We performed numerical simulations to verify a model of spontaneous collapse of the wavefunction by an infinitesimally small, non-unitary noise field. This noise field breaks time reversal and...Show moreWe performed numerical simulations to verify a model of spontaneous collapse of the wavefunction by an infinitesimally small, non-unitary noise field. This noise field breaks time reversal and translation symmetry of the Hamiltonian and depends only linearly on the wavefunction itself. We found that the probabilty of collapse from a uniform wavefunction goes to infinity in the limit of continuous space and depends on B^{2}m. Here B is the strength of the noise and m the mass of the system. Furthermore, we investigated the stability of a collapsed state and found that this depends on the shape of the noise distribution: an asymmetrical, positive distribution seems to enhance the stabilty. We finally performed analytical calculations to further understand this dependency and the role of normalisation of the wavefunction in our model.Show less
Curved crystals provide the possibility to study different vicinal surfaces in a single crystal. In this thesis, we analyzed a curved Pt (111) single crystal with kinked steps under UHV conditions...Show moreCurved crystals provide the possibility to study different vicinal surfaces in a single crystal. In this thesis, we analyzed a curved Pt (111) single crystal with kinked steps under UHV conditions using STM images to characterize the sample. We present and compare terrace width histograms of different images taken on the crystal.Show less
Majorana quasiparticles can arise at the ends of one dimensional superconducting quantum wires. As a true one-dimensional experimental realization of such a quantum wire, a carbon nanotube can be...Show moreMajorana quasiparticles can arise at the ends of one dimensional superconducting quantum wires. As a true one-dimensional experimental realization of such a quantum wire, a carbon nanotube can be employed. The one-dimensional carbon nanotube can inherit the superconducting properties by bringing it in close contact to a superconductor, such as van der Waals superconductor niobium diselenide. In this work, the design and fabrication of devices are discussed that contain a carbon nanotube connected to a few atomic layer thick niobium diselenide. Bi- or trilayers of niobium diselenide crystal flakes are obtained using mechanical exfoliation techniques in inert conditions. A stamping resolution of about 1 mm is obtained in positioning the flakes with respect to each other which is shown by Atomic Force Microscopy. Initial characterizations have shown an improvement of the conductance of more than two orders of magnitude. The stability diagrams, however, exhibit a complex behaviour which we were unable to explain in terms of a proximitized carbon nanotube. We have shown that it is possible to fabricate the complete hybrid device that is predicted to host Majorana Fermions in its non-trivial phase. This work was conducted at Regensburg University in the group of Professor Christoph Strunk.Show less
While Magnetic Resonance Force Microscopy is capable of imaging three dimensional structures on nanoscopic scales, the number of practical applications so far has been limited, partly due to the...Show moreWhile Magnetic Resonance Force Microscopy is capable of imaging three dimensional structures on nanoscopic scales, the number of practical applications so far has been limited, partly due to the complexity of the device. In this thesis we introduce the Easy MRFM, a way to increase the usability of MRFM. By seperating all MRFM components from the sample, we hope to remove some of the drawbacks of the previous Oosterkamp MRFM, allowing for easier data analysis and sample exchange. This thesis provides the theoretical calculations for the optimal set-up of the Easy MRFM and a preliminary proof of concept. Furthermore it describes a new way to analyse the measurements of the cantilever properties which would be better suited for the Easy MRFM. It also It includes the characterization of a new cantilever which could possibly be used inside the Easy MRFM to increase its sensitivity.Show less
For a phenomenological explanation of the absence of macroscopic superpositions, mass-dependent nonlinear and stochastic terms are added to the Schrödinger equation in some models of wave function...Show moreFor a phenomenological explanation of the absence of macroscopic superpositions, mass-dependent nonlinear and stochastic terms are added to the Schrödinger equation in some models of wave function collapse. This thesis describes a feasibility study of a microwave interferometer experiment with the purpose of falsifying the existence of spontaneous wave function collapse. Traveling wave parametric amplifiers in the interferometer arms effectively increase the mass of these superpositions, resulting in an interference visibility and an expected vanishing visibility in case of wave function collapse. The main question arises if the visibilities for these cases can be distinguished from each other in case of a gain of 20 dB and a (typical) insertion loss of 4 dB of the parametric amplifiers. Calculations of the interference visibilities were extended and performed by a Python program with the QuTiP module by using a Master Equation solver and Monte Carlo simulations on different computer infrastructures with up to 1.5 TB of RAM available. The limitations of the solvers were the QuTiP internals and computational time respectively. Visibilities are calculated using the Master Equation solver for gains up to 13.4 dB when neglecting losses, and for gains up to 5.3 dB and insertion losses up to 6.5 dB when including the effect of dissipation using both solvers. The differences between both visibilities appear to converge to constant values in the limit of large gain. Further calculations can be carried out on the Lisa Cluster to explore this promising observation. In addition, a cryogenic calorimeter for determining the insertion loss of an amplifier is characterized by its thermal time constants. Efforts were made to reduce the time constant attributed to a 3 dB attenuator, allowing for a precise determination of its power dissipation. On the basis of the results of this study, it can be concluded that significant steps in determining the feasibility of the proposed interferometer experiment are taken and future research is encouraged.Show less
In this thesis we describe the potential application of Si3N4 cantilevers in a Magnetic Resonance Force Microscopy (MRFM) setup. In a characterization of these cantilevers we find quality factors...Show moreIn this thesis we describe the potential application of Si3N4 cantilevers in a Magnetic Resonance Force Microscopy (MRFM) setup. In a characterization of these cantilevers we find quality factors up to 26000 at 100 mK and determine the thermal force noise SF to be 0.66 aN/√(Hz), which is competitive with currently used single crystal silicon cantilevers. With this we show that Si3N4 cantilevers are suitable replacements for the currently used MRFM cantilevers. We perform a study of the higher order resonance modes of this cantilever and compare this to a simulation of the eigenfrequencies of the cantilever. Lastly we describe a method of applying feedback with a specific phase or gain to the cantilever. We use this feedback to cool the effective temperature of the fundamental resonance mode of the cantilever from a saturation temperature of 100 mK to 28 mK. We show that this result is limited by the high detection noise in the setup and make suggestions for further improvements. This new, more convenient, feedback scheme should allow for easier implementation of feedback cooling in future MRFM experiments.Show less
