Exotic superfluid states of ultra-cold Fermi gases

This is a study of ultra-cold Fermi gases in different systems. This thesis is focused on exotic superfluid states, for an example on the three component Fermi gas and the FFLO phase in optical lattices. In the two-components case, superfluidity is studied mainly in the case of the spin population imbalanced Fermi gases and the phase diagrams are calculated from the mean-field theory. Different methods to detect different phases in optical lattices are suggested. In the three-component case, we studied also the uniform gas and harmonically trapped system. In this case, the BCS theory is generalized to three-component gases. It is also discussed how to achieve the conditions to get an SU(3)-symmetric Hamiltonian in optical lattices. The thesis is divided in chapters as follows: Chapter 1 is an introduction to the field of cold quantum gases. In chapter 2 optical lattices and their experimental characteristics are discussed. Chapter 3 deals with two-components Fermi gases in optical lattices and the paired states in lattices. In chapter 4 three-component Fermi gases with and without a harmonic trap are explored, and the pairing mechanisms are studied. In this chapter, we also discuss three-component Fermi gases in optical lattices. Chapter 5 devoted to the higher order correlations, and what they can tell about the paired states. Chapter 6 concludes the thesis.

Novel Organo-Noble-Gas Hydrides

Noble gases are mostly known as inert monatomic gases due to their limited reactivity with other elements. However, the first predictions of noble-gas compounds were suggested by Kossel in 1916, by von Antropoff in 1924, and by Pauling in 1930. It took many decades until the first noble-gas compound, XePtF6, was synthesized by Neil Bartlett in 1962. This was followed by gradual development of the field and many noble-gas compounds have been prepared. In 1995, a family of noble-gas hydride molecules was discovered at the University of Helsinki. These molecules have the general formula of HNgY, where H is a hydrogen atom, Ng is a noble-gas atom (Ar, Kr, or Xe), and Y is an electronegative fragment. The first molecular species made include HXeI, HXeBr, HXeCl, HKrCl and HXeH. Nowadays the total number of prepared HNgY molecules is 23 including both inorganic and organic compounds. The first and only neutral ground-state argon compound, HArF, was synthetized in 2000. Helium and neon are the only elements in the periodic table that do not form neutral, ground-state molecules. In this Thesis, experimental preparation of eight novel xenon- and krypton-containing organo-noble-gas hydrides made from acetylene (HCCH), diacetylene (HCCCCH) and cyanoacetylene (HCCCN) are presented. These novel species include the first organic krypton compound, HKrCCH, as well as the first noble-gas hydride molecule containing two Xe atoms, HXeCCXeH. Other new compounds are HXeCCH, HXeCC, HXeC4H, HKrC4H, HXeC3N, and HKrC3N. These molecules are prepared in noble-gas matrices (krypton or xenon) using ultraviolet photolysis of the precursor molecule and thermal mobilization of the photogenerated H atoms. The molecules were identified using infrared spectroscopy and ab initio calculations. The formation mechanisms of the organo-noble-gas molecules are studied and discussed in this context. The focus is to evidence experimentally the neutral formation mechanisms of HNgY molecules upon global mobility of H atoms. The formation of HXeCCXeH from another noble-gas compound (HXeCC) is demonstrated and discussed. Interactions with the surrounding matrix and molecular complexes of the HXeCCH molecule are studied. HXeCCH was prepared in argon and krypton solids in addition to a Xe matrix. The weak HXeCCH∙∙∙CO2 complex is prepared and identified. Preparation of the HXeCCH∙∙∙CO2 complex demonstrates an advanced approach to studies of HNgY complexes where the precursor complex (HCCH∙∙∙CO2) is obtained using photolysis of a larger molecule (propiolic acid).

Intermolecular Interactions of Noble-Gas-Containing Species

The importance of intermolecular interactions to chemistry, physics, and biology is difficult to overestimate. Without intermolecular forces, condensed phase matter could not form. The simplest way to categorize different types of intermolecular interactions is to describe them using van der Waals and hydrogen bonded (H-bonded) interactions. In the H-bond, the intermolecular interaction appears between a positively charged hydrogen atom and electronegative fragments and it originates from strong electrostatic interactions. H-bonding is important when considering the properties of condensed phase water and in many biological systems including the structure of DNA and proteins. Vibrational spectroscopy is a useful tool for studying complexes and the solvation of molecules. Vibrational frequency shift has been used to characterize complex formation. In an H-bonded system A∙∙∙H-X (A and X are acceptor and donor species, respectively), the vibrational frequency of the H-X stretching vibration usually decreases from its value in free H-X (red-shift). This frequency shift has been used as evidence for H-bond formation and the magnitude of the shift has been used as an indicator of the H-bonding strength. In contrast to this normal behavior are the blue-shifting H-bonds, in which the H-X vibrational frequency increases upon complex formation. In the last decade, there has been active discussion regarding these blue-shifting H-bonds. Noble-gases have been considered inert due to their limited reactivity with other elements. In the early 1930 s, Pauling predicted the stable noble-gas compounds XeF6 and KrF6. It was not until three decades later Neil Bartlett synthesized the first noble-gas compound, XePtF6, in 1962. A renaissance of noble-gas chemistry began in 1995 with the discovery of noble-gas hydride molecules at the University of Helsinki. The first hydrides were HXeCl, HXeBr, HXeI, HKrCl, and HXeH. These molecules have the general formula of HNgY, where H is a hydrogen atom, Ng is a noble-gas atom (Ar, Kr, or Xe), and Y is an electronegative fragment. At present, this class of molecules comprises 23 members including both inorganic and organic compounds. The first and only argon-containing neutral chemical compound HArF was synthesized in 2000 and its properties have since been investigated in a number of studies. A helium-containing chemical compound, HHeF, was predicted computationally, but its lifetime has been predicted to be severely limited by hydrogen tunneling. Helium and neon are the only elements in the periodic table that do not form neutral, ground state molecules. A noble-gas matrix is a useful medium in which to study unstable and reactive species including ions. A solvated proton forms a centrosymmetric NgHNg+ (Ng = Ar, Kr, and Xe) structure in a noble-gas matrix and this is probably the simplest example of a solvated proton. Interestingly, the hypothetical NeHNe+ cation is isoelectronic with the water-solvated proton H5O2+ (Zundel-ion). In addition to the NgHNg+ cations, the isoelectronic YHY- (Y = halogen atom or pseudohalogen fragment) anions have been studied with the matrix-isolation technique. These species have been known to exist in alkali metal salts (YHY)-M+ (M = alkali metal e.g. K or Na) for more than 80 years. Hydrated HF forms the FHF- structure in aqueous solutions, and these ions participate in several important chemical processes. In this thesis, studies of the intermolecular interactions of HNgY molecules and centrosymmetric ions with various species are presented. The HNgY complexes show unusual spectral features, e.g. large blue-shifts of the H-Ng stretching vibration upon complexation. It is suggested that the blue-shift is a normal effect for these molecules, and that originates from the enhanced (HNg)+Y- ion-pair character upon complexation. It is also found that the HNgY molecules are energetically stabilized in the complexed form, and this effect is computationally demonstrated for the HHeF molecule. The NgHNg+ and YHY- ions also show blue-shifts in their asymmetric stretching vibration upon complexation with nitrogen. Additionally, the matrix site structure and hindered rotation (libration) of the HNgY molecules were studied. The librational motion is a much-discussed solid state phenomenon, and the HNgY molecules embedded in noble-gas matrices are good model systems to study this effect. The formation mechanisms of the HNgY molecules and the decay mechanism of NgHNg+ cations are discussed. A new electron tunneling model for the decay of NgHNg+ absorptions in noble-gas matrices is proposed. Studies of the NgHNg+∙∙∙N2 complexes support this electron tunneling mechanism.

Sticking and erosion at carbon-containing plasma-facing materials in fusion reactors

Controlled nuclear fusion is one of the most promising sources of energy for the future. Before this goal can be achieved, one must be able to control the enormous energy densities which are present in the core plasma in a fusion reactor. In order to be able to predict the evolution and thereby the lifetime of different plasma facing materials under reactor-relevant conditions, the interaction of atoms and molecules with plasma first wall surfaces have to be studied in detail. In this thesis, the fundamental sticking and erosion processes of carbon-based materials, the nature of hydrocarbon species released from plasma-facing surfaces, and the evolution of the components under cumulative bombardment by atoms and molecules have been investigated by means of molecular dynamics simulations using both analytic potentials and a semi-empirical tight-binding method. The sticking cross-section of CH3 radicals at unsaturated carbon sites at diamond (111) surfaces is observed to decrease with increasing angle of incidence, a dependence which can be described by a simple geometrical model. The simulations furthermore show the sticking cross-section of CH3 radicals to be strongly dependent on the local neighborhood of the unsaturated carbon site. The erosion of amorphous hydrogenated carbon surfaces by helium, neon, and argon ions in combination with hydrogen at energies ranging from 2 to 10 eV is studied using both non-cumulative and cumulative bombardment simulations. The results show no significant differences between sputtering yields obtained from bombardment simulations with different noble gas ions. The final simulation cells from the 5 and 10 eV ion bombardment simulations, however, show marked differences in surface morphology. In further simulations the behavior of amorphous hydrogenated carbon surfaces under bombardment with D^+, D^+2, and D^+3 ions in the energy range from 2 to 30 eV has been investigated. The total chemical sputtering yields indicate that molecular projectiles lead to larger sputtering yields than atomic projectiles. Finally, the effect of hydrogen ion bombardment of both crystalline and amorphous tungsten carbide surfaces is studied. Prolonged bombardment is found to lead to the formation of an amorphous tungsten carbide layer, regardless of the initial structure of the sample. In agreement with experiment, preferential sputtering of carbon is observed in both the cumulative and non-cumulative simulations

Computational fluid dynamics simulations in aerosol and nucleation studies

Nucleation is the first step in the formation of a new phase inside a mother phase. Two main forms of nucleation can be distinguished. In homogeneous nucleation, the new phase is formed in a uniform substance. In heterogeneous nucleation, on the other hand, the new phase emerges on a pre-existing surface (nucleation site). Nucleation is the source of about 30% of all atmospheric aerosol which in turn has noticeable health effects and a significant impact on climate. Nucleation can be observed in the atmosphere, studied experimentally in the laboratory and is the subject of ongoing theoretical research. This thesis attempts to be a link between experiment and theory. By comparing simulation results to experimental data, the aim is to (i) better understand the experiments and (ii) determine where the theory needs improvement. Computational fluid dynamics (CFD) tools were used to simulate homogeneous onecomponent nucleation of n-alcohols in argon and helium as carrier gases, homogeneous nucleation in the water-sulfuric acid-system, and heterogeneous nucleation of water vapor on silver particles. In the nucleation of n-alcohols, vapor depletion, carrier gas effect and carrier gas pressure effect were evaluated, with a special focus on the pressure effect whose dependence on vapor and carrier gas properties could be specified. The investigation of nucleation in the water-sulfuric acid-system included a thorough analysis of the experimental setup, determining flow conditions, vapor losses, and nucleation zone. Experimental nucleation rates were compared to various theoretical approaches. We found that none of the considered theoretical descriptions of nucleation captured the role of water in the process at all relative humidities. Heterogeneous nucleation was studied in the activation of silver particles in a TSI 3785 particle counter which uses water as its working fluid. The role of the contact angle was investigated and the influence of incoming particle concentrations and homogeneous nucleation on counting efficiency determined.

Interatomic potentials for fusion reactor material simulations

Fusion energy is a clean and safe solution for the intricate question of how to produce non-polluting and sustainable energy for the constantly growing population. The fusion process does not result in any harmful waste or green-house gases, since small amounts of helium is the only bi-product that is produced when using the hydrogen isotopes deuterium and tritium as fuel. Moreover, deuterium is abundant in seawater and tritium can be bred from lithium, a common metal in the Earth's crust, rendering the fuel reservoirs practically bottomless. Due to its enormous mass, the Sun has been able to utilize fusion as its main energy source ever since it was born. But here on Earth, we must find other means to achieve the same. Inertial fusion involving powerful lasers and thermonuclear fusion employing extreme temperatures are examples of successful methods. However, these have yet to produce more energy than they consume. In thermonuclear fusion, the fuel is held inside a tokamak, which is a doughnut-shaped chamber with strong magnets wrapped around it. Once the fuel is heated up, it is controlled with the help of these magnets, since the required temperatures (over 100 million degrees C) will separate the electrons from the nuclei, forming a plasma. Once the fusion reactions occur, excess binding energy is released as energetic neutrons, which are absorbed in water in order to produce steam that runs turbines. Keeping the power losses from the plasma low, thus allowing for a high number of reactions, is a challenge. Another challenge is related to the reactor materials, since the confinement of the plasma particles is not perfect, resulting in particle bombardment of the reactor walls and structures. Material erosion and activation as well as plasma contamination are expected. Adding to this, the high energy neutrons will cause radiation damage in the materials, causing, for instance, swelling and embrittlement. In this thesis, the behaviour of a material situated in a fusion reactor was studied using molecular dynamics simulations. Simulations of processes in the next generation fusion reactor ITER include the reactor materials beryllium, carbon and tungsten as well as the plasma hydrogen isotopes. This means that interaction models, {\it i.e. interatomic potentials}, for this complicated quaternary system are needed. The task of finding such potentials is nonetheless nearly at its end, since models for the beryllium-carbon-hydrogen interactions were constructed in this thesis and as a continuation of that work, a beryllium-tungsten model is under development. These potentials are combinable with the earlier tungsten-carbon-hydrogen ones. The potentials were used to explain the chemical sputtering of beryllium due to deuterium plasma exposure. During experiments, a large fraction of the sputtered beryllium atoms were observed to be released as BeD molecules, and the simulations identified the swift chemical sputtering mechanism, previously not believed to be important in metals, as the underlying mechanism. Radiation damage in the reactor structural materials vanadium, iron and iron chromium, as well as in the wall material tungsten and the mixed alloy tungsten carbide, was also studied in this thesis. Interatomic potentials for vanadium, tungsten and iron were modified to be better suited for simulating collision cascades that are formed during particle irradiation, and the potential features affecting the resulting primary damage were identified. Including the often neglected electronic effects in the simulations was also shown to have an impact on the damage. With proper tuning of the electron-phonon interaction strength, experimentally measured quantities related to ion-beam mixing in iron could be reproduced. The damage in tungsten carbide alloys showed elemental asymmetry, as the major part of the damage consisted of carbon defects. On the other hand, modelling the damage in the iron chromium alloy, essentially representing steel, showed that small additions of chromium do not noticeably affect the primary damage in iron. Since a complete assessment of the response of a material in a future full-scale fusion reactor is not achievable using only experimental techniques, molecular dynamics simulations are of vital help. This thesis has not only provided insight into complicated reactor processes and improved current methods, but also offered tools for further simulations. It is therefore an important step towards making fusion energy more than a future goal.

Computer simulation of H and He effects in fusion reactor materials

Fusion power is an appealing source of clean and abundant energy. The radiation resistance of reactor materials is one of the greatest obstacles on the path towards commercial fusion power. These materials are subject to a harsh radiation environment, and cannot fail mechanically or contaminate the fusion plasma. Moreover, for a power plant to be economically viable, the reactor materials must withstand long operation times, with little maintenance. The fusion reactor materials will contain hydrogen and helium, due to deposition from the plasma and nuclear reactions because of energetic neutron irradiation. The first wall divertor materials, carbon and tungsten in existing and planned test reactors, will be subject to intense bombardment of low energy deuterium and helium, which erodes and modifies the surface. All reactor materials, including the structural steel, will suffer irradiation of high energy neutrons, causing displacement cascade damage. Molecular dynamics simulation is a valuable tool for studying irradiation phenomena, such as surface bombardment and the onset of primary damage due to displacement cascades. The governing mechanisms are on the atomic level, and hence not easily studied experimentally. In order to model materials, interatomic potentials are needed to describe the interaction between the atoms. In this thesis, new interatomic potentials were developed for the tungsten-carbon-hydrogen system and for iron-helium and chromium-helium. Thus, the study of previously inaccessible systems was made possible, in particular the effect of H and He on radiation damage. The potentials were based on experimental and ab initio data from the literature, as well as density-functional theory calculations performed in this work. As a model for ferritic steel, iron-chromium with 10% Cr was studied. The difference between Fe and FeCr was shown to be negligible for threshold displacement energies. The properties of small He and He-vacancy clusters in Fe and FeCr were also investigated. The clusters were found to be more mobile and dissociate more rapidly than previously assumed, and the effect of Cr was small. The primary damage formed by displacement cascades was found to be heavily influenced by the presence of He, both in FeCr and W. Many important issues with fusion reactor materials remain poorly understood, and will require a huge effort by the international community. The development of potential models for new materials and the simulations performed in this thesis reveal many interesting features, but also serve as a platform for further studies.

Radiation effects in supported nanoparticles

Nanotechnology applications are entering the market in increasing numbers, nanoparticles being among the main classes of materials used. Particles can be used, e.g., for catalysing chemical reactions, such as is done in car exhaust catalysts today. They can also modify the optical and electronic properties of materials or be used as building blocks for thin film coatings on a variety of surfaces. To develop materials for specific applications, an intricate control of the particle properties, structure, size and shape is required. All these depend on a multitude of factors from methods of synthesis and deposition to post-processing. This thesis addresses the control of nanoparticle structure by low-energy cluster beam deposition and post-synthesis ion irradiation. Cluster deposition in high vacuum offers a method for obtaining precisely controlled cluster-assembled materials with minimal contamination. Due to the clusters small size, however, the cluster-surface interaction may drastically change the cluster properties on deposition. In this thesis, the deposition process of metal and alloy clusters on metallic surfaces is modelled using molecular dynamics simulations, and the mechanisms influencing cluster structure are identified. Two mechanisms, mechanical melting upon deposition and thermally activated dislocation motion, are shown to determine whether a deposited cluster will align epitaxially with its support. The semiconductor industry has used ion irradiation as a tool to modify material properties for decades. Irradiation can be used for doping, patterning surfaces, and inducing chemical ordering in alloys, just to give a few examples. The irradiation response of nanoparticles has, however, remained an almost uncharted territory. Although irradiation effects in nanoparticles embedded inside solid matrices have been studied, almost no work has been done on supported particles. In this thesis, the response of supported nanoparticles is studied systematically for heavy and light ion irradiation. The processes leading to damage production are identified and models are developed for both types of irradiation. In recent experiments, helium irradiation has been shown to induce a phase transformation from multiply twinned to single-crystalline nanoparticles in bimetallic alloys, but the nature of the transition has remained unknown. The alloys for which the effect has been observed are CuAu and FePt. It is shown in this thesis that transient amorphization leads to the observed transition and that while CuAu and FePt do not amorphize upon irradiation in bulk or as thin films, they readily do so as nanoparticles. This is the first time such an effect is demonstrated with supported particles, not embedded in a matrix where mixing is always an issue. An understanding of the above physical processes is essential, if nanoparticles are to be used in applications in an optimal way. This thesis clarifies the mechanisms which control particle morphology, and paves way for the synthesis of nanostructured materials tailored for specific applications.

Dark solitons in holographic superfluids

We construct dark soliton solutions in a holographic model of a relativistic superfluid. We study the length scales associated with the condensate and the charge density depletion, and find that the two scales differ by a non-trivial function of the chemical potential. By adjusting the chemical potential, we study the variation of the depletion of charge density at the interface.

Inhomogeneous Structures in Holographic Superfluids I

We begin an investigation of inhomogeneous structures in holographic superfluids. As a first example, we study domain wall like defects in the 3+1 dimensional Einstein-Maxwell-Higgs theory, which was developed as a dual model for a holographic superconductor. In [1], we reported on such "dark solitons" in holographic superfluids. In this work, we present an extensive numerical study of their properties, working in the probe limit. We construct dark solitons for two possible condensing operators, and find that both of them share common features with their standard superfluid counterparts. However, both are characterized by two distinct coherence length scales (one for order parameter, one for charge condensate). We study the relative charge depletion factor and find that solitons in the two different condensates have very distinct depletion characteristics. We also study quasiparticle excitations above the holographic superfluid, and find that the scale of the excitations is comparable to the soliton coherence length scales.

Holographic Superfluids and Solitons

Superfluidity is perhaps one of the most remarkable observed macroscopic quantum effect. Superfluidity appears when a macroscopic number of particles occupies a single quantum state. Using modern experimental techniques one dark solitons) and vortices. There is a large literature on theoretical work studying the properties of such solitons using semiclassical methods. This thesis describes an alternative method for the study of superfluid solitons. The method used here is a holographic duality between a class of quantum field theories and gravitational theories. The classical limit of the gravitational system maps into a strong coupling limit of the quantum field theory. We use a holographic model of superfluidity to study solitons in these systems. One particularly appealing feature of this technique is that it allows us to take into account finite temperature effects in a large range of temperatures.