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arXiv:1510.04502 · Physical review. B./Physical review. B

Shaped electric fields for fast optimal manipulation of electron spin and position in a double quantum dot

J. A. Budagosky, D. V. Khomitsky, Eugene Ya. Sherman, Alberto Castro

Published Jan 14, 2016• 5 citations
arXivHTMLPDF

Abstract

We use quantum optimal control theory algorithms to design external electric fields that drive the coupled spin and orbital dynamics of an electron in a double quantum dot, subject to the spin-orbit coupling and Zeeman magnetic fields. We obtain time profiles of multifrequency electric field pulses which increase the rate of spin-flip transitions by several orders of magnitude in comparison with monochromatic fields, where the spin Rabi oscillations were predicted to be very slow. This precise (with fidelity higher than $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$) and fast (at the time scale of the order of 0.1 ns, comparable with the Zeeman spin rotation and the interdot tunneling time) simultaneous control of the spin and position is achieved while keeping the electron in the four lowest tunneling- and Zeeman-split levels through the duration of the pulse. The proposed algorithms suggest effective applications in spintronics and quantum information devices.

DOI
10.1103/physrevb.93.035423

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The techniques of shortcuts to adiabaticity have been proposed to accelerate the "slow" adiabatic processes in various quantum systems with the applications in quantum information processing. In this paper, we study the counter-diabatic driving for fast adiabatic spin manipulation in a two-electron double quantum dot by designing time-dependent electric fields in the presence of spin-orbit coupling. To simplify implementation and find an alternative shortcut, we further transform the Hamiltonian in term of Lie algebra, which allows one to use a single Cartesian component of electric fields. In addition, the relation between energy and time is quantified to show the lower bound for the operation time when the maximum amplitude of electric fields is given. Finally, the fidelity is discussed with respect to noise and systematic errors, which demonstrates that the decoherence effect induced by stochastic environment can be avoided in speeded-up adiabatic control.
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We apply the transitionless quantum driving method to control the electron spin of a two-electron double quantum dot with spin-orbit coupling by time-dependent electric fields. The xxx and yyy components of applied electric fields in each dot are designed to achieve fast adiabatic-like passage in the nanosecond timescale. To simplify the setup, we can further transform Hamiltonian by z axis to design an alternative speed-up adiabatic passage, without using the applied electric field in yyy direction.
Abstract A protocol for controlling the localization of an electron with a fixed projection of spin between two quantum dots in a material with spin-orbit (SO) interaction is studied. Due to SO coupling, the manipulation of the electron shuttling between both quantum dots also leads to a mixing between spin projections near to the avoided crossing of levels. We use a transitionless quantum driving approach, neglecting SO interaction, to analytically design simple electric and magnetic pulses able to rapidly drive the electron along an adiabatic Landau–Zener manifold. We show that the same fields in the presence of SO interaction can also give a fast high-fidelity transition between the qubit states. The performance of the proposed protocol is assessed in the presence of SO interactions of typical semiconductor materials. It is shown that it provides a fast and efficient spin-conserving method for controlling the electron position in a double quantum dot.
We consider joint effects of tunneling and spin-orbit coupling on driven by electric field spin dynamics in a double quantum dot with a multilevel resonance scenario. We demonstrate that tunneling plays the crucial role in the formation of the Rabi-like spin-flip transitions. In contrast to the linear behavior for weak electric fields, the spin-flip rate becomes much smaller than expected for the two-level model and shows oscillating dependence on the driving field amplitude in stronger fields. In addition, the full spin flip is very difficult to achieve in a multilevel resonant system. These two effects have a similarity with the Zeno effect of slowing down the dynamics of an observable by its measurement. As a result, spin manipulation by electric field becomes much less efficient than expected.