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arXiv:1803.04677 · Physical review. B./Physical review. B

Fast electron spin flips via strong subcycle electric excitation

Máté Tibor Veszeli, András Pályi

Published Jun 21, 2018• 5 citations
arXivHTMLPDF

Abstract

An important goal in quantum information processing is to reduce the duration of quantum-logical operations. Motivated by this, we provide a theoretical analysis of electrically induced fast dynamics of a single-electron spin-orbit qubit. We study the example of a one-dimensional quantum dot with Rashba spin-orbit interaction and harmonic driving, and focus on the case of strong driving, when the real-space oscillation amplitude of the driven electron is comparable to the width of its wave function. We provide simple approximate analytical relations between the qubit Larmor frequency, the shortest achievable qubit-flip time, and the driving amplitude required for the shortest achievable qubit flip. We find that these relations compare well with results obtained from numerical simulations of the qubit dynamics. Based on our results, we discuss practical guidelines to maximize speed and quality of electric single-qubit operations on spin-orbit qubits.

DOI
10.1103/physrevb.97.235433

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An important goal in quantum information processing is to reduce the duration of quantum-logical operations. Motivated by this, we provide a theoretical analysis of electrically induced fast dynamics of a single-electron spin-orbit qubit. We study the example of a one-dimensional quantum dot with Rashba spin-orbit interaction and harmonic driving, and focus on the case of strong driving, when the real-space oscillation amplitude of the driven electron is comparable to the width of its wave function. We provide simple approximate analytical relations between the qubit Larmor frequency, the shortest achievable qubit-flip time, and the driving amplitude required for the shortest achievable qubit flip. We find that these relations compare well with results obtained from numerical simulations of the qubit dynamics. Based on our results, we discuss practical guidelines to maximize speed and quality of electric single-qubit operations on spin-orbit qubits.
The spin-orbit interaction permits to control the state of a spin qubit via electric fields. For holes it is particularly strong, allowing for fast all electrical qubit manipulation, and yet an in-depth understanding of this interaction in hole systems is missing. Here we investigate, experimentally and theoretically, the effect of the cubic Rashba spin-orbit interaction on the mixing of the spin states by studying singlet-triplet oscillations in a planar Ge hole double quantum dot. Landau-Zener sweeps at different magnetic field directions allow us to disentangle the effects of the spin-orbit induced spin-flip term from those caused by strongly site-dependent and anisotropic quantum dot g tensors. Our work, therefore, provides new insights into the hole spin-orbit interaction, necessary for optimizing future qubit experiments.
Electrically driven spin resonance (EDSR) is an established tool for controlling semiconductor spin qubits. Here, we theoretically study a frequency-mixing variant of EDSR, where two driving tones with different drive frequencies are applied, and the resonance condition connects the spin Larmor frequency with the sum of the two drive frequencies. Focusing on flopping-mode operation of a single electron in a double quantum dot with spin-orbit interaction, we calculate the parameter dependence of the Rabi frequency and the Bloch-Siegert shift. A shared-control spin qubit architecture could benefit from this bichromatic EDSR scheme, as it enables simultaneous single-qubit gates.
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.
Performing qubit gate operations as quickly as possible can be important to minimize the effects of decoherence. For resonant gates, this requires applying a strong ac drive. However, strong driving can present control challenges by causing leakage to levels that lie outside the qubit subspace. Strong driving can also present theoretical challenges because preferred tools such as the rotating wave approximation can break down, resulting in complex dynamics that are difficult to control. Here we analyze resonant XXX rotations of a silicon-quantum-double-dot hybrid qubit within a dressed-state formalism, obtaining results beyond the rotating wave approximation. We obtain analytic formulas for the optimum driving frequency and the Rabi frequency, which are both affected by strong driving. While the qubit states exhibit fast oscillations due to counter-rotating terms and leakage, we show that they can be suppressed to the point that gate fidelities above 99.9999.99%99.99 are possible, in the absence of decoherence. Hence decoherence mechanisms, rather than strong-driving effects, should represent the limiting factor for resonant-gate fidelities in quantum dot hybrid qubits.
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.
We propose to use the spin-orbit interaction as a means to control electron spins in quantum dots, enabling both single-qubit and two-qubit operations. Very fast single-qubit operations may be achieved by temporarily displacing the electrons. For two-qubit operations the coupling mechanism is based on a combination of the spin-orbit coupling and the mutual long-ranged Coulomb interaction. Compared to existing schemes using the exchange coupling, the spin-orbit induced coupling is less sensitive to random electrical fluctuations in the electrodes defining the quantum dots.