Numerical simulation of coherent spin-shuttling in a QuBus with charged defects

TL;DR

This work tackles the challenge of maintaining spin-qubit coherence during conveyor-mode shuttling in a Si/SiGe QuBus in the presence of sparse, negatively charged defects. It develops a time-dependent, adiabatic quantum-dynamics framework that combines a realistic electrostatic potential (V(t) = V_def + V_gates(t)) with a multi-orbital, spinful Hamiltonian H(t) = H_o(t) + H_Z(t) and phonon-mediated orbital relaxation via a Lindblad equation, solved using a second-order Magnus expansion. The study shows that proximal defects can cause orbital excitations and spin dephasing through Landau–Zener transitions and g-factor inhomogeneities, with dephasing increasing for center-channel defects and weaker confinement, but mitigated by stronger confinement and larger drive amplitudes. The results provide quantitative guidelines for device design and operation, and establish a practical framework to assess robustness of conveyor-mode spin shuttling against electrostatic disorder, with potential extensions to valley physics and spin–orbit coupling in related materials.

Abstract

Recent advances in coherent conveyor-mode spin qubit shuttling are paving the way for large-scale quantum computing platforms with qubit connectivity achieved by spin qubit shuttles. We developed a simulation tool to investigate numerically the impact of device imperfections on the spin-coherence of conveyor-mode shuttling in Si/SiGe. We simulate the quantum evolution of a mobile electron spin-qubit under the influence of sparse and singly charged point defects placed in the Si/SiGe heterostructure in close proximity to the shuttle lane. We consider different locations of a single charge defect with respect to the center of the shuttle lane, multiple orbital states of the electron in the shuttle with $g$-factor differences between the orbital levels, and orbital relaxation induced by electron-phonon interaction. With this simulation framework, we identify the critical defect density of charged point defects in the heterostructure for conveyor-mode spin qubit shuttle devices and quantify the impact of a single defect on the coherence of a qubit.

Figures (8)

• Figure 1: (a) Scanning electron micrograph of one of the QuBus devices that we model. This device has a set of shuttling gates shown in red and green (labeled S$_1$--S$_4)$, two screening gates (Scr.) in purple, and individually controllable clavier gates and a single-electron transistor in yellow. We consider a numerical model of the unit cell (b) contained in the orange rectangle (a) and impose periodic boundary conditions along the channel ($x$-direction), see Appendix \ref{['app:comsol']} for details. (c) The heterostructure and gate stack consists of a large SiGe substrate upon which an isotopically purified 28Si layer with a thickness of 7 nm is grown. This is the electron channel, where we can accumulate a 2DEG and shuttle the electrons. On top of that, we consider another SiGe buffer and a thin Si cap layer. A SiO$_2$ layer separates the semiconductor from the metallic gates to avoid Schottky contacts.
• Figure 2: (a) Voltages applied to the shuttling gates and simulated potential. Each voltage $U_i(t)$ may have a different offset $U_{i}^\text{DC}$ and amplitude $U_{i}^\text{AC}$. For simplicity, we used the same offset and amplitudes for all the gates in this case. (b) Calculated potential in the shuttling channel at a fixed time $t=0$. Here, we applied $U_\text{S$_1$}^\text{DC} = U_\text{S$_3$}^\text{DC} = 550\,$mV and $U_\text{S$_2$}^\text{DC} = U_\text{S$_4$}^\text{DC} = 700\,$mV, with a pulse amplitude $U_\text{S$_1$}^\text{AC} = U_\text{S$_2$}^\text{AC} = U_\text{S$_3$}^\text{AC} = U_\text{S$_4$}^\text{AC} = 280\,$mV, which results in a fairly sinusoidal spatial confinement along the shuttling direction.
• Figure 3: Influence of the defect on the energy spectrum and the wave function of the shuttled electron. Energy spectra of the minimum of the QD (a) without and (b) with a defect as a function of traveled distance ($d=vt$). In (b) the defect is localized at $d=0$ nm, and in both cases we consider a magnetic field $B=0$ T and plot the energy levels of one spin component only. (c-d) Envelope wave function of the shuttled electron (red) in a QD (c) away from the defect and (d) at the defect position. In all panels, the confinement potential is the same as in Fig. \ref{['fig:clav_gates']}.
• Figure 4: Numerically computed two-dimensional potential at the center of the QW at a fixed time. The sinusoidal potential applied to the S$_i$ gates combined with the effect of the screening gates results in a periodic array of QDs. (a) At $t=0$ ns the electron (red circle) is confined in one of the dots, away from the charge defect (red star). (b) Via time-dependent modulation of the confinement potential, the electron is shuttled towards the defect. (c) Longitudinal cross-section of the potential landscape. The potential barrier induced by the point-like defect exhibits a $1/r$ singularity at the defect position. The red full circle indicates the electron's initial position ($t=0$ ns) and the empty one shows the electron's position after being shuttled at $t=15$ ns.
• Figure 5: Occupation of the orbital excited states as $1-p_0$, after tracing out the spin state. Each data point corresponds to the result of a single defect being placed at the center of the channel with offsets in (a) the $y$-direction, (b) the $z$-direction, with respect to the center of the QW, and (c) the $x$-direction. The center of the channel in the $x$-direction is defined as the mid-point between an upper and a lower clavier gate. The numerical uncertainty floor, resulting from limited computational resources, lies below $10^{-3}$. In the simulations we used a strong driving amplitude (blue squares) and a weak driving amplitude (orange triangles).