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Modern cavity QED and cavity optomechanical systems realize the interaction of light with mesoscopic devices, which exhibit discrete (atom-like) energy spectra or perform micromechanical motion. In this thesis we have studied the crossover from the quantum regime to the classical limit of two prototypical models, the Dicke model and the generic optomechanical model. The physical problems considered in this approach range from a ground state phase transition, its dynamical response to general nonequilibrium dynamics including Hamiltonian and driven dissipative chaotic motion. The classical limit of these models follows from the classical limit of at least one of its subsystems. The classical equations of motion result from the respective quantum equations through the application of the semiclassical approximation, i.e., the neglect of quantum correlations. The approach of the results from quantum mechanics to the prediction of the classical equations can be obtained by subsequently decreasing the respective scaling parameter. In order to obtain exact results we have utilized advanced numerical methods, e.g., the Lanczos diagonalization method for ground state calculations, the Kernel Polynomial Method for dynamical response functions, Chebyshev recursion for time propagation, and quantum state diffusion for open system dynamics. We have studied the quantum phase transition of the Dicke model in the classical oscillator limit. Our work shows that in this limit the transition occurs already for finite spin length but with the same critical behavior as in the classical spin limit. We have derived an effective model for the oscillator degrees of freedom and have discussed the differences of both classical limits with respect to quantum fluctuations around the mean-field ground state and spin-oscillator entanglement. In this thesis we have proposed a variational ansatz for the Dicke model which extends the mean-field description through the inclusion of spin-oscillator correlations. The ansatz becomes correct in the limit of large oscillator frequency and in the limit of a large spin. For the latter it captures the leading quantum corrections to the classical limit exactly including the spin-oscillator entanglement entropy. We have studied the dynamics of spin and oscillator coherent states in the nonresonant Dicke model at weak coupling. In this regime periodic collapses and revivals of Rabi oscillations occur, which are accompanied by the buildup and decay of atom-field entanglement. The spin-oscillator wave function evolves into a superposition of multiple field coherent states that are correlated with the spin configuration. In our work we provide a description of the underlying dynamical mechanism based on perturbation theory. Our analysis shows that collapse and revival at nonresonance is distinguished from the resonant case treated within the rotating wave approximation by the appearance of two time scales instead of one. We have extended our study of the Dicke dynamics to the case of increasing spin length, as the system approaches the classical spin limit. We described the emergence of collective excitations above the ground state that converge to the coupled spin-oscillator oscillations observed in the classical limit. With increased spin length the corresponding Green functions thus reveal quantum dynamical signatures of the quantum phase transition. For the dynamics at larger coupling and energy, classical phase space drift and quantum diffusion hinders the direct comparison of quantum and classical observables. As we show in our work, signatures of classical quasiperiodic orbits can be identified in the Husimi phase-space functions of the propagated wave function and individual eigenstates with energies close to that of the quasiperiodic orbits. The analysis of the generic optomechanical system complements our study of cavity QED systems by a quantum dissipative system. In this thesis we have shown for the first time, how the route to chaos in the classical optomechanical system takes place, given as a sequence of consecutive period doubling bifurcations of self-induced cantilever oscillations. In addition to the semiclassical dynamics we have analyzed the possibility of chaotic motion in the quantum regime. Our results showed that quantum mechanics protects the optomechanical system against irregular dynamics. In sufficient distance to the semiclassical limit simple periodic orbits reappear and replace the classically chaotic motion. In this way direct observation of the dynamical properties of an optomechanical system makes it possible to pin down the crossover from quantum to classical mechanics.
The laser-matter interaction is a topic of current research. In this context, the interaction of intensive laser radiation with atomic clusters is of special interest. Du to the small cluster size, the laser field can penetrate the whole cluster volume, which leads to a high absorption of energy in the cluster. As a result, plasmas with high density and high temperature are produced. In the early phase of the laser-cluster interaction, free electrons are initially created in the cluster due to tunnel ionization or photoionization. Via collisions of these electrons with the cluster atoms, the ionization is increased and thus a dense nanoplasma is produced, which is heated by the laser. If free electrons leave the cluster during the laser-cluster interaction (outer ionization), a positive charge buildup is created. The associated charge repulsion finally can lead to the fragmentation of the cluster due to Coulomb explosion. Experimentally, interesting phenomena emerging from laser-excited clusters are observed, e.g., the creation of fast electrons, the production of highly charged ions, and X-ray emission. In this dissertation, the interaction of Gaussian laser pulses in the infrared regime with argon and xenon clusters is simulated by means of a nanoplasma model. Considering laser intensities in the non-relativistic regime, the relevant processes such as ionization, heating and expansion are theoretically described in this model with a set of coupled rate equations and hydrodynamic equations. One focus of the thesis is on the heating of the nanoplasma via inverse bremsstrahlung (IB), which is due to the absorption of laser photons in electron-ion collisions. In particular, the important question is investigated whether the consideration of the ionic structure – that means, the nuclear charge and the bound electrons – modifies the electron-ion collisions and thus the IB heating rate. Starting from a quantum statistical description, effective electron-ion potentials are used which account for both the screening due to the dense plasma and the inner ionic structure. Within the quantum mechanical first Born approximation, the consideration of the ionic structure leads to a drastic increase of the IB heating rate, in particular for high nuclear charges and low ionic charge states. However, for the parameters relevant in experiments, the applicability of the first Born approximation is questionable. Therefore, quantum mechanical calculations going beyond the first-order perturbation theory are performed. In addition, the IB heating rate is investigated with different classical methods. These are based either on transport cross sections for elastic electron-ion scattering or on classical simulations of inelastic scattering processes. Also within the classical approaches, the consideration of the ionic structure leads to an increase of the heating rate. However, this increase is shown to be only moderate. In a further part, the thesis focuses on the question how the dynamics of the laser-cluster interaction is influenced by the consideration of excited states. This is explored exemplarily for argon clusters excited by single or double laser pulses. The consideration of excitation processes in the nanoplasma leads to a decrease of the electron temperature and to an increase of the density of free electrons. Moreover, it is shown that the consideration of excitation processes results in an essential acceleration of the ionization dynamics. As a consequence, the mean ionic charge state in the plasma as well as the number of highly charged ions is significantly increased. For the population of ground states and excited states within an ionic charge state Z, collisional deexcitation processes play an important role. By means of an analytical relation between excitation and deexcitation cross sections, the rates for the respective processes in the presence of the laser field are calculated. The role of deexcitation processes is studied in detail, showing that the inclusion of these processes is essential for the correct theoretical description of the photon emission from laser-excited clusters. Based on these results, the photon yield is calculated for selected radiative transitions resulting from highly charged argon ions in the UV and X-ray regime.
Energetic ions are made to collide with atmospheric molecules. Positively charged ions of argon (Ar^+), helium (He^+), hydrogen (H_2^+ ), and protons (H^+) with energies of 50 keV to 350 keV are used as the bombarding ion. The ion beam of desired energy is produced using a linear ion accelerator at the University of Greifswald. The mass and energy distribution of sputtered particles were analysed using an Electrostatic Quadrupole SIMS (EQS) analyser. The target gases used are oxygen (O_2), sulfur hexafluoride (SF_6), and nitrogen (N_2). The ionized and fragmented particles due to collisions have been investigated. We have discovered a new process for negative ion formation in energetic ion collision with O_2 and SF_6 molecules. The process is a two body reaction between the projectile and the molecule without the need for a third particle (such as an external electron). It requires a direct charge transfer from the projectile to the molecule leaving it intact as O_2^- or SF_6^- . The process is experimentally confirmed by using a proton as projectile which does not have an electron to transfer. In comparison with positive ion fractions (O_2^+ , SF_5^+ ), the negative ions fraction is smaller by 2 orders of magnitude. This shows that the two body charge exchange process is weak due to the larger energy transfer required compared to the positive ion forming mechanisms. The two body charge exchange mechanism is not observed for ion collisions with N_2 molecule. No stable negative ion exist for N_2 molecule. The collision cross section for the ion formation during energetic ion – O_2 collision has been determined within the investigated impact energy. For SF_6 molecule the partial ion fraction of the secondary ions are determined for different projectiles involved. This kind of investigation is of great importance mainly in atmospheric physics. Energetic ions are constantly emitted from mass of the energy sources in the universe (e.g. sun). They interact with planetary objects or atmosphere on their way. A deep knowledge about the interaction processes is necessary to understand the ionospheric physics and space exploration. As second part of my thesis, a GaAs(100) surface is bombarded with 150 keV Ar^+ ion beam. From etching the surface to thin film coating, ion bombardment on solid surface found great role in the fabrication process of modern electronic and optical devices. In order to increase the knowledge on sputtering materials and because of profound importance in modern electronics, we choose GaAs(100) as our target. Among the sputtered atoms and ions, small sized cluster ions having more than 6 atoms have been identified. GaAs is a heteroatomic semiconductor containing gallium and arsenic in equal ratio. A preferential phenomenon of ’abundant sputtering’ of gallium compared to little arsenic (GaAs) has been investigated from their mass intensity. The experimental ion counts are compared with theoretically predicted relative abundance. This phenomenon of preferential sputtering is known for atomic species of sputtered GaAs but not for the sputtered cluster ions. The main reasons for this abundant sputtering of one element is attributed to the difference in ion formation energies and surface compositional change taking place during the sputtering process. Another notable characteristics is the preference in charge state among the sputtered ions. For instance, among sputtered atomic ions the ion counts of Ga^+ is 3 orders larger than As^+ ion and As^- is 2 orders larger than Ga^- ion. To get a clue for this behavior, we have investigated the energy distribution of both negatively and positively charged clusters. Different ion formation mechanisms were discussed. The energy distribution of atomic ion is partially explained by using a modified theory given by M. W. Thompson.
During the past decade, various physical properties of the Yukawa ball, like structure and energy states, were unraveled using experiments. However, the dynamical features served further attention. Therefore, the main aim of my thesis was to investigate and understand how a finite system-represented by Yukawa clusters-evolves from a solid, crystalline structure to a liquid-like system, how it behaves in this phase and in what manner the reordering back into the solid state can be described. As a method of choice to reach this goal, laser heating has been proven successful. Moreover, the special importance of wakefields for dust clusters confined at low neutral gas pressure was addressed. Melting of finite dust clouds can be induced in two ways, either by altering the properties of the ambient plasma or by laser heating. The latter was shown to be a generic melting scenario, allowing to estimate a critical coupling parameter at the melting point. Moreover, the melting transition of finite 3D dust systems was found to be a two-step process where angular order is lost before the radial order starts to diminish at higher energies. Next, the mode dynamics of finite 3D dust ensembles in the solid and the liquid phase was studied. Crystal and fluid modes revealed the main spectral properties of the system. The normal modes are mainly suited to describe crystalline states. Fluid modes were excited naturally and via laser heating, with excitation frequencies almost independent of the coupling parameter in the solid and the liquid-like regime. Tuning the plasma parameters can be used to vary the particle-particle interaction via the ion focus. Both methods, even though assuming equilibrium situations, allowed to hint at these wakefields. The corresponding peaks in the fluid and normal mode spectra were no eigenmodes, confirming the nonequilibrium character of the ion focusing effect. First steps to extend the normal mode theory to achieve the dynamics of wake-affected nonequilibrium dust clusters were presented. Statistical quantities were obtained evaluating long-run experiments and transport coeffcients for finite dust systems were calculated via the instantaneous normal mode technique. Diffusion was found considerably higher for 3D than for 2D dust clusters. Using the configurational entropy, we have shown that in 2D and 3D disorder increases with increasing size of the system, in agreement with simulations. The temperature dependence of the configurational entropy differs for 2D and 3D dust clouds, with a threshold behavior found for finite 2D ensembles only. Finally, using instantaneous normal modes to reveal the total fraction of unstable modes, the predictive connection of Keyes (Phys Rev E 62, p7905, 2000), between transport and disorder was tested and verified for 2D, but not for 3D clusters. The reason for this has to be left open. Finally, laser-mediated recrystallization processes of finite 3D dust clouds were investigated. First, the temporal evolution of the Coulomb coupling parameter was traced during heating and recrystallization. A cooling rate has been determined from the initial phase of recrystallization. This cooling rate is lower than damping by the neutral gas, in agreement with simulations. We have observed a large fraction of metastable states for the final cluster configurations. Further, we have revealed that the time scale for the correlation buildup in the finite 3D ensemble was on even slower scales than cooling. Thus, different time scales can be attributed to the fast emergence of the shells and to the slower individual ordering within the shells.
The extraction of raw materials in mining, as for example copper, generally requires a separation of the natural resources quarried. In most cases complex ores, mixtures of different minerals and gangue have to be separated in order to enable an economic processing. In particular for the extraction of sulfides, oxides, carbonates, phosphates, but also of coal, froth flotation is mainly used for this purpose, therefore it is considered as the most important separation process in raw material industries. Several billion tons of ores are processed annually. The principle of flotation is based on the surface properties of the mixtures components and the separation efficiency, which decisively determines the required amount of water and various chemicals, if nothing else, is an important criterion in mineral exploration and it also significantly influences the environmental impact of mineral processing. The aim of, this work was to investigate the influence, of, low-temperature plasmas on the mineral surface and, based on the acquired knowledge, to develop and verify strategies that would increase the efficiency of flotation processes through plasma pre-treatment of mineral mixtures. Since these studies are unprecedented, the results presented can be classified as a contribution to application-oriented basic research. Powder of the sulfide minerals, pyrite (FeS2), chalcopyrite (CuFeS2), chalcocite (Cu2S) and molybdenum sulfide (MoS2), were treated with plasmas of a radiofrequency and a microwave discharge and the resulting surface modifications were investigated by structure analysis such as X-ray photoelectron spectroscopy (XPS) and X-ray diffraction (XRD). During the plasma process, the argon/oxygen and argon/hydrogen process gas mixtures used were analyzed by mass spectrometry (MS), taking into account the quantity of gaseous reaction products released, in order to estimate the rate at which chemical reactions occur. Furthermore, Langmuir and thermal probes, as well as different methods of optical emission spectrometry (OES) were utilized, which enabled a characterization of the discharges used with regard to different plasma parameters. It has been shown that sulfur dioxide (SO2) in Ar/O2 plasmas and hydrogen sulfide (H2S) in Ar/H2 plasmas are the only reaction products which can be detected by MS during the mineral treatments. Thus, the resulting sulfur rate loss could be time-resolved determined by means of additional calibrations with calibrating gases. Especially at Ar/O2-MW plasma treatments two fundamental mechanisms of mineral modification could be separated by time. Pure plasma-surface interactions at the beginning and, additionally, thermally induced reactions in during the evolution of the treatments. Comparisons regarding the relative sulfur loss during plasma-surface interactions between the investigated minerals have shown a strong influence of the process parameters whereas, under identical conditions, CuFeS2 reacted up to eight and nineteen times faster reacted than FeS2 or Cu2S. This result represents the basis of the strategy to optimize the flotation of the minerals investigated: The selective generation of oxides on the surface of one component in a mixture of sulphide minerals. In particular, at the separation of CuFeS2/FeS2 mixtures by using the oxide collectors Flotinor Fs-2 in a micro flotation cell, a high selectivity could be achieved. The recovery of CuFeS2 amounted to 100 % while less than 10 % of FeS2 was recovered and no other modifying reagents were used. XPS and XRD analyses indicate the possibility that metal oxide are created upon the CuFeS2 surface, while the formation of iron sulfates upon the FeS2 surface prevented the oxide collector adsorption. An increased intensity of the plasma treatment leads to an increased sulphate formation also on CuFeS2, whereas the recovery, and thus the selectivity of the flotation, was reduced again. It could be shown that this effect can be utilized for the separation of, CuFeS2/MoS2 mixtures by using both, oxide and sulfide collectors, because sulfates are not formed on molybdenum sulfide during Ar/O2 plasmas treatments. By means of the plasma diagnostics used the energy input onto the substrate, the gas temperature and the degree of dissociation of molecular gases were estimated and correlations regarding the surface modification have been worked out. Thereby, the region investigated within the parameter space could be enlarged due to the use of different excitation frequencies, 13.56 MHz and 2.45 GHz, and additional insights have been provided. Further studies, beyond the scope of this work, are, nevertheless, required in order to generate a more comprehensive picture of plasma-mineral interactions and to enable an optimal application of the obtained results.
In this thesis we have revisited the formation of the excitonic insulator (EI), which realizes an exciton condensate. In contrast to optically created exciton condensates, the EI forms in thermal equilibrium and is solely driven by the Coulomb attraction between electrons and holes. The EI phase is anticipated to occur near the semimetal-semiconductor (SM-SC) transition at low temperatures. Depending from which side the EI is approached, it forms due to a BCS-type condensation of electron-hole pairs or a Bose-Einstein condensation (BEC) of excitons. The extended Falicov-Kimball model (EFKM) is the minimal model the EI can be described with. This model describes spinless fermions in two dispersive bands (f band and c band), that interact via a local Coulomb repulsion. The EFKM is also used to describe electronic ferroelectricity (EFE). Both phases, the EI and EFE-type ordering, are characterized by a spontaneous f-c hybridization in the EFKM. We have presented the EI phase, the EFE phase, and the orderings they compete with. Moreover, we have determined the ground-state phase diagram of the EFKM. We have focused particularly on the anticipated BCS-BEC crossover within the EI and have analyzed the formation scenarios. The exciton spectrum and the exciton density in the normal phase close to the critical temperature give information about relevant particles and therefore the nature of the transition. We have demonstrated that the whole EI is surrounded by a halo", that is, a phase composed of electrons, holes and excitons. However, on the SM side, only excitons with a finite momentum exist. These excitons appear only in a small number and barely influence the SM-EI transition. This phase transition is driven by critical electron-hole fluctuations, generated by electrons and holes at the Fermi surface. On the SC side, excitons with arbitrary momenta exist. Most notably, we have found the number of zero-momentum excitons to diverge at the SC-EI transition, signaling the BEC of these particles. Within the EI phase, there is a smooth crossover from the BCS regime to the BEC regime. One of the promising candidates to observe the EI experimentally, is the transition-metal dichalcogenide 1T-TiSe2. Strong evidences were found favoring an EI scenario of the charge-density-wave (CDW) formation in this material. However, some aspects point to a lattice instability to drive the CDW transition. We have addressed this issue by analyzing the recently discovered chiral property of the CDW in 1T-TiSe2. We have found that the EI scenario is insufficient to explain a stable, long range chiral charge ordering. Lattice degrees of freedom must be taken into account. In particular, nonlinear electron-phonon coupling and phonon-phonon interaction are crucial. By estimating appropriate model parameters for 1T-TiSe2, we have suggested a combination of excitonic and lattice instability to drive the CDW transition in this material. Experiments in 1T-TiSe2 and other materials suggest that the coupling to the lattice is non-negligible. We have extended therefore the model by an explicit exciton-phonon interaction, and have analyzed crucial effects of this interaction. While the single-particle spectrum is not modified qualitatively, the electron-hole pair spectrum changes significantly. The inclusion of the phonons lead to a massive collective mode in the ordered ground state in contrast to the case for vanishing exciton-phonon coupling, where the mode is acoustic. We have suggested that a gapless collective mode leads to off-diagonal long range order. This questions that the ground state for finite exciton-phonon coupling represents a condensate.