Abstract
In this paper, we investigate the Berry phase and Hannay's angle of an electromagnetic mode system driven by harmonic field with Born-Oppenheimer approximation and obtain their algebraic expressions by theoretical calculation. The semiclassical relation between Berry phase and Hannay's angle is discussed. We find that besides the usual connection term, the Berry phase of BO hybrid system contains a novel term brought forth by the coupling induced effective gauge potential. This quantum modification can be viewed as an effective Aharonov-Bohm effect. Moreover, a similar phenomenon is founded in the Hannay's angle of classical BO hybrid system, which indicates that the Berry phase and Hannay's angle possess the same relation as the usual one. Besides, our theory can also be used to generate Artificial gauge potentials for neutral atoms.
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