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The dynamical characters owned by inner and external states of a Bose-Einstein condensate are generally different and independent, and thereby requires experimentally distinct manipulation techniques. The recently realized spin-orbit coupling in Bose-Einstein condensates essentially connects spin and motional degrees of freedom, which endows spin states with ability to respond to orbit operations and vice versa. In this paper, a dynamical response effect, triggered by simultaneously manipulating the inner and external states of a spin-orbit-coupled Bose-Einstein condensate, is predicted. Here, the “simultaneously manipulation of the inner and external states” means that the driving fields incorporate both the Zeeman field, which imposed on the atomic inner states, and the orbit potential, which influences the external states of atoms. Specifically, the Bose-Einstein condensate is assumed to be activated by an abruptly applied Zeeman field and a sudden shake of the trapping potential. After some reasonable simplification and approximation of the model (i.e., neglecting the inter-atomic interactions and modelling the shake of the trapping potential by a short time-dependent pulse), an analytical relation bridging the spin frequency spectrum and the parameters of the driving fields, is derived. The numerical calculations based on directly integrating the Gross-Pitaevskii equation are in great agreement with the analytical relation. The physical origin of the predicted spin dynamical response can be traced back to the quantum interference among different spin-orbit states. As a series of characteristic parameters of the condensate can be manifested in the spin frequency spectrum, the dynamical response effect predicted here offers a candidate method to determine and calibrate various system parameters by measuring the spin frequency spectrum.
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