Current in Hubbard rings manipulated via magnetic flux

摘要

We study currents in a quantum ring threaded by a magnetic flux which is varied in an arbitrary way from an initial constant value φ _1 at time t_1 to a final constant value φ _2 at time t _2. We analyze how the induced currents for t > t_2 can be controlled by the rate of flux variation φ=(φ_2- φ_1)/(t_2-t_1). The dynamics of electrons in the ring is described using the Hubbard and the extended Hubbard models. In the Hubbard model with infinite on-site repulsion the current for t > t _2 is shown to be independent of the flux variation before t _2 and is fully determined by a solution of the initial equilibrium problem and by the value φ _2 of the flux. For intermediate values of the interaction strength the current displays regular or irregular time oscillations and the amplitude of oscillations is sensitive to the rate of the flux changing φ_2: slow changes of the flux result in small amplitudes of the current oscillations and vice versa. We demonstrate that the time dependence of the induced current bears information on electronic correlations. Our results have important implications for not only mesoscopic rings but also the designing of quantum motors built out of ring-shaped optical lattices.