| Summary: | 博士 === 國立交通大學 === 電子物理系所 === 103 === Coherent state is of significance for exploring the boundary between the microscopic (quantum; wave) and macroscopic (classical; ray) worlds. In mesoscopic quantum systems, experimental and theoretical studies have verified that the coherent superposition of degenerate or nearly degenerate quantum states can result in wave functions localized on classical periodic orbits. Numerous modern laser systems have been developed as analogous systems to visualize various quantum phenomena.
In this thesis several optical experiments provide fresh insights for the ray-wave duality by use of Nd-doped YVO4 laser with the off-axis pumping scheme. We originally exploit the inhomogeneous Helmholtz equation to perform a theoretical analysis for manifesting the influence of the fractional degeneracy and the pump distribution on the resonant lasing mode. We also explore thorough laser experiments that clearly reveal the relationship between the effect of fractional degeneracy and the emergence of the ray-wave duality. It has been found that the lasing modes have a preference to be localized on the periodic ray trajectories when the cavity lengths are close to the degenerate cavities. When the astigmatism is involved with the coherent superposition, we also observe the tiny symmetry breaking not only induces fine level degeneracy but also leads to nonplanar periodic orbits of three-dimensional coherent waves. Furthermore, experimental results also indicate that the structurally stable mode-locking effects generated from the coherent waves associated with periodic orbits.
In addition to laser resonators, the optical-mechanical analogy has been verified that the free-time evolution of quantum waves exhibits to be mathematically similar to the free-space propagation of the coherent light. We analyze the formation of two-dimensional quasicrystalline patterns from the quantum diffraction of matter waves, and exploit an optical diffraction experiment to analogously demonstrate the time evolution and recurrence of quasicrystalline patterns in the quantum dynamics.
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