Simulating two-level quantum systems via classical orbit motion: Adiabatic cyclic evolution and Berry phase

We propose a method to simulate adiabatically driven two-level quantum systems and detect the Berry phase induced in the cyclic evolution by observing the classical orbit motion of a charged particle under a time-varying magnetic field. Analogy between the dynamics of these two species of systems is revealed and the correspondence relationship is established by virtue of their equations of motion, i.e., the von Neumman equation of the quantum binary system and the Newton-Lorentz equation of the charged particle. In particular, we show how the complex phase information of the quantum system, say, the Berry phase shift acquired by its wave function during the loop evolution, can be visually captured by examining the spatial motion of the classical particle.