A method is proposed for the optical rotation of the spin of an electron in aquantum dot using excited trion states to implement operations up to two ordersof magnitude faster than those of most existing proposals. Key ingredients arethe geometric phase induced by 2$\pi$ hyperbolic secant pulses, use ofcoherently trapped states and use of naturally dark states. Our proposal coversa wide variety of quantum dots by addressing different parameter regimes. Inone case the treatment provides an exact solution to the three-level system.Numerical simulations with typical parameters for InAs self-assembled quantumdots, including their dissipative dynamics, give fidelities of the operationsin excess of 99%.
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