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arXiv:1203.5287 · Physical Review B

Spin dynamics in a strongly driven system: Very slow Rabi oscillations

D. V. Khomitsky, L. V. Gulyaev, Eugene Ya. Sherman

Published Mar 23, 2012• 75 citations
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Abstract

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.

DOI
10.1103/physrevb.85.125312

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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.
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.
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The spin dynamics in two electron double quantum dots embedded in a two-dimensional electron gas at the interface between SrTiO3{\mathrm{Sr}\mathrm{Ti}\mathrm{O}}_{3}SrTiO3​ and LaAlO3{\mathrm{La}\mathrm{Al}\mathrm{O}}_{3}LaAlO3​ is studied by an exact numerical solution of the time-dependent Schr\"odinger equation in the context of the electric-dipole-spin-resonance experiment. On the basis of the three-band model of 3d3d3d electrons localized at Ti\mathrm{Ti}Ti ions on the square lattice, we analyze in detail the singlet-triplet transition induced by the ac electric field, in the magnetic field range close to the avoided crossing that appears as a result of the spin-orbit coupling. For symmetric double quantum dots the single-photon spin-flip transition is prohibited due to the parity symmetry, and the transition can occur only by the higher-order two-photon processes. For a weakly asymmetric system, when the first-order singlet-triplet transitions are released due to the parity symmetry breaking, the spin-flip transition has a character of the Rabi oscillations for a low electric field amplitude. As the amplitude is increased, the frequency of the transition is blueshifted (redshifted) for the magnetic field below (above) the single-triplet avoided crossing. For a sufficiently high magnetic field and high ac-field amplitude, the electric field drives the system across the avoided crossing, inducing the spin flip by the Landau-Zener-Stueckelberg-Majorana effect. Finally, the optimization of the geometrical parameters of the system with respect to the time of spin flip of its fidelity is also presented.
We analyze the charge and spin dynamics in a DC biased double quantum dot driven by crossed DC and AC magnetic fields. In this configuration, spatial delocalization due to inter-dot tunnel competes with intra-dot spin rotations induced by the time dependent magnetic field, giving rise to a complicated time dependent behavior of the tunnelling current. When the Zeeman splitting has the same value in both dots and spin flip is negligible, the electrons remain in the triplet subspace (dark subspace) performing coherent spin rotations and the current does not flow. This electronic trapping is removed either by finite spin relaxation or when the Zeeman splitting is different in each quantum dot. In the first case, our results show that measuring the current will allow to get information on the spin relaxation time. In the last case, we will show that applying a resonant bichromatic magnetic field, the electrons become trapped in a coherent superposition of states and electronic transport is blocked. Then, manipulating AC magnetic fields, electrons are driven to perform coherent spin rotations which can be unambiguously detected by direct measurement of the tunneling current.
In the framework of the nonsecular perturbation theory based on the Bogoliubov averaging method, the coherent dynamics of multiphoton Raman transitions in a two-level spin system driven by an amplitude-modulated microwave field is studied. Closed-form expressions for the Rabi frequencies of these transitions are obtained beyond the rotating-wave approximation for the low-frequency driving component. It is shown that spin states dressed by the high-frequency component of the driving field are shifted due to the Bloch-Siegert-like effect caused by antiresonant interactions with the strong low-frequency driving. We predict that with increasing the order of the Raman transition, the Rabi frequency decreases and the contribution of the Bloch-Siegert shift to this frequency becomes dominant. It is found that the amplitude and phase of the Rabi oscillations strongly depend on the initial phase of the low-frequency field as well as on detuning from multiphoton resonance. The recent experimental data for the second- and third-order Raman transitions observed for the nitrogen-vacancy center in diamond (Z. Shu et al., arXiv:1804.10492) are well described in the frame of our approach. Our results may provide new possibilities for coherent control of quantum systems.