Field-driven geometrical phases in a time-periodic quantum system

We apply Floquet theory to explore the geometry of the Hilbert space under the influence of a time-periodic field. The geometrical phase is found to be induced by field-driven hybridizations when the photon energy of the driving field is close to the transition energies of the states of a quantum system. The phases of two hybridized states are phase locked to each other. We show that the geometrical phase is in general related to the Rabi frequency of the hybrid states. We also show that when the photon energy is equal to the transition energy of two states the geometrical phase acquired by each state is given exactly by an integer multiple of pi, independent of the strength of the driving field. We illustrate the derived generic properties of the geometric phase with an experimentally realizable quantum-wire system. It is shown that the interference between conductance channels in the wire presents a way to identify the geometrical phase.