Abstract
We investigate an explicitly time-dependent quantum system driven by a secant-pulse external field. By solving the Schr\"{o}dinger equation exactly, we elucidate exotic properties of the system with respect to its dynamical evolution: on the one hand, the system is shown to be essentially nonadiabatic, which prohibits an adiabatic approximation for its dynamics; on the other hand, the loop evolution of the model can induce a geometric phase which, analogous to the Berry phase of the cyclic adiabatic evolution, is in direct proportion to the solid angle subtended by the path of the state vector. Moreover, we extend the model and show that the described properties coincide in a special family of secant-pulse-driven models.