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

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

2002-10-26

arxiv.org/abs/quant-ph/0210182v1

Physics

Quantum Physics

15pages,6figures

Scientific paper

10.1088/0305-4470/36/44/010

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 $\pi$-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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