Abstract
We investigate the particle transition dynamics in two-component Bose-Einstein condensates dominated by pair-particle transitions by introducing weak periodic perturbations to the initial states. We show that the transitions can be well controlled by varying the perturbation period while maintaining the external fields and nonlinear parameters during the transition process. In particular, there exists a critical period at which the transition efficiency is approximately $100%$, with a numerical error of 0.72%. Analytic Akhmediev breather solutions and linear stability analyses show that modulation instability is the underlying mechanism for these transition dynamics. Furthermore, we establish a quantitative relation between the transition efficiency and phase shifts induced by the modulation instability. This relation can be used to measure the phase shift of the plane-wave background in well-known Akhmediev breathers.
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