Counter-diabatic driving for fast spin control in a two-electron double quantum dot

TL;DR

The counter-diabatic driving for fast adiabatic spin manipulation in a two-electron double quantum dot is studied by designing time-dependent electric fields in the presence of spin-orbit coupling by transforming the Hamiltonian in term of Lie algebra.

Abstract

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.

Figures (6)

• Figure 1: Schematic diagram of a two-electron double quantum dot in the presence of external electric fields and spin-orbit coupling, where the singlet state and the lowest one of triplet states are considered as effective two-level system, when $|J+\Delta| \ll J$ with Zeeman term $\Delta =g \mu_B B$.
• Figure 2: (a) Time dependence of $Y$ (solid blue line) and $Z$ (dashed red line) terms of $H_0$. (b) The applied electric fields ${\mathcal{E}}^x_L$ (solid blue line) and ${\mathcal{E}}^x_R$ (dashed red line) drive the state transition of $H_0$ adiabatically, with $t_f =11$ ns. (c) The applied electric fields ${\mathcal{E}}^x_L$ (solid blue line), ${\mathcal{E}}^x_R$ (dashed red line) and ${\mathcal{E}}^y_D$ (dot-dashed green line) drive the state transition of $H$ in a fast adiabatic way with shorter time $t_f=2$ ns.
• Figure 3: Electric fields of ${\mathcal{E}}^{xn}_L$ (solid blue line) and ${\mathcal{E}}^{xn}_R$ (dashed red line), designed from the Hamiltonian $\Tilde{H}$, see Eq. (\ref{["Hs'"]}).
• Figure 4: Dependence of ${\mathcal{E}_{\textrm{max}}}$ on short time $t_f$ (solid blue line), where the dashed straight line shows the asymptotic exponent of $t_f$, i.e. ${\mathcal{E}}_{\textrm{max}} \propto 1/t_f^2$.
• Figure 5: Fidelity $F$ versus dephasing rate $\gamma$ with respect to $t_f = 2$ ns (solid blue line), $t_f = 3$ ns (dashed red line), $t_f = 4$ ns (dot-dashed black line).