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International Journal of Theoretical Physics

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

Zhao-Xian Yu, Zhi-Yong Jiao

Published Jan 29, 2010• 0 citations
Publisher
DOI
10.1007/s10773-010-0258-9

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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.
The algebriaic dynamics is applied to investigate the geometric phase of a Heisenberg-chain in a rotating magnetic field.It is a su(2) algebraically symmetric 3-spin12 system with partially anisotropic coupling.The exact analytical solution of the time dependent Schrdinger equation and the geometric phases of this system are obtained in terms of gauge transformation and algebriaic dynamics.The partially anisotropic coupling is then extended to a more general coupling and the adiabatic geometric phases of the extended system are calculated.We find that the coupling strengths have no impact on the adiabatic geometric phases of the system.