Extending Qubit Coherence Time via Hybrid Dynamical Decoupling

Abstract

Dynamical decoupling (DD) and bath engineering are two parallel techniques employed to mitigate qubit decoherence resulting from their unavoidable coupling to the environment. Here, we present a hybrid DD approach that integrates pulsed DD with bath spin polarization to enhance qubit coherence within the central spin model. This model, which can be realized using GaAs semiconductor quantum dots or analogous quantum simulators, demonstrates a significant extension of the central spin's coherence time by approximately 2 to 3 orders of magnitude that compared with the free-induced decay time, where the dominant contribution from DD and a moderate improvement from spin-bath polarization. This study, which integrates uniaxial dynamical decoupling and auxiliary bath-spin engineering, paves the way for prolonging coherence times in various practical quantum systems, including GaAs/AlGaAs, silicon and Si/SiGe. And this advancement holds substantial promise for applications in quantum information processing.

Figures (5)

• Figure 1: Central spin model and bath spin polarization. One of realizing central spin model is semiconductor QD structure, an electron spin $\mathbf{S}$ interacting with surrounding $N=20$ nuclear spins $\mathbf{I}$ in a QD at a bias magnetic field $\mathbf{b}_e$, the electron is confined in a Gaussian-like form. The electronic spatial orbital is represented by its shaded surface, with the electronic density $|\psi(x_i,y_i)|^2$ depicted as a contour envelope in normalized 2D spatial coordinates. The nuclear spins are also sketched within the $x$-$y$ contour envelope. When partially polarizing the nuclear-spin bath Hogele2012Dynamicchekhovich2017measurementchekhovich2020nuclear (with averaged polarization ratio $p=0.60$), the polarization ratio $p_k$ (blue circle) of the $k$-th spin is observed through its $z$-component expectation $2\langle I_k^z \rangle$.
• Figure 2: The dynamic of the electronic spin under various polarized nuclear-spin bath state without the external magnetic field $\textbf{b}_{e}$, where time is measured in units of inverse $A_k$ [cf. Ref. Coish2004Hyperfine]. (a) The minimal fidelity $F_w$ as a function of three polarization cases: the no polarized nuclear-spin bath with averaged polarization ratio $p\simeq$0 (black circle line), the partial polarized nuclear-spin bath with $p$=0.60 (blue triangle line), the full polarized nuclear-spin bath with $p$=1 (red plus line) vs time $t$, respectively. (b) The corresponding Fourier transform of the data from the left panel.
• Figure 3: The effects of the Uni-DD and the hybrid DD protocols is analyzed by narrowing the size of the QD or polarizing its nuclear-spin bath. The minimal fidelity $F_w$ as a function of external magnetic field $(\omega-\omega_m)/\gamma$ or in three polarized nuclear-spin bath cases. For the Uni-DD protocol, two types of $A_k$-distribution are considered: the normal case (a) and the narrow case (c). The magic condition is satisfied with $\omega_m=2\pi/\tau$ (red solid line) or not satisfied at $\omega-\omega_m=\pm2$ (magenta square or dashed line), $\pm1$ (blue circle or dashed line). For the hybrid DD protocol, the normal (b) and narrow cases (d) with the same $\tau$ are illustrated in three scenarios: the unpolarized nuclear-spin bath with bath polarization ratio $p$=0 (red star line), the partially polarized nuclear-spin bath with $p$=0.60 (blue triangle line), and the fully-polarized nuclear-spin bath with $p$=1 (green plus line). The pure free-evolution (black dashed line) is added for easier comparisons in the log-linear scale, where the pulse delay $\tau=0.05$. The timestamp is identical to that in Fig. \ref{['fig:rb']}.
• Figure 4: In the hybrid DD protocol, the characteristic coherence time $T_{0.9}$ where the minimal fidelity $F_w$ drops to 0.9, is benchmarked as the function of $\omega-\omega_m$ and the polarized parameter $\beta$ in the normal case. In the vicinity of $\omega_m\approx 126$, scanning $\gamma b_e^z$ at intervals of 1 to capture the Overhauser field $\overline{h_o^z}$, thereby matching the magic condition in different polarization situations. The inset gives the nuclear-spin bath polarization ratio $p$ vs the polarized parameter $\beta$.
• Figure 5: Electronic spin quantum memory sketch: The process begins with an electron being injected into the right QD, where the nuclear-spin bath is partially polarized, while the bath in the left QD remains unchanged with $| \psi_b(0)\rangle$. This results in the collective bath state $|\psi_b^{'}(0)\rangle$ in the right QD. Then, electronic spin is dynamically preserved by pulse sequences, including hybrid DD (Uni-DD) and its symmetrized hybrid DD (Uni-DD) and concatenated hybrid DD (Uni-DD). Finally, the electron spin is ejected into the left QD to read its memory information.