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International Journal of Theoretical Physics

Geometric Phase of Quantum Dots in the Time-Dependent Isotropic Magnetic Field

Zhao-Xian Yu, Zhi-Yong Jiao

Published Jan 12, 2010• 6 citations
Publisher
DOI
10.1007/s10773-010-0245-1

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We demonstrate optical control of the geometric phase acquired by one of the spin states of an electron confined in a charge-tunable InAs quantum dot via cyclic 2pi excitations of an optical transition in the dot. In the presence of a constant in-plane magnetic field, these optically induced geometric phases result in the effective rotation of the spin about the magnetic field axis and manifest as phase shifts in the spin quantum beat signal generated by two time-delayed circularly polarized optical pulses. The geometric phases generated in this manner more generally perform the role of a spin phase gate, proving potentially useful for quantum information applications.
In this paper, the geometric and dynamic phase components of overall phase induced by 2π hyperbolic secant pulses in a quantum dot is analyzed. 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 magnetic field and decay of the trion state are compared and discussed. The results show the crucial role of weak magnetic field for high fidelity (above 99.3%).