Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Reduction of the impact of the local valley splitting on the coherence of conveyor-belt spin shuttling in $^{28}$Si/SiGe

Mats Volmer, Tom Struck, Jhih-Sian Tu, Stefan Trellenkamp, Davide Degli Esposti, Giordano Scappucci, Łukasz Cywiński, Hendrik Bluhm, Lars R. Schreiber

Abstract

Silicon quantum chips offer a promising path toward scalable, fault-tolerant quantum computing, with the potential to host millions of qubits. However, scaling up dense quantum-dot arrays and enabling qubit interconnections through shuttling are hindered by uncontrolled lateral variations of the valley splitting energy $E_{VS}$. We map $E_{VS}$ across a $40 \, $nm x $400 \, $nm region of a $^{28}$Si/Si$_{0.7}$Ge$_{0.3}$ shuttle device and analyze the spin coherence of a single electron spin transported by conveyor-belt shuttling. We observe that the $E_{VS}$ varies over a wide range from $1.5 \, μ$eV to $200 \, μ$eV and is dominated by SiGe alloy disorder. In regions of low $E_{VS}$ and at spin-valley resonances, spin coherence is reduced and its dependence on shuttle velocity matches predictions. Rapid and frequent traversal of low-$E_{VS}$ regions induces a regime of enhanced spin coherence explained by motional narrowing. By selecting shuttle trajectories that avoid problematic areas on the $E_{VS}$ map, we achieve transport over tens of microns with coherence limited only by the coupling to a static electron spin entangled with the mobile qubit. Our results provide experimental confirmation of the theory of spin-decoherence of mobile electron spin-qubits and present practical strategies to integrate conveyor-mode qubit shuttling into silicon quantum chips.

Reduction of the impact of the local valley splitting on the coherence of conveyor-belt spin shuttling in $^{28}$Si/SiGe

Abstract

Silicon quantum chips offer a promising path toward scalable, fault-tolerant quantum computing, with the potential to host millions of qubits. However, scaling up dense quantum-dot arrays and enabling qubit interconnections through shuttling are hindered by uncontrolled lateral variations of the valley splitting energy . We map across a nm x nm region of a Si/SiGe shuttle device and analyze the spin coherence of a single electron spin transported by conveyor-belt shuttling. We observe that the varies over a wide range from eV to eV and is dominated by SiGe alloy disorder. In regions of low and at spin-valley resonances, spin coherence is reduced and its dependence on shuttle velocity matches predictions. Rapid and frequent traversal of low- regions induces a regime of enhanced spin coherence explained by motional narrowing. By selecting shuttle trajectories that avoid problematic areas on the map, we achieve transport over tens of microns with coherence limited only by the coupling to a static electron spin entangled with the mobile qubit. Our results provide experimental confirmation of the theory of spin-decoherence of mobile electron spin-qubits and present practical strategies to integrate conveyor-mode qubit shuttling into silicon quantum chips.

Paper Structure

This paper contains 15 sections, 7 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Results
  3. Discussion
  4. Methods
  5. Data availability
  6. Acknowledgements
  7. Author contributions
  8. Competing interests

Figures (4)

  • Figure 1: Device and method. (a) False-colored scanning electron micrograph of the three labeled metal-layers of the device identical to the one used in this experiment. Electrical connection of S-gates according to solid lines. Scalebar is 500 nm. (b) Schematic cross-section of the device including Si-buffer, relaxed SiGe (dark gray), Si (white), metallic gates (blue) isolated by Al$_2$O$_3$ (orange). (c) Pulse-sequence of the experiment explained by the schematic electrostatic potential at the left side of the one dimensional electron channel (1DEC). Three stages -- singlet preparation, shuttling and Pauli Spin Blockade (PSB) readout are explained in the text. Horizontal lines represent gates and numbers are QD occupation. All pulse-sequence are parametrized by {$d, \tau_\text{W}, \tau_\text{S}, n_\text{rep}, B$}. (d) Singlet return probability $P_\text{S}$ as a function of magnetic field $B$ and shuttle distance $d$ for $y=6n m$ set by constant voltages 0.2V and 0.1V applied to gates ST and SB, respectively. $P_\text{S}(d, B)$ is composed of five measurements (each enclosed by dashed lines). (e) Same as d but $E_\mathrm{VS} (d)$ is highlighted by the black, dashed spline. Right: Wait time $\tau_\text{W}(B)$.
  • Figure 2: Valley splitting map. (a) Valley splitting traces as a function of shuttle distance $d$ for different 1DEC positions $y$. (b) Histogram of the valley splitting measurements. A fit of a Rice probability density (black dashed line) is parameterized by mean $\gamma$ and width $\sigma$ (cmp. Ref. volmer24). (c) Autocorrelation function ($\text{acf}$) of the valley splitting as a function of shuttle distance $d$ (averaged over all traces). A Gaussian fit (dashed, purple) is included. Inset: Zoom-out. (d) Two-dimensional valley splitting map $E_\mathrm{VS} (d,y)$ by linear interpolation of the traces in a.
  • Figure 3: Impact of $E_\mathrm{VS}$ on coherent spin shuttling. (a) Valley splitting trace at $y=0n m$ from Fig. \ref{['fig:VS_map']}a with colored horizontal lines indicating the Zeeman energy for $B \in \{1.7, 0.3, 0.1\}$ T. Spin-valley resonances are marked by vertical dashed lines and a region of low $E_\mathrm{VS}$ by a dotted line. (b,c,d) Singlet-return probability $P_\text{S}$ as a function of shuttle distance $d$ and shuttle time $\tau_\text{S}$ (for one direction) measured with the fixed three magnetic fields $B \in \{1.7, 0.3, 0.1\}$ T are shown in b,c and d, respectively. Vertical lines indicate spin-valley resonances and region of low $E_\mathrm{VS}$ from a. Traces for fixed shuttle velocities (e,f,g) are indicated by the arrows in c. (e,f,g) FFT along $\tau_\text{S}$ of the data shown above as a function of integrated g-factor difference $\overline{\Delta g}$ for magnetic fields $B \in \{1.7, 0.3, 0.1\}$ T.
  • Figure 4: Repetitive impact of shuttling through an $E_\mathrm{VS} (x)$ landscape on coherent spin shuttling. (a) Zoom-in of $E_\mathrm{VS}$ trace at $y=18n m$ from Fig. \ref{['fig:VS_map']}a with colored horizontal lines indicating the Zeeman energy for $B=20$ mT. (b) $P_\text{S}$ as a function of total shuttle time $\tau=2n_\text{rep}\tau_\text{S}$ recorded at $B=20$ mT and at labeled shuttle velocity $v_\text{S}$. Every data point represents $n_\text{rep}$ shuttling of distance 280nm and back at $y=18n m$. Solid gray lines are least-squares fits to the data. Dashed horizontal lines are the mean of all data points in the scan. Data points are scaled by given factor to normalized visibility to 1. $P_\text{S}$ is offset vertically by 1 for clarity. (c) Zoom-in of valley splitting trace at $y=0n m$ from Fig. \ref{['fig:VS_map']}a with colored horizontal lines indicating the Zeeman energy for $B \in \{10, 20, 40\}$ mT. (d) Same as in b, but $y=0n m$ and fixed shuttle velocity $v_\text{S}=5.6m / s$ and $B \in \{10, 20, 40\}$ mT. $P_\text{S}$ is offset vertically by 0.5 for clarity. (e) Same as in c, but larger zoom. (f) Same as in d, but for fixed magnetic field $B=40$ mT and shuttle velocities $v_\text{S}\in \{5.6, 11.2, 16.8, 22.4\}m / s$. For the fit of the 22.4m / s dataset, we exclude the first three points for fitting. (g) Modeled exponential decay $T$ for repetitive impact of $E_\mathrm{VS}$ minimum as a function of valley excitation rate $\gamma$ and $B$ (solid lines) with the six fitted $T$ values (see also Tab. \ref{['tab:Fit_params_cum_shut']}) from panels d and f marked as solid circles. (h) $P_\text{S}$ as a function of total shuttle distance $D=2n_\text{rep}\lambda$ for various $(v_\text{S},B,y)$. Data and fits are taken from panels b,d,f and rescaled according to label with $P_\text{S}$ offset vertically for clarity.