Optimal laser control of double quantum dots

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Coherent single-electron control in a realistic semiconductor double quantum dot is studied theoretically. Using optimal-control theory we show that the energy spectrum of a two-dimensional double quantum dot has a fully controllable transition line. We find that optimized picosecond laser pulses generate population transfer at significantly higher fidelities (> 0.99) than conventional sinusoidal pulses. Finally we design a robust and fast charge switch driven by optimal pulses that are within reach of terahertz laser technology. Double quantum dots (DQDs), i.e., coupled twodimensional (2D) electron traps, have been under recent and extensive studies both experimentally 1,2,3 and theoretically. 4,7,8 The main interest in DQDs arises from their potential for solid-state quantum computation that could be achieved in principle by rapidly switching voltages of electrostatic gates. The gates permit to tune at will the system geometry and hence the electronic properties of DQDs. Coherent manipulation of a single charge 2 and coupled spins 1 has already been achieved, and recently a coherence time of ∼ 200 ns was obtained for a well isolated silicon DQD. 3 Theoretical studies on single-electron transport inside the DQD driven by linear switches and linearly polarized continuous waves (CWs) were reported very recently. 4 In the latter case the transport is rather sensitive to possible anharmonicity of the potential and limited to uncoupled dots far apart from each other. Electron control in DQDs has been studied also using genetic algorithms 5 as well as rotating-wave and resonant approximations leading to a reduction to a threelevel system. 6 To the best of our knowledge, however, a general N-level control scheme by using direct external electric fields has not been introduced for 2D-DQDs until now. In this paper we discuss the controllability criteria for single-electron states of DQDs by means of external laser pulses. We show that at certain interdot distances some of the single-electron states allow full population transfer from the ground state to those states. We apply quantum optimal-control theory (OCT) 9 which yields the optimal laser pulses for predefined transitions. We obtain high occupations (& 99%) of the target states in a realistic DQD in a few picoseconds, which is well in the coherent regime. If the initial and final states are chosen to have full localization of the electron in one or the other dot, this scheme enables rapid and controlled transport which is not sensitive to the interdot distance or to the inevitable anharmonicities in the confining potential.