  We study the dynamics of an electron confined in a one-dimensional double
quantum dot in the presence of driving external magnetic fields. The orbital
motion of the electron is coupled to the spin dynamics by spin orbit
interaction of the Dresselhaus type. We derive an effective time-dependent
Hamiltonian model for the orbital motion of the electron and obtain a
synchronization condition between the orbital and the spin dynamics. From this
model we deduce an analytical expression for the Arnold tongue and propose an
experimental scheme for realizing the synchronization of the orbital and spin
dynamics.
