Bose-Einstein condensates (BECs), with their superfluid behavior, quantized vortices, and high-level of control over trap geometry and other system parameters provide a compelling environment for studies of quantum fluid dynamics. Recently there has been an influx of theoretical and numerical progress in understanding the superfluid dynamics associated with two-dimensional quantum turbulence, with expectations that complementary experiments will soon be realized. In this dissertation I present progress in the development of an experimental toolkit that will enable such experimental studies of two-dimensional quantum turbulence. My approach to developing this toolkit has been twofold: first, efforts aimed at the development of experimental techniques for generating large disordered vortex distributions within a BEC; and second, efforts directed towards the design, implementation, and characterization of a quantum vortex microscope. Quantum turbulence in a superfluid is generally regarded as a disordered tangle of quantized vortices in three dimensions, or a disordered planar distribution of quantized vortices in two dimensions. However, not all vortex distributions, even large disordered ones, are expected to exhibit robust signatures of quantum turbulence. Identification and development of techniques for controlled forcing or initialization of turbulent vortex distributions is now underway. In this dissertation, I will discuss experimental techniques that were examined during the course of my dissertation research, namely generation of large disordered distributions of vortices, and progress towards injecting clusters of vortices into a BEC. Complimentary to vortex generation is the need to image these vortex distributions. The nondeterministic nature of quantum turbulence and other far-from-equilibrium superfluid dynamics requires the development of new imaging techniques that allow one to obtain information about vortex dynamics from a single BEC. To this end, the first vortex microscope constructed as part of my dissertation research enabled the first in situ images of quantized vortices in a single-component BEC, obtained without prior expansion. I have further developed and characterized a second vortex microscope, which has enabled the acquisition of multiple in situ images of a lattice of vortex cores, as well as the acquisition of single in situ images of vortex cores in a BEC confined in a weak hybrid trap. In this dissertation, I will discuss the state-of-the-art of imaging vortices and other superfluid phenomena in the University of Arizona BEC lab, as indicated by the examined performance of the quantum vortex microscope.

In the present thesis, “Hydrodynamics of Binary Bose-Einstein Condensates and Hydro-elasticity of the Inner Crust of Neutron Stars”, the hydrodynamic effects, instabilities and superfluid turbulence in binary immiscible ultracold gases, and hydro-elastic macroscopic coupled modes and microscopic structure of the inner layers of the crust of neutron stars, are studied. The ultracold gas dynamics can be realized in the laboratory. The excitation modes of the inner crust determine a number of observable properties such as elasticity, thermal properties and mass transport properties. Here we focus on expanding the details, rather than repeating the results presented in the published articles. In the part of the thesis related to atomic ultracold gases, we utilize the physical parameters in the experimentally realizable parameter region. We numerically simulate the coupled non-linear Schrödinger equations, and calculate observable quantities, such as phase and modulus of the order parameter, conditions needed for observation of the Rayleigh-Taylor instability and for turbulence generation. The numerical calculations are accompanied by analytical description of the processes. The dispersion relation for capillary-gravitational waves at the interface between two ultracold gases, is derived straightforwardly from the superfluid Lagrangian. The equations of motion for centre-of-mass of the superfluids are derived, and then used in our model of the quantum swapping of immiscible superfluids pressed by a strong external force. By numerical simulation, we find that the Kelvin-Helmholtz instability which occurs at the non-linear stage of the Rayleigh-Taylor instability, can generate quantum turbulence with peculiar properties. We find that two-dimensional superfluid systems with weak inter-component repulsion are different from previously studied strongly repulsive binary superfluids, because the quantum Kelvin-Helmholtz instability in weakly repulsive superfluids rolls up the whole interface forming a vortex bundle, similarly to dynamics of the shear fluid layers in the classical hydrodynamics. Production of vortex bundles favours the Kolmogorov spectrum of turbulence, and we find that the Kolmogorov scaling indeed is present in a freely decaying turbulence. In the part of the thesis related to neutron stars, we study the inner crust of neutron stars, where the fully ionized atomic nuclei coexist with a superfluid of neutrons. The interaction between superfluid neutrons and the crystallized Coulomb plasma is due to the interaction between density perturbations (interaction of the scalar type), and between the current - the non-dissipative entrainment effect (interaction of the vector type). We calculate velocities of the collective modes of the crystal coupled to superfluid neutrons. As an input we use the results of microscopic nuclear calculations in the framework of the compressible liquid drop model (the Lattimer and Swesty equation of state), and more recent effective Thomas-Fermi calculations with shell corrections (N. Chamel, and the Brussels theoretical nuclear physics group). Knowledge of velocities as functions of the matter density in the inner crust is important for calculation of a number of dynamic and transport properties. The heat transport properties of the inner crust are directly observable in accreting binary systems (low-mass x-ray binaries). The mass transport properties of the inner crust are directly linked to the rotational evolution, being a key physical ingredient of the pulsar glitch phenomenon. The elastic properties are related to the vibrational modes of the star, and to the breaking stress of the crust. In the second part of our work on neutron stars we investigate the microscopic structure of the inner crust treating the structure as an anisotropic crystal coupled to s-wave superfluid neutron liquid. As we analyse dynamics of the elementary excitations at higher wavenumbers (smaller scales), we reach the edge of the first Brillouin zone. The Lattimer-Swesty data is applicable for wavenumbers much smaller than the edge of the first Brillouin zone. We extrapolate the data through the whole first Brillouin zone to calculate the fastest growth rate of the unstable modes. The crucial step is to calculate the mode velocities in anisotropic crystal incorporating both the induced neutron-proton interactions, and the electron screening properties. We find that the combined influence of these two effects leads to softening of the longitudinal phonon of the lattice above about the Thomas-Fermi screening wavenumber of the electrons. The critical wavenumber when the frequency becomes purely imaginary is about  1/5 - 2/3  of the reciprocal lattice vector, thus validating our assumption. The imaginary mode frequency implies instability at finite wavenumbers. Our calculations suggest that the mode at the first Brillouin zone edge is the most unstable, and thus the structure experiences a displacive phase transition when the central ion of a unit cell of the body-cubic-centred lattice, is displaced to the cube face. Thus, the electronic structure of matter at densities above the neutron drip [1], is richer than previously appreciated, and new microscopic calculations of nuclear structure are necessary which take into account the high-wavenumber physics. Such calculations will provide crucial input to models interpreting the quasi-periodic oscillations in Soft Gamma Repeaters as magnetar x-ray flares, and to the theory of glitches of neutron stars. [1] The neutron drip density is ~3×1011 g cm-3.

This thesis is devoted to the study of excitations in atomic and polariton Bose-Einstein condensates (BEC). These two specimens are prime examples for equilibrium and non equilibrium BEC. The corresponding condensate wave function of each system satisfies a particular partial differential equation (PDE). These PDEs are discussed in the beginning of this thesis and justified in the context of the quantum many-body problem. For high occupation numbers and when neglecting quantum fluctuations the quantum field operator simplifies to a semiclassical wave. It turns out that the interparticle interactions can be simplified to a single parameter, the scattering length, which gives rise to an effective potential and introduces a nonlinearity to the PDE. In both cases, i.e. equilibrium and non equilibrium, the main model corresponding to the semiclassical wave is the Gross-Pitaevskii equation (GPE), which includes certain mathematical adaptions depending on the physical context of the consideration and the nature of particles/quasiparticles, such as additional complex pumping and growth terms or terms due to motion. In the course of this work I apply a variety of state-of-the-art analytical and numerical tools to gain information about these semiclassical waves. The analytical tools allow e.g. to determine the position of the maximum density of the condensate wave function or to find the critical velocities at which excitations are expected to be generated within the condensate. In addition to analytical considerations I approximate the GPE numerically. This allows to gain the condensate wave function explicitly and is often a convenient tool to study the emergence of excitations in BEC. It is in particular shown that the form of the possible excitations significantly depends on the dimensionality of the considered system. The generated excitations within the BEC include quantum vortices, quantum vortex rings or solitons. In addition multicomponent systems are considered, which enable more complex dynamical scenarios. Under certain conditions imposed on the condensate one obtains dark-bright soliton trains within the condensate wave function. This is shown numerically and analytical expressions are found as well. In the end of this thesis I present results as part of an collaborative effort with a group of experimenters. Here it is shown that the wave function due to a complex GPE fits well with experiments made on polariton condensates, statically and dynamically.

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Orderliness, speed, and rhythm in biochemistry are vital for cellular function. In order to achieve this, cells implement compartmentalization via several methods, one of which is the formation of membrane-less compartments. These compartments, often referred to as “biomolecular condensates”, are understood to be formed by separation of proteins and other biomolecules into dense and dilute phases. While the formation of the resulting protein-rich condensates is fundamental for spatiotemporal organization of biochemistry within the cell, a vast majority of proteins found to phase separate in vitro do so at a concentration an order of magnitude above their endogenous expression levels. Recently, a theoretical study has shown that membrane binding of phase separating proteins can result in phase separation spatially occurring at the membrane well below bulk saturation concentrations. However, much remains unknown about the formation mechanism and function of these condensates. To that end, for my doctoral project, I used a synthetic system composed of supported lipid bilayers decorated with lipid-bound NTA(Ni) to allow for coordination and thus membrane binding of the well-characterized protein FUS via a C-terminal His-tag. Through this model system I found that 2D phase separation of FUS could occur an order of magnitude below the experimentally determined bulk saturation concentration. FUS was able to form dense and dilute phases in 2D and the transition point to form these phases could be controlled by modulating buffer conditions. Additionally, membrane-bound FUS condensates were able to further recruit FUS from the bulk to form a multilayer of protein through a prewetting transition. With this characterization of 2D phase separation of FUS, I then explored a physiologically relevant protein in the form of PAR-3, a fundamental protein of the PAR polarity system, which is necessary for the establishment of polarity in the C. elegans zygote. I found that full-length PAR-3 was able to phase separate under physiological salt conditions with a Csat of 100nM. Further, I identified a C-terminal predicted prion-like domain to act as a driver for phase separation. Additionally, I determined PAR-3’s affinity and specificity for PI(4,5)P2 and found that it could form 2D condensates upon binding to the membrane at physiological concentrations. Furthermore, these condensates were able to recruit PAR-6 alone and PAR-6 in complex with PKC-3 to the membrane, ultimately resulting the reconstitution of the anterior PAR complex which is known to exist in a condensed clustered form in vivo. Taken together, this work provides insight into a mechanism where phase separation can be locally triggered by membrane binding under sub-saturation concentration, offering a robust and potentially universal mechanism by which cells can spatially control phase separation and pattern cellular membranes.

Bose-Einstein condensates (BECs) of ultra-cold atoms have been subjects of a large research effort, that started a century ago as a purely theoretical subject and is now, since the invention of evaporative cooling thirty years ago, a rich research topic with many experimental apparatuses around the world. A deep knowledge of its underlying physics has been now acquired, for example on the thermodynamics of the gas, superfluidity, topological excitations and many-body physics. However, many topics are still open for investigation, thanks to the flexibility and the high degree of control of these systems. During the course of my PhD, I developed and realized a new experimental apparatus for the realization of coherently-coupled mixtures of sodium BECs. The highly stable and low-noise magnetic environment of this apparatus enables the experimental investigation of a previously inaccessible regime, where the energy of the coupling becomes comparable to the energy of spin excitations of the mixture. With this apparatus, I concluded two experimental investigations: I produced and investigated non-dispersive spin-waves in an two-component BEC and I experimentally observed the quantum spin-torque effect on a elongated bosonic Josephson junction.The research activity in multi-component BECs of alkali atoms begun shortly after the first realization of a condensate, thanks to the low energy splitting between the internal sub-states of the electronic ground state. These internal states can be coherently coupled with an external electromagnetic field and can interact via mutual mean-field interaction, generating interestinc effects such as ground states with different magnetic ordering depending on their interaction constants, density as well as spin dynamics and internal Josephson effects. The research interest on mixtures of sodium atoms sparks from the peculiar characteristic of the system: in the $ket{F = 1, m_F = pm 1}$ states, the interaction constants are such that the ground state has anti-ferromagnetic ordering and the system is perfectly symmetric for exchanges of the two species. In these peculiar system, density- and spin-excitations have very different energetic cost, with the latter being much less energetic, and can be completely decoupled. Moreover, spin-excitations, that are connected to excitations in the relative-phase between the components, change drastically in nature when a coupling of comparable energy is added between the states. The presence of the coupling effectively locks the relative-phase in the bulk and spin excitations become localized. While extensive theoretical predictions on the spin dynamics of this system has been already performed, experimental confirmation was still lacking because of the high sensitivity to external forces (due to the very low energy of the spin excitations) and the impossibility of realizing a low-energy coupling between these states in the presence of environmental magnetic noise. During my PhD, I realized an experimental apparatus where magnetic noises are suppressed by five orders of magnitude using a multi-layer magnetic shield made of an high-permeability metal alloy (μ-metal), that encases the science chamber. In this apparatus, I developed a protocol, compatible with the technical limitations of the magnetic shield, to produce BECs in a spin-insensitive optical trapping potential. I then characterized the residual magnetic noise and found it compatible with the requirements for observing spin-dynamics effects. Finally, I realized a system and a set of protocols for the manipulation of the internal state of the sample allowing arbitrary preparation of the sample while maintaining the long coherence times necessary to observe the spin dynamics, that have been used in the subsequent experimental observations. The first experimental result discussed in this thesis, is the production of magnetic solitons and the observation of their dynamic in a trapped sample. Waves in general spread during their propagation in a medium, however this tendency can be counterbalanced by a self-focusing effect if dispersion of the wave is non-linear, generating non-dispersive and long-lived wavepackets commonly named solitons. These have been found in many fields of physics, such as fluid dynamics, plasma physics, non-linear optics and cold-atoms BECs, attracting interest because of their ability to transport information or energy unaltered over long distances, as they are robust against the interaction with in-homogeneities in the medium. Of these systems, cold-atoms can be widely manipulated to generated different kinds of solitons, both in single and in multi-components systems. A new kind of them, named magnetic solitons, has been predicted in a balanced mixture of BECs of sodium in $ket{F = 1, m_F = pm 1}$, however experimental observation was still lacking. I deterministically produced magnetic solitons via phase engineering of the condensate using a spin-sensitive optical potential. I then developed a tomographic imaging technique to semi-concurrently measure the densities of both components and the discontinuities in their relative phase, allowing for the reconstruction of all the relevant quantities of the spinor wavefunction. This allowed to observe the dispersionless dynamics of the solitons as they perform multiple oscillation in the trapped sample in a timescale of the order of the second. Moreover, I engineered collisions between different kinds of magnetic solitons and observed their robustness to mutual interaction. The second experimental results presented in this thesis is the observation of the breaking of magnetic hetero-structures in BECs due to the quantum spin torque effect, an effect with strong analogies with electronic spins traveling through magnetic devices. Spins in magnetic material precess around the axis of the effective magnetic field, and their dynamics must take into account the external field as well as non-linear magnetization and the inhomogeneity of the material. These effects are commonly described by the Landau-Lifshitz equation and have been mainly studied for electronic spins in magnetic hetero-structures, where the inhomogeneity in the material at the interfaces enhances the exchange effects between spins. For homogeneous materials, this description reduces to the Josephson system, a closely related effect that is more known in cold-atoms systems. The Josephson effect arises when a macroscopic number of interacting bosonic particles are distributed in two possible states, weakly tunnel-coupled together, with the average energy of particles occupying each of the states depending on the occupation number itself. In these conditions, the dynamics of the system depends on the difference in occupation numbers, the relative phase between the states and the self-interaction to tunneling ratio, giving raise to macroscopic quantum effects such as oscillating AC and DC Josephson currents and self-trapping. While these phenomena has been historically studied in junctions between superconducting systems, they can be also realized with cold-atoms systems, allowing the study of Josephson junctions with finite dimensions and in regimes that are hard to reach for superconducting systems. In this thesis, I realized a magnetic hetero-structure in a two-component elongated BECs thanks to the simultaneous presence of self-trapped (ferromagnetic) and oscillating (paramagnetic) regions in the sample. While the dynamics at short times is correctly described by the Josephson effects, at the interface between the regions the particle nature of the gas creates a strong exchange effect, named the quantum spin torque, that produces magnetic excitations that spread trough the sample and break the local Josephson behaviour. I experimentally studied the spread and nature of these magnetic excitations, while numerical simulations confirmed the dominant role played by the quantum spin torque effect. The structure of this thesis is the following: in the first chapter is given a review of theoretical concepts and existing literature. In the second chapter is described the experimental apparatus and the protocols developed to prepare the ultra-cold atoms sample. In the third chapter is presented the experimental observation of magnetic solitons. In the fourth chapter is presented the experimental investigation of the quantum spin torque effect in magnetic heterostructures. The last chapter is devoted to conclusions and outlook of this work.

The human genome is characterized by an extent of functions that act further than its genetic role. Indeed, the genome can also affect cellular processes by nongenetic means through its physical and structural properties, specifically by exerting mechanical forces that shape nuclear morphology and architecture. The balancing between two chromatin compartments with antagonist functions, namely Transcriptional and Polycomb condensates, is required for preserving nuclear mechanical properties and its perturbation is causative of the pathogenic condition Kabuki syndrome (KS) (Fasciani et al., 2020). KS is a rare monogenic disease caused by the haploinsufficiency in the KMT2D gene encoding for MLL4, a H3K4-specific methyltransferase important for the regulation of gene expression. By interrogating the effect of KMT2D haploinsufficiency in Mesenchymal Stem Cells (MSCs) we discovered that MLL4 loss of function (LoF) impaired Polycomb-dependent chromatin compartmentalization, altering the nuclear architecture and the cell mechanoresponsiveness during differentiation (Fasciani et al., 2020). These results suggest that altered nuclear mechanics rely on chromatin architecture and could potentially lead to changes in cell responses to external mechanical stimuli. In the present work, we investigated the role of Transcriptional and Polycomb condensates in tuning nuclear responses to different external mechano-physical conditions. To affect nuclear mechanics, we employed the use of several mechanical devices (e. g. substrate stiffness, microchannels with constrictions, and cell confinement). We found that Polycomb and Transcriptional condensates are modulated by changes in substrate rigidity in healthy conditions and that MLL4 LoF impairs the MSCs nuclear condensates-driven mechanical response. Furthermore, we observed that MLL4 LoF impacts nuclear adaptation to confined spaces by incrementing susceptibility to nuclear envelope rupture. We also showed that the increased nuclear fragility in MLL4 LoF is accompanied by an alteration of cell migratory capacity and survival rate. Altogether these findings suggest that MLL4 LoF impairs cell responses to external mechanical stimuli, shedding light on the pathological connection between the altered cell mechanoresponsiveness during differentiation and KS phenotype in terms of skeletal and cartilage anomalies.

Eukaryotic cells are characterized by having a clearly defined nucleus that encloses genetic material, separating it from the rest of the cell. The regulation of protein partitioning between the nucleus and cytoplasm is crucial for controlling specific cellular functions; any imbalance in protein partitioning can lead to a range of diseases, highlighting its significance in cellular physiology. The major mechanism for establishing nuclear composition is the trafficking of proteins in and out of the nucleus by karyopherins after the formation of the nuclear envelope. Regulating protein partitioning is particularly challenging during early embryonic development due to the rapid and successive cell divisions that lead to a dramatic reduction in cell size. Further, the embryo is maternally deposited with vast quantities of proteins that must be appropriately incorporated into an exponentially increasing number of nuclei. How such large quantities of proteins are robustly partitioned into the nucleus during these dynamic developmental processes remains unclear. During my Ph.D., I studied the nuclear partitioning of the Xenopus laevis embryonic linker histone H1.8, a protein that alters the chromatin structure in a concentration-dependent manner. By using quantitative microscopy of Xenopus laevis egg extract, I provide evidence H1.8 is partitioned into the nucleus through a mechanism independent of nuclear import. H1.8 has already been shown to be one of the earliest proteins to partition within the nucleus during embryonic development. However, I demonstrate that the import kinetics of H1.8 is insufficient to account for its rapid nuclear partitioning. Further, I discovered that H1.8 is present in the nucleus and cytoplasm as liquid condensates. As the nucleus expands and grows in interphase, the nuclear condensates dissolve, suggesting that they act as reservoirs of proteins, potentially for DNA replication. The dissolution also suggests that most nuclear H1.8 is already present during the nuclear assembly, thus indicating that the partition of H1.8 inside the nucleus is not solely dependent on its import. Prior to the formation of the nucleus, I observe that the surface of the chromatid nucleates H1.8 as condensates similar to the formation of dew droplets on a cold surface. These condensates are then sequestered into the nucleus as the cell cycle progresses, leading to the protein reservoirs we observe in the nucleus. Such a mechanism allows for instantaneous enrichment of excess H1.8 inside the nucleus. Furthermore, I demonstrate that the cytoplasmic H1.8 condensates modulate the nucleation of H1.8 on the chromatid surface by buffering the soluble concentration of H1.8. This ensures that the amount of surface condensates is independent of the nucleus-to-cytoplasmic ratio, thus potentially allowing for a fixed enrichment of proteins despite the reduction in cell size during embryonic development. Such a mechanism would be crucial for key structural proteins, like H1.8, that maintain DNA packaging and structure in a concentration-dependent manner. Taken together, I propose that the nucleation of condensates on the surface of mitotic chromatids and subsequent wetting can provide an alternative mechanism to nuclear trafficking in regulating nuclear composition.:1) Introduction 2) This work – aim and scope 3) The dynamics of H1.8 nuclear localization 4) H1.8 undergoes liquid-liquid phase separation in Xenopus laevis egg extract. 5) H1.8 condenses on the surface of chromatids. 6) Cytoplasmic condensates buffer the amount of surface condensates on chromatids. 7) Summary. 8) Future perspectives. 9) Methods

Biomolecular condensates are dynamic intracellular structural units or distinct reaction spaces that can form by condensation of their constituents from the cytoplasm or the nucleoplasm. It is generally not clear yet, how dynamic, continuum-like condensate properties relevant for large-scale intracellular organisation emerge from the interplay of proteins and nucleic acids on the level of few individual molecules. With this work, we expand the portfolio of methods to investigate the role of protein-nucleic acid interactions in biomolecular condensates by introducing optical tweezers-based mechanical micromanipulation of single DNA molecules combined with confocal fluorescence microscopy to the field. We used this approach to characterise how the two landmark proteins1 Fused in Sarcoma and Heterochromatin Protein 1 form condensates with single DNA molecules. Fused in Sarcoma (FUS) is a key protein for various aspects of the nucleic acid metabolism and evidence is accumulating that biomolecular condensation is crucial for both, its physiological functions and its role in pathological aggregate formation. In this thesis, we directly visualised the formation of FUS condensates with single molecules of ssDNA and dsDNA. We showed that the formation of these microcondensates is based on nucleic acid scaffolding. We explored their mechanical properties and found that the mechanical tension that (FUS dsDNA) condensates can withstand or exert is in the range below 2 pN. We further demonstrated that already on this fundamental scale and with limited amounts of constituent molecules, dynamic properties like shape relaxations, reminiscent of viscoelastic materials, can emerge. Heterochromatin Protein 1 (HP1) is a prototypic chromatin organising factor that is in particular involved in the formation of dynamically compacted heterochromatin domains. HP1 forms biomolecular condensates and compacts DNA strands in vitro. In this work, we measured the influence of HP1 on the mechanical properties of individual DNA molecules and demonstrated the response of HP1-DNA condensates to different environmental conditions. We contributed a methodological framework to characterise viscoelastic-like systems on the single molecule level. Taken together, our optical tweezers-based approach revealed structural and mechanical properties of prototypic protein-DNA condensates and hence helped to elucidate mechanisms underlying their formation in unprecedented spatiotemporal and mechanical detail. We anticipate that this method can become a valuable tool to investigate how large-scale intracellular organisation based on protein-nucleic acid condensation emerges from interactions between individual building blocks.