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The quantum mechanical geometric phase of a particle in a resonant vibrating cavity

K. W. Yuen·H. T. Fung·K. M. Cheng·M. -C. Chu·K. Colanero
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Abstract

We study the general-setting quantum geometric phase acquired by a particle in a vibrating cavity. Solving the two-level theory with the rotating-wave approximation and the SU(2) method, we obtain analytic formulae that give excellent descriptions of the geometric phase, energy, and wavefunction of the resonating system. In particular, we observe a sudden $π$-jump in the geometric phase when the system is in resonance. We found similar behaviors in the geometric phase of a spin-1/2 particle in a rotating magnetic field, for which we developed a geometrical model to help visualize its evolution.

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K. W. Yuen, H. T. Fung, K. M. Cheng, M. -C. Chu, K. Colanero. 2002-10-26. The quantum mechanical geometric phase of a particle in a resonant vibrating cavity. https://doi.org/10.1088/0305-4470/36/44/010

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