We calculate the first-order energy shifts for the N-dimensional hydrogen atom exposed to a static electric field. The results are compared with numerical diagonalization of the Hamiltonian in a finite basis. Using simple scaling relations, we show how corrections to arbitrarily high order may be obtained from known results for the three-dimensional Coulomb problem.
The dynamics of two electrons in a 2-dimensional quantum dot molecule in the presence of a time-dependent electromagnetic field is calculated from first principles. We show that carefully selected microwave pulses can exclusively populate a single state of the first excitation band and that the transition time can be further decreased by optimal pulse control. Finally we demonstrate that an oscillating charge localized state may be created by multiple transitions using a sequence of pulses.
We investigate optimal control strategies for state to state transitions in a model of a quantum dot molecule containing two active strongly interacting electrons. The Schrödinger equation is solved nonperturbatively in conjunction with several quantum control strategies. This results in optimized electric pulses in the terahertz regime which can populate combinations of states with very short transition times. The speed-up compared to intuitively constructed pulses is an order of magnitude. We furthermore make use of optimized pulse control in the simulation of an experimental preparation of the molecular quantum dot system. It is shown that exclusive population of certain excited states leads to a complete suppression of spin dephasing, as was indicated in Nepstad et al (2008 Phys. Rev. B 77 125315).
We derive an accurate molecular orbital based expression for the coherent time evolution of a two-electron wave function in a quantum dot molecule where the electrons interact with each other, with external timedependent electromagnetic fields and with a surrounding nuclear spin reservoir. The theory allows for direct numerical modeling of the decoherence in quantum dots due to hyperfine interactions. Calculations result in good agreement with recent singlet-triplet dephasing experiments by Laird et al. ͓Phys. Rev. Lett. 97, 056801 ͑2006͔͒, as well as analytical model calculations. Furthermore, it is shown that using a much faster electric switch than applied in these experiments will transfer the initial state to excited states where the hyperfine singlet-triplet mixing is negligible.
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