in different countries: SLAC (USA), KEK (Japan) and UCLA (Los Angeles USA).

The absence of a cheap and easily scalable synthesis technique for nitrogen-vacancy (NV) centers enriched nanodiamonds (NDs) is a critical factor for the development of devices based on this very peculiar nanoparticle. Indeed, the combination between the unique NV fluorescence properties and NDs characteristics allow to obtain a tool having quantum sensing capabilities, with nanometric spatial resolution, which is able to operate in a wide range of temperature, pressures and in harsh chemical conditions. NVenriched NDs applications in nanothermometry, nanomagnetometry and in bio-imaging have already been reported. However, most of the standard fluorescent NDs production techniques present common drawbacks: poor control in NDs size distribution and in nitrogen concentration, as well as the need of post-synthesis process to clean the NDs surface from impurities and to increase the NV density. In this thesis, an alternative method for fluorescent NDs synthesis based on pulsed laser ablation (PLA) of graphite is demonstrated. After the introductory chapters on NV-centers physics and NDs properties (Chapter 2 and 3), the demonstration that PLA is a viable route for synthesis of NDs is given in Chapter 4. In particular, PLA of graphite and of diamond-like carbon is performed in water. Here, a thermodynamic model taking into account the peculiar physical processes occurring during PLA is developed to explain NDs formation. Then, synthesis of NV-enriched NDs is demonstrated through PLA of graphite in a nitrogen atmosphere (Chapter 5) and in liquid nitrogen (Chapter 6). In both chapters, the thermodynamic model is adapted to explain diamond phase formation in a gaseous environment and in a cryogenic liquid. Furthermore, NV centers optical properties are fully characterized with optically detected magnetic resonance (ODMR) spectroscopy. Finally, in Chapter 7, fluorescent NDs are produced by laser ablation of N-doped graphite in water. This particular target is then used for a quantitative comparison between the other fluorescent NDs laser-synthesis, with the aim of establishing in which condition the highest NV-center formation efficiency is achieved.

Looking at state of the art of optical devices, it is evident that glass-based rare-earth-activated optical structures represent the technological pillar of a huge number of photonic applications covering Health and Biology, Structural Engineering, Environment Monitoring Systems, Lighting, Laser sources and Quantum Technologies. Among different glass-based systems, a strategic place is assigned to transparent glass-ceramics, nanocomposite materials, which offer specific characteristics of capital importance in photonics. Following this strategy, this PhD thesis exploits tin dioxide (SnO2)-based glass-ceramic activated by erbium ions (Er3+) to put the basis for the fabrication of solid state and integrated lasers. The research discussed in my PhD thesis gives a possible solution to two crucial and decisive points in the development of an optically pumped rare-earth-based laser: (i) the low absorption cross section of the rare-earth ions; (ii) the writing of channels and mirrors in the case of waveguide integrated laser, thanks to the demonstration of two innovative and unique characteristics of SnO2-based transparent glass-ceramics, i.e. luminescence sensitizing and photorefractivity. The role of SnO2 nanocrystals as rare-earth ion luminescence sensitizers allows to overcome the low absorption cross section of the Er3+ ion. The photorefractivity in range of 10-3 of SiO2-SnO2:Er3+ glass-ceramics allows applying the robust direct laser photoinscription technique on the systems to fabricate Bragg gratings and channel waveguides for waveguide integrated lasers. Based on an application-oriented approach, a comprehensive study on SiO2-SnO2:Er3+ glass-ceramic planar waveguides and monoliths, has been carried out. The work covers different research stages and aspects from the material preparation to a complete assessment of systems for the applications employing a rich number and variety of experimental techniques. The energy transfer from SnO2 to Er3+ and the efficient pumping scheme exploiting SnO2 as Er3+ luminescence sensitizers were demonstrated. The relaxation dynamic of the electronic states as well as the location of the dopant and density of states are discussed, and a specific modeling has been developed to the proof of concept realization of the considered devices. The obtained photorefractivity in range of 10-3 allowed the inscription of gratings on the fabricated SiO2-SnO2:Er3+ planar waveguides using UV laser direct writing technique. Exploiting the robust femtosecond laser micromachining, the optical waveguides were inscribed in the fabricated SiO2-SnO2:Er3+ monolithic squares. Another important outcome of this research is the design of a solid state laser with lateral pumping scheme and of an integrated waveguide laser in two different distributed feedback structures using all the parameters measured during the experimental activity.

Questa tesi di dottorato studia l’interazione della cooperatività con il rumore in sistemi realistici, focalizzandosi principalmente sulla superradianza. Gli effetti cooperativi emergono dall’interazione collettiva di un insieme di elementi con un campo esterno. Esempi degni di nota sono la superconduttività, dove le coppie di Cooper elettroniche interagiscono con le vibrazioni reticolari, le eccitazioni di plasma, che sorgono dall'interazione collettiva degli elettroni in un metallo con il campo coulombiano, e la superradianza, ovvero quel processo di emissione spontanea cooperativa che sorge da un aggregato di emettitori identici. Gli effetti cooperativi sono tipicamente robusti al disordine e al rumore, cosa che li rende interessanti per delle applicazioni a dispositivi quantistici che possano operare a temperatura ambiente. In questo lavoro, inizialmente, introduciamo un formalismo di “master equations” che descrive l’accoppiamento collettivo di un aggregato di emettitori/assorbitori con il campo elettromagnetico, valido quando le dimensioni dell'aggregato sono sia maggiori che minori della lunghezza d’onda emessa/assorbita. Inoltre, il formalismo è valido per accoppiamento sia debole che forte con il campo elettromagnetico e, cosa più importante, permette di descrivere correttamente la superradianza in diversi regimi. In tale formalismo, studiamo l’interazione tra superradianza e rumore termico sia per nanotubi molecolari (di dimensioni minori della lunghezza d’onda associata alla transizione) che sono presenti nei complessi antenna fotosintetici dei Green Sulfur Bacteria, sia pure per superreticoli di quantum dots di nuova generazione, aventi dimensioni maggiori della lunghezza d’onda emessa. In entrambi i casi si dimostra che la coerenza può permanere in presenza di rumore termico alle temperature a cui questi sistemi sono stati analizzati sperimentalmente (temperatura ambiente per i nanotubi molecolari, e 6 K per i superreticoli di quantum dots). Nello specifico, nei nanotubi molecolari mostriamo che la macroscopica delocalizzazione coerente delle eccitazioni a temperatura ambiente, che copre centinaia di molecole, può essere considerata un effetto emergente che origina dall’effetto combinato della specifica disposizione geometrica delle molecole e della presenza di accoppiamenti tra subunità del cilindro, incrementati dagli effetti cooperativi. Questi risultati aprono la strada a nuovi modi per ingegnerizzare dei “quantum wires” robusti al rumore grazie alla cooperatività. Inoltre, la presente analisi di sistemi allo stato solido basati su superreticoli di “quantum dots” di perovskite (CsPbBr3) fornisce una base teorica in grado di comprendere recenti osservazioni di emissione superradiante. Sulla base della nostra teoria, suggeriamo che futuri esperimenti dove si utilizzino quantum dots più piccoli, potrebbe aumentare significativamente la robustezza del sistema al rumore termico, aprendo la strada verso la superradianza a temperatura ambiente in sistemi allo stato solido. Si considerano anche i complessi antenna dei Purple Bacteria, dove è ben risaputo che gli effetti cooperativi incrementano il trasferimento e l’accumulo di eccitazioni generate dalla luce assorbita. Mostriamo come queste proprietà possono essere sfruttate per creare un laser ispirato a sistemi biologici e basato su aggregati molecolari, dove la luce solare, benché debole, sarebbe utilizzata come sorgente di pompaggio. Il trasferimento efficiente di energia dentro questo sistema, all’atto pratico, focalizzerebbe l’eccitazione assorbita in direzione di un dimero molecolare, composto da una coppia di molecole interagenti, opportunamente scelte. L’orientazione dei momenti di dipolo di transizione in ciascun dimero è tale da concentrare tutta l’intensità del dipolo nel livello a più alta energia, lasciando lo stato eccitonico inferiore otticamente inattivo. Un dimero molecolare in tale configurazione, che è ideale per ottenere inversione di popolazione, è chiamato “H-dimer”. Tale H-dimer, nell’archittettura qui proposta per un laser ispirato a sistemi biologici, è posto al centro di un aggregato molecolare ispirato a sistemi biologici. Gli H-dimers, eccitati dagli aggregati molecolari circostanti, raggiungono inversione di popolazione e, dunque, possono emettere luce laser quando tali aggregati sono posti in una cavità ottica. Convertire l’energia incoerente fornita dal Sole in un fascio laser coerente supererebbe diverse limitazioni pratiche inerenti all’utilzzo della luce solare come sorgente di energia pulita. Per esempio, i fasci laser sono molto efficienti nell’avviare reazioni chimiche che convertono la luce solare in energia chimica. Inoltre, dal momento che i complessi fotosintetici batterici tendono ad operare nella regione spettrale del vicino infrarosso, la nostra proposta si presta in modo naturale a realizzare laser a infrarossi a corta lunghezza d’onda, i cui fasci viaggerebbero per lunghe distanze senza quasi perdere energia, quindi distribuendo in modo efficiente l’energia solare raccolta. Nella ricerca di un meccanismo comune alla cooperatività e alla sua robustezza, abbiamo confrontato il modello delle coppie di Cooper della superconduttività con la superradianza in singola eccitazione, mostrando molte somiglianze tra i due fenomeni: in particolare, i sistemi superradianti presentano una “gap” immaginaria nel piano complesso (ovvero, una segregazione tra i tempi di vita degli autostati del sistema) che, in modo simile alla gap superconduttiva, rende questi sistemi robusti al rumore statico. Più in generale, mostriamo che ogni interazione a lungo raggio tra i costituenti di un sistema induce effetti collettivi, manifestati da delle gap nello spettro eccitonico. Perciò, la nostra analisi successiva considera l’effetto delle interazioni a lungo raggio sul trasporto eccitonico lungo catene disordinate. Dimostriamo che la presenza di uno stato collettivo ben separato dagli altri stati influenza tutto lo spettro del sistema, generando dei regimi molto controintuitivi dove il trasporto è incrementato dal disordine o è indipendente da esso, e tali regimi si estendono su molti ordini di grandezza nell’intensità del disordine. Dimostriamo anche che una catena fortemente accoppiata a un modo del campo elettromagnetico in una cavità ottica è equivalente a una catena con interazione a lungo raggio, mostrandosi dunque molto promettente per esperimenti e applicazioni future. Nello specifico, mostriamo che catene molecolari realistiche, ioni intrappolati realizzati allo stato dell’arte e atomi di Rydberg sono tutti in grado di raggiungere l’intensità di interazione a lungo raggio tale per cui il trasporto sarebbe incrementato dal disordine o indipendente da esso, puntando alla realizzazione di un trasporto di energia senza dissipazione in “quantum wires” disordinati. / This Ph.D. thesis studies the interplay of cooperativity and noise in realistic systems, largely focusing on superradiance. Cooperative effects emerge from the collective interaction of an ensemble of elements to an external field. Notable examples are superconductivity, where the electron Cooper pairs interact with the lattice vibrations, plasmon excitations, arising from the collective interaction of electrons in a metal with the Coulomb field, and superradiance, that is a cooperative spontaneous emission process stemming from an aggregate of identical emitters. Cooperative effects are typically robust to disorder and noise, making them interesting for applications to quantum devices operating at room temperature. In this work, we first present a general master equation formalism that describes the collective coupling of an aggregate of emitters/absorbers to the electromagnetic field, valid both when the size of the aggregate is larger or smaller than the emitted/absorbed wavelength. Also, the formalism is valid both for weak and strong coupling of the emitters to the electromagnetic field and, most importantly, it allows to correctly describe superradiance in different regimes. Within such formalism, the interplay of superradiance and thermal noise is studied both for molecular nanotubes (of size smaller than the transition wavelength) that are present in the antenna complexes of photosynthetic Green Sulfur Bacteria, and also for novel solid state quantum dot superlattices, having size larger than the emitted wavelength. In both cases it is shown that coherence can persist in presence of thermal noise at the temperatures where these systems have been experimentally analyzed (room temperature for molecular nanotubes, and 6 K for quantum dot superlattices). Specifically, in natural molecular nanotubes we show that the macroscopic coherent delocalization of the excitation at room temperature, covering hundreds of molecules, can be considered an emergent effect originating from the combined effect of the specific geometric disposition of the molecules and the presence of cooperatively enhanced couplings between cylinder subunits. These results open the path to new ways of engineering quantum wires robust to noise thanks to cooperativity. Moreover, our analysis of solid state systems based on perovskite (CsPbBr3) quantum dot superlattices provides a theoretical framework able to explain recent observations of superradiant emission. Based on our theory, we suggest that further experiments, using smaller quantum dots, could significantly increase the robustness of the system to thermal noise, paving the way towards room-temperature superradiance in solid-state systems. We also considered the antenna complexes of Purple Bacteria, where cooperative effects are well known to boost the transfer and storage of photo-absorbed excitations. We show how these properties can be exploited to create a bio-inspired molecular aggregate laser medium, where natural sunlight, although weak, would be used as a pumping source. The efficient energy transfer within this system would effectively focus the absorbed excitation on a suitably chosen molecular dimer, composed by a pair of interacting molecules. The orientation of the molecule transition dipole moment in each dimer is such to concentrate all the dipole strength in the highest energy level, leaving the lower excitonic state dark. A molecular dimer in such configuration, which is ideal to achieve population inversion, is called H-dimer. Such an H-dimer in our proposed architecture for a bio-inspired laser medium, is placed at the center of the bio-inspired molecular aggregates. The H-dimers, pumped by the surrounding molecular aggregates, reach population inversion and, therefore, can lase when such aggregates are placed in an optical cavity. Turning the incoherent energy supply provided by the Sun into a coherent laser beam would overcome several of the practical limitations inherent in using sunlight as a source of clean energy. For example, laser beams are highly effective at driving chemical reactions which convert sunlight into chemical energy. Further, since bacterial photosynthetic complexes tend to operate in the near-infrared spectral region, our proposal naturally lends itself for realising short-wavelength infrared lasers which would allow their beams to travel nearly losslessly over large distances, thus efficiently distributing the collected sunlight energy. In search of a common mechanism to cooperativity and its robustness, we have compared the Cooper pair model of superconductivity and single-excitation superradiance, showing many similarities between the two: in particular, superradiant systems present an imaginary gap in the complex plane (that is, a segregation between the lifetimes of the system eigenstates) that, similarly to the superconducting gap, makes these systems robust to static disorder. More in general, we show that any long-range interaction between the constituents of a system generates collective behaviours, manifested by gaps in the excitonic spectrum. Therefore, our further analysis considers the effect of long-range interactions on excitation transport along disordered chains. We show that the presence of a gapped, collective state affects the whole spectrum of the system, generating quite counter-intuitive disorder-enhanced and disorder-independent transport regimes, that extend over many orders of magnitude of the disorder strength. We also prove that a chain strongly coupled to a cavity mode is equivalent to a long-range interacting chain, thus being very promising for future experiments and applications. Specifically, we show that realistic molecular chains, state-of-the-art trapped ions and Rydberg atoms are all able to reach the needed long-range interaction strength that would show disorder-enhanced or disorder-independent transport, aiming to the realization of dissipationless transport of energy in disordered quantum wires.

A new approach to obtain visible luminescence from sol-gel derived SiOC films is proposed. This novel method is based on a simple processing route to produce nanostructured multicomponent ceramics. According to this route, hybrid sol-gel derived precursors are converted to ceramic materials by a pyrolysis process in controlled atmosphere at 800-1000°C. Higher temperatures lead to formation of Si-rich SiOC, C-rich SiOC or stoichiometric SiOC according to the starting composition. The final composition, which is relevant to line emission, can be easily controlled through a number of processing parameters like the composition of the preceramic gel and the heat treatment conditions. Thus, this new processing method seems very well suited for the production of white emitting materials since the Si- and C-based emission can be tuned across the visible spectral range from UV-blue to red by controlling film composition. A further advantage of this method is that the thin films can be formed on Si or quartz wafers and this can serve as starting material to process more complex photonic devices such as waveguides or LEDs. In the amorphous state (800-100°C), all SiOC films showed UV-blue luminescence peaking at about 410 nm, which is attributed to defect states present in the matrix such as dangling bonds. The increase of the pyrolysis temperature (≥1100°C) led to the partition of SiOC and formation of SiC, C and Si phases. The intense green-yellow luminescence observed in stoichiometric SiOC films caused by the presence of SiC and very low amount of free C. On the other hand, Si rich SiOC film showed a very broad and extremely intense white luminescence peak centred at 620 nm covering almost all visible range (430 nm-900 nm) at 1200 °C. This behaviour is explained by the simultaneous presence of SiC, C and Si in the film. External quantum efficiency measurements yielded 11.5% and 5% efficiencies in Si rich SiOC and stoichiometric SiOC films, respectively, pyrolysed at 1200°C. On the other hand, C rich SiOC films did not show any noticeable improvement in PL, indicating that C excess in the SiOC system is detrimental for the luminescence behaviour. Solutions which used in thin film production have been characterized extensively by means of several characterization properties. Moreover, the related powders and bulks have been characterized for the sake of coherency and widen the study. In addition, a study on volumetric shrinkage of films and powders has been done. The results showed that the shrinkage in films happens almost 200°C earlier than powder and higher amount of siloxane release due to the low dimension, the shrinkage is higher than powders. The last part of the study dedicated to two different systems, SiBOCs and SiOCNs, in order to understand the effect of the boron addition on SiOC system and study the optical properties of the SiOCN. Tunable (color emission change) SiOC films is obtained with high quantum efficiency by adding very few amount of boron in SiOC. Moreover, the processing temperature is decreased and very broad emission is obtained. Finally, results showed that SiOCN PDC gives very high emission in UV range and they are promising materials for UV-LEDs.

The physics of ultracold atomic gases has been the subject of a long standing theoretical and experimental research over the last half century. The development of evaporative cooling techniques and the realization of the first Bose-Einstein Condensate (BEC) in 1995 gave a great advantage to the field. A great experimental knowledge of the fundamental properties of BECs, such as long-range coherence, superfluidity and topological excitations, has now been acquired. On top of these advances, current research on ultracold atoms is also focusing on quantum simulations, which aim at building analogue models of otherwise difficult to compute physical systems in the lab. In this context, BECs, with their enhanced coherence, many-body dynamics and superfluid character offer a powerful platform for advances in the field. Shortly after the first realization of a BEC, research started also investigating the physics of quantum mixtures of a BECs, either composed of different atomic species or isotopes, or of atoms occupying different hyperfine states. The latter are known as spin mixtures, or spinor condensates. The presence of multiple components interacting through mutual contact interactions enriches the physics of the condensate, introducing ground states with magnetic ordering as well as spin dynamics, which can be order of magnitudes less energetic than the density one. On top of this, hyperfine states can be coherently coupled with an external resonant radiation. Interesting physics arises when the strength of the coupling is comparable with the energy of spin excitations, an example of which is given by the emergence of the internal Josephson effect. This regime has been the subject of intense theoretical studies in the past twenty years, however its experimental realization on ultracold atomic platforms have been proven to be challenging, with experiments strongly limited by coherence times of few tens of milliseconds. In fact, the small energy scale of spin excitations reflects in a high sensitivity coupling to environmental magnetic noise, which affects the resonant condition. The experimental apparatus on which I worked during my Ph.D. solve this problem employing a magnetic shield that surrounds the science chamber, attenuating external magnetic fields by 6 orders of magnitudes. During my Ph.D., I investigated the properties of a coherently coupled mixture of BEC of Sodium 23, performing different experiments in two atomic configurations. The first configuration consist of a mixture of hyperfine states, namely the |F=1, mF = -1> and |F=1, mF = +1>, coupled by a two-photon transition, which is characterized by miscibility in the ground state. Another configuration was instead realized working with a strongly immiscible mixture of |F=1, mF=-1> and |F=2, mF = -2>, realized through with a one photon transition. My first experiment was devoted to the characterization of different methods of manipulation of the coupled miscible mixture in an elongated quasi-1D geometry. In Local Density Approximation (LDA), The dynamics of the system, depends on the atom number difference, the relative phase, and coupling to mean field energy ratio, can be fully described as an internal Josephson junction. We characterized this dynamics on a sample an inhomogeneous spatial profile, developing three different protocols for state manipulations. In a second experiment, I developed a protocol to generate Faraday waves in an unpolarized miscible mixture. Faraday waves are classical non-linear waves characterized by a regular pattern, that originate in classical and quantum fluids via a parametric excitation in the fluid. Interestingly enough, this process resembles the phase of reheating of the early universe, where the oscillation of the inflaton field is thought to have excited particles out of the vacuum. In analogy with this phenomenon, the oscillation of the inflaton field can be simulated with the periodic modulation of the trapping potential. On top of this, in a spin mixture, the parametric modulation can excite either in-phase (density) modes or out-of-phase (spin) modes, as two possible elementary excitations are present in the system. By extracting the spatial periodicity of the generated pattern at different modulation frequencies, I was then able to measure the dispersion relations for both density and spin modes of the system. In the presence of the coherent coupling, when spin excitations becomes gapped, we further demonstrate the scaling of the gap with the strength of the coupling radiation. The third experiment I realized concerned the characterization of the magnetic ground state of a spatially extended immiscible mixture in the presence of the coherent coupling. The Hamiltonian of such a system is formally equivalent to a continuous version of the transverse field Ising model, which describes magnetic materials at zero temperature. In this mapping, a nonlinear interaction term arises from the ratio between the self-interaction energy and the strength of the coupling, which acts as the transverse field. As the ratio between the two quantities is varied above and below one, the ground state of the system spontaneously changes from a paramagnetic phase to an ordered ferromagnetic phase, featuring two equivalent and opposite magnetizations, a signature of the occurrence of a second order quantum phase transition (QPT). Furthermore, in the magnetic model, the degeneracy between the two ferromagnetic ground states can be broken by introducing an additional longitudinal field. In the atomic case, the role of this additional field is taken by the detuning between the coupling radiation and the resonant transition frequency of non-interacting atoms. I characterized the QPT developing protocols to manipulate the spin mixture in its spatially extended ground state, varying the longitudinal field. Leveraging on the inhomogeneity of a BEC trapped in the harmonic potential, a smooth variation of the spin self-interaction energy occurs spontaneously in space, introducing different magnetic regimes at fixed coupling strength. These protocols gave access to a characterization of static properties typical of magnetic materials, such as the presence of an hysteresis cycle. The occurrence of the phase transition was instead validated by a measurement of the magnetic susceptibility and corresponding fluctuations, which both show a divergence when crossing the QPT critical point. At last, I developed a protocol to smoothly manipulate the position of magnetic domain walls, the least energetic excitations in a ferromagnet. While the previous study focused on static properties, the last experimental investigation presented in this thesis was devoted to the study of the dynamics of the metastable ferromagnetic region of the BEC. As a result of the presence of an hysteresis cycle, it is possible to engineer states of the ferromagnetic energy landscape that are homogeneously prepared either in the global minimum, with trivial dynamics, or in the metastable, higher energy, local minima. In the latter case, a classical system should eventually decay towards the global minimum, driven by temperature fluctuations which overtop the energy barrier separating the two minima. For a quantum system described by a field theory, such as a ferromagnetic BEC, the decay towards the global minimum occurs by tunneling through the barrier, triggered by quantum fluctuations. The event of tunneling is known as False Vacuum Decay (FVD), and is of outstanding relevance also for high energy physics and cosmology, were the first theoretical models were developed. In the FVD model, the decay towards the global minimum, the true vacuum, is a stochastic process that occurs only if a resonant bubble of true vacuum is formed. Once formed, the bubble will eventually expand throughout the whole system, as the true vacuum is energetically favorable. The probability for such a bubble to form can be approximately calculated analytically in 1D, and should depend exponentially on the height of the barrier the field has to tunnel through. Due to the exponentially long time scale of the process, experimental observations of FVD were still lacking. Thanks to the enhanced coherence time of the superfluid ferromagnetic mixture, and to the precise control of the barrier height through the detuning from atomic resonance, we were able to observe the event of bubble nucleation in a ferromagnetic BEC. To corroborate the observation, I measured the characteristic timescale of the decay for different values of the control parameters. Results were successfully compared first with numerical simulation, and then validated by instanton theory.

Cold-atom quantum simulators offer unique possibilities to prepare, manipulate, and probe quantum many-body systems. However, despite the high level of control in modern experiments, not all observables of interest are easily accessible. This thesis aims at establishing protocols to measure currently elusive static and dynamic properties of quantum systems. The experimental feasibility of these schemes is illustrated by means of numerical simulations for relevant applications in many-body physics and quantum simulation. In particular, we introduce a general method for measuring dynamical correlations based on non-Hermitian linear response. This enables unbiased tests of the famous fluctuation-dissipation relation as a probe of thermalization in isolated quantum systems. Furthermore, we develop ancilla-based techniques for the measurement of currents and current correlations, permitting the characterization of strongly correlated quantum matter. Another application is geared towards revealing signatures of supersolidity in spin-orbit-coupled Bose gases by exciting the relevant Goldstone modes. Finally, we explore a scenario for quantum-simulating post-inflationary reheating dynamics by parametrically driving a Bose gas into the regime of universal far-from-equilibrium dynamics. The presented protocols also apply to other analog quantum simulation platforms and thus open up promising applications in the field of quantum science and technology. / I simulatori quantistici ad atomi freddi offrono possibilità uniche per preparare, manipolare e sondare sistemi quantistici a molti corpi. Tuttavia, nonostante l'alto livello di controllo raggiunto negli esperimenti moderni, non tutte le osservabili di interesse sono facilmente accessibili. Lo scopo di questa tesi è quello di stabilire protocolli per misurare delle proprietà statiche e dinamiche dei sistemi quantistici attualmente inaccessibili. La fattibilità sperimentale di questi schemi è illustrata mediante simulazioni numeriche per applicazioni rilevanti nella fisica a molti corpi e nella simulazione quantistica. In particolare, introduciamo un metodo generale per misurare le correlazioni dinamiche basato su una risposta lineare non hermitiana. Ciò consente test imparziali della famosa relazione fluttuazione-dissipazione come sonda di termalizzazione in sistemi quantistici isolati. Inoltre, sviluppiamo tecniche basate su ancilla per la misura di correnti e correlazioni di corrente, consentendo la caratterizzazione della materia quantistica fortemente correlata. Un'altra applicazione è orientata a rivelare l'impronta della supersolidità nei gas Bose con accoppiamento spin-orbita eccitando il corrispondente modo di Goldstone. Infine, esploriamo uno scenario per la simulazione quantistica della dinamica di riscaldamento post-inflazione modulando parametricamente un gas Bose e portandolo nel regime della dinamica universale lontana dall'equilibrio. I protocolli presentati si applicano anche ad altre piattaforme di simulazione quantistica analogica e aprono quindi applicazioni promettenti nel campo della scienza e della tecnologia quantistica. / Quantensimulatoren auf Basis ultrakalter Atome eröffnen einzigartige Möglichkeiten zur Präparation, Manipulation und Untersuchung von Quanten-Vielteilchen-Systemen. Trotz des hohen Maßes an Kontrolle in modernen Experimenten sind jedoch nicht alle interessanten Observablen auf einfache Weise zugänglich. Ziel dieser Arbeit ist es, Protokolle zur Messung aktuell nur schwer erfassbarer statischer und dynamischer Eigenschaften von Quantensystemen zu etablieren. Die experimentelle Realisierbarkeit dieser Verfahren wird durch numerische Simulationen anhand relevanter Anwendungen in der Vielteilchenphysik und Quantensimulation veranschaulicht. Insbesondere wird eine allgemeine Methode zur Messung dynamischer Korrelationen basierend auf der linearen Antwort auf nicht-hermitesche Störungen vorgestellt. Diese ermöglicht unabhängige Tests des berühmten Fluktuations-Dissipations-Theorems als Indikator der Thermalisierung isolierter Quantensysteme. Darüber hinaus werden Verfahren zur Messung von Strömen und Strom-Korrelationen mittels Kopplung an einen Hilfszustand entwickelt, welche die Charakterisierung stark korrelierter Quantenmaterie erlauben. Eine weitere Anwendung zielt auf die Enthüllung spezifischer Merkmale von Supersolidität in Spin-Bahn-gekoppelten Bose-Einstein-Kondensaten ab, indem die relevanten Goldstone-Moden angeregt werden. Schließlich wird ein Szenario zur Quantensimulation post-inflationärer Thermalisierungsdynamik durch die parametrische Anregung eines Bose-Gases in das Regime universeller Dynamik fern des Gleichgewichts erschlossen. Die dargestellten Protokolle lassen sich auch auf andere Plattformen für analoge Quantensimulation übertragen und eröffnen damit vielversprechende Anwendungen auf dem Gebiet der Quantentechnologie.

The physics of ultracold quantum gases has been the subject of a long-lasting and intense research activity, which started almost a century ago with purely theoretical studies and had a fluorishing experimental development after the implementation of laser and evaporative cooling techniques that led to the first realization of a Bose Einstein condensate (BEC) over 25 years ago. In recent years, a great interest in ultracold atoms has developed for their use as platforms for quantum technologies, given the high degree of control and tunability offered by ultracold atom systems. These features make ultracold atoms an ideal test bench for simulating and studying experimentally, in a controlled environment, physical phenomena analogous to those occurring in other, more complicated, or even inaccessible systems, which is the idea at the heart of quantum simulation. In the rapidly developing field of quantum technologies, it is highly important to acquire an in-depth understanding of the state of the quantum many-body system that is used, and of the processes needed to reach the desired state. The preparation of the system in a given target state often involves the crossing of second order phase transitions, bringing the system strongly out-of-equilibrium. A better understanding of the out-of-equilibrium processes occurring in the vicinity of the transition, and of the relaxation dynamics towards the final equilibrium condition, is crucial in order to produce well-controlled quantum states in an efficient way. In this thesis I present the results of the research activity that I performed during my PhD at the BEC1 laboratory of the BEC center, working on ultracold gases of 23Na atoms in an elongated harmonic trap. This work had two main goals: the accurate determination of the equilibrium properties of a Bose gas at finite temperature, by the measurement of its equation of state, and the investigation of the out-of-equilibrium dynamics occurring when a Bose Einstein condensate is prepared by cooling a thermal cloud at a finite rate across the BEC phase transition.To study the equilibrium physics of a trapped atomic cloud, it is crucial to be able to observe its density distribution in situ. This requires a high optical resolution to accurately obtain the density profile of the atomic distribution, from which thermodynamic quantities can then be extracted. In particular, in a partially condensed atomic cloud at finite temperature, it is challenging to resolve well also the boundaries of the BEC, where the condensate fraction rapidly drops in a narrow spatial region. This required an upgrade of the experimental apparatus in order to obtain a high enough resolution. I designed, tested and implemented in the experimental setup new imaging systems for all main directions of view. Particular attention was paid for the vertical imaging system, which was designed to image the condensates in trap with a resolution below 2 μm, with about a factor 4 improvement compared to the previous setup. The implementation of the new imaging systems involved a partial rebuilding of the experimental apparatus used for cooling the atoms. This created the occasion for an optimization of the whole system to obtain more stable working conditions. Concurrently I also realized and included in the experiment an optical setup for the use of a Digital Micromirror Device (DMD) to project time-dependent arbitrary light patterns on the atoms, creating optical potentials that can be controlled at will. The use of this device opens up exciting future scenarios where it will be possible to locally modify the trapping potential and to create well-controlled barriers moving through the atomic cloud. Another challenge in imaging the density distribution in situ is determined by the fact that the maximum optical density (OD) of the BEC, in the trap center, exceeds the low OD of the thermal tails by several orders of magnitude. In order to obtain an accurate image of the whole density profile, we developed a minimally destructive, multi-shot imaging technique, based on the partial transfer of a fraction of atoms to an auxiliary state, which is then probed. Taking multiple images at different extraction fractions, we are able to reconstruct the whole density profile of the atomic cloud avoiding saturation and maintaining a good signal to noise ratio. This technique, together with the improvements in the imaging resolution, has allowed us to accurately obtain the optical density profile of the Bose gas in trap, from which the 3D density profile was then calculated applying an inverse Abel transform, taking advantage of the symmetry of the trap. From images of the same cloud after a time-of-flight expansion, we measured the temperature of the gas. From these quantities we could find the pressure as a function of the density and temperature, determining the canonical equation of state of the weakly interacting Bose gas in equilibrium at finite temperature. These measurements also allowed us to clearly observe the non-monotonic temperature behavior of the chemical potential near the critical point for the phase transition, a feature that characterizes also other superfluid systems, but that had never been observed before in weakly interacting Bose gases. The second part of this thesis work is devoted to the study of the dynamical processes that occur during the formation of the BEC order parameter within a thermal cloud. The cooling at finite rate across the Bose-Einstein condensation transition brings the system in a strongly out-of-equilibrium state, which is worth investigating, together with the subsequent relaxation towards an equilibrium state. This is of interest also in view of achieving a better understanding of second order phase transitions in general, since such phenomena are ubiquitous in nature and relevant also in other platforms for quantum technologies. A milestone result in the study of second order phase transitions is given by the Kibble-Zurek mechanism, which provides a simple model capturing important aspects of the evolution of a system that crosses a second-order phase transition at finite rate. It is based on the principle that in an extended system the symmetry breaking associated with a continuous phase transition can take place only locally. This causes the formation of causally disconnected domains of the order parameter, at the boundaries of which topological defects can form, whose number and size scale with the rate at which the transition is crossed, following a universal power law. It was originally developed in the context of cosmology, but was later successfully tested in a variety of systems, including superfluid helium, superconductors, trapped ions and ultracold atoms. The BEC phase transition represents in this context a paradigmatic test-bench, given the high degree of control at which this second-order phase transition can be crossed by means of cooling ramps at different rates. Already early experiments investigated the formation of the BEC order parameter within a thermal cloud, after quasi-instantaneous temperature quenches or very slow evaporative cooling. In the framework of directly testing the Kibble-Zurek mechanism, further experiments were performed, both in 2D and 3D systems, focusing on the emergence of coherence and on the statistics of the spontaneously generated topological defects as a function of the cooling rate. The Kibble-Zurek mechanism, however, does not fully describe the out-of-equilibrium dynamics of the system at the transition, nor the post-quench interaction mechanisms between domains that lead to coarse-graining. Most theoretical models are based on a direct linear variation of a single control parameter, e.g. the temperature, across the transition. In real experiments, the cooling process is controlled by the tuning of other experimental parameters and a global temperature might not even be well defined, in a thermodynamic sense, during the whole process. Moreover, the temperature variation is usually accompanied by the variation of other quantities, such as the number of atoms and the collisional rate, making it difficult to accurately describe the system and predict the post-quench properties. Recent works included effects going beyond the Kibble-Zurek mechanism, such as the inhomogeneity introduced by the trapping potential, the role of atom number losses, and the saturation of the number of defects for high cooling rates. These works motivate further studies, in particular of the dynamics taking place at early times, close to the crossing of the critical point. The aim of the work presented in this thesis is to further investigate the timescales associated to the formation and evolution of the BEC order parameter and its spatial fluctuations, as a function of the rate at which the transition point is crossed. We performed experiments producing BECs by means of cooling protocols that are commonly used in cold-atom laboratories, involving evaporative cooling in a magnetic trap. We explored a wide range of cooling rates across the transition and found a universal scaling for the growth of the BEC order parameter with the cooling rate and a finite delay in its formation. The latter was already observed in earlier works, but for a much more limited range of cooling rates. The evolution of the fluctuations of the order parameter was also investigated, with an analysis of the timescale of their decay during the relaxation of the system, from an initial strongly out-of-equilibrium condition to a final equilibrium state. This thesis is structured as follows: The first chapter presents the theoretical background, starting with a brief introduction to the concept of Bose Einstein condensation and a presentation of different models describing the thermodynamics of an equilibrium Bose gas. The second part of this chapter then deals with the out-of-equilibrium dynamics that is inevitably involved in the crossing of a second-order phase transition such as the one for Bose-Einstein condensation. The Kibble-Zurek mechanism is briefly reviewed and beyond KZ effects are pointed out, motivating a more detailed investigation of the timescales involved in the BEC formation. In the second chapter, I describe the experimental apparatus that we use to cool and confine the atoms. Particular detail is dedicated to the parts that have been upgraded during my PhD, such as the imaging system. In the third chapter I show our experimental results on the measurement of the equation of state of the weakly interacting uniform Bose gas at finite temperature. In the fourth chapter I present our results on the out-of-equilibrium dynamics in the formation of the condensate order parameter and its spatial fluctuations, as a function of different cooling rates.