Dokument

Summary:
In this work, open microwave resonators have been investigated as a model system of a quantum dot. Since quantum dots are micrometer-sized, measurements in quantum dots are still very difficult except for transport measurement, but relatively simple in a microwave resonator. We fabricated a flat resonator and a resonator with soft-wall potential so that the shape corresponded to a quantum dot which has been investigated in the laboratory of J.P. Bird. For a flat resonator, i.e. a resonator with a hard-wall potential, periodically occurring scarred wave function families are analyzed, and the associated orbits are identified. For complicated wave function families, we use a Fourier spectroscopy. Influence of an absorber center is investigated using Fourier transform of transmission between the input and output leads. The Fourier map is analyzed to identify scar families. The calculated orbits lengths and the experimentally obtained values show very good agreement. By varying the height of the resonator, potentials can be simulated, using the correspondence between quantum mechanics and electrodynamics. Using this relation, a resonator with soft-wall potential was fabricated. The shape of the potential corresponds to the above mentioned quantum dot. The measured eigenfrequencies for the periodic bouncing-ball scar families agree very well with the theoretical values from a WKB approximation . The wave function family of an X-like cross bouncing ball is used to obtain evidence of dynamical tunneling. By phase difference analysis and transport behavior, the presence of dynamical tunneling is proven. In the last part of this work, the statistical properties of the wave functions of an asymmetric open flat resonator are discussed. Opening to the outside world of billiard makes the wave function complex, since there is transport. This cross-over regime, from real to imaginary of wave functions is investigated opening of the billiard by frequency increasing. The phase rigidity distribution which give the ratio between the real and imaginary parts of the wave function, the long-range correlation of intensity and the current density are compared with the theoretical values calculated from the random superposition of plane waves theory. For all investigated quantities, a very good agreement between experiment and theory is found.

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