Nonadiabatic geometric rotation of an electron spin in a quantum dot by 2π hyperbolic secant pulses

In this paper, the geometric and dynamic phase components of the overall phase induced by 2π hyperbolic secant pulses in a quantum dot are analysed. The dependence of two phase components on the ratio of the Rabi frequency to the detuning is investigated. Numerical results indicate that only for one resonant pulse the induced overall phase is purely the geometric phase. With other values of the ratio the overall phase consists of a nonzero dynamic part. The effect of spin precession to decrease the dynamic phase is characterized and discussed by analytical and numerical techniques. Utilizing the symmetry relations of the phases, a scheme to eliminate the dynamic phase by multipulse control is proposed. By choosing the proper parameter for each pulse, the dynamic phases induced by different pulses cancel out. The total pure geometric phase varies from -π to π, which realizes the arbitrary geometric rotation of spin. Average fidelity is calculated and the effects of the magnetic field and decay of the trion state are compared and discussed. The results show the crucial role of the weak magnetic field for high fidelity (above 99.3%).