A heat-resilient hole spin qubit in silicon

TL;DR

This work addresses heating-induced Larmor shifts in silicon spin qubits by measuring the temperature dependence of the Larmor frequency $f_L$ for a single hole spin in a MOS nanowire. It shows that the thermal susceptibility $d f_L / d T$ (LTS) correlates with the longitudinal spin-electric susceptibility $β_{∥}$, pointing to an electric-origin mechanism via spin-orbit coupling. A random-field dipole-bath model, combined with device-scale six-band $k·p$ simulations, reproduces the data and yields quantitative dipole parameters ($|oldsymbol{p}|\approx 0.6\,e\cdot\mathrm{pm}$, density $\rho\approx 3.5\times10^{18}\ \mathrm{cm^{-3}}$); it also predicts thermal sweet spots where LTS vanishes. The results imply a route to heat-resilient qubit operation by exploiting field-induced cancellation of LTS, though full protection against decoherence will require tuning of LSES through gate-controlled confinement to approach a dual sweet spot that is insensitive to both charge noise and heating.

Abstract

Recent advances in scaling up spin-based quantum processors have revealed unanticipated issues related to thermal effects. Microwave pulses required to manipulate and read the qubits are found to overheat the spins environment, which unexpectedly induces Larmor frequency shifts, reducing thereby gate fidelities. In this study, we shine light on these elusive thermal effects, by experimentally characterizing the temperature dependence of the Larmor frequency for a single hole spin in silicon. Our results unambiguously reveal an electrical origin underlying the thermal susceptibility, stemming from the spin-orbit-induced electric susceptibility. We perform an accurate modeling of the spin electrostatic environment and gyromagnetic properties, allowing us to pinpoint electric dipoles as responsible for these frequency shifts, that unfreeze as the temperature increases. Surprisingly, we find that the thermal susceptibility can be tuned with the magnetic field angle and can even cancel out, unveiling a sweet spot where the hole spin is rendered immune to thermal effects. These findings bear important implications for optimizing spin-based quantum processors fidelity.

Figures (9)

• Figure 1: Device characterization and temperature dependence. a. Top view of the device. Blue: Accumulation gates. Yellow: Silicon nanowire, the narrow part is undoped and fully depleted while the sides are highly positively doped. Red: figurative hole accumulation in the charge sensor and in the dot hosting a single hole. b. (resp. c.) g-factor (resp. longitudinal spin electric susceptibilities) as a function of the magnetic field orientation. Scattered points are measured data, and the solid lines are fits (see Appendix \ref{['app:fit']} for the fit formulas). The colored circles and triangles correspond to the selected orientations of the field for which we measure the temperature dependence of the Larmor frequency. d. Larmor frequency shift measured as a function of temperature, defined as $\delta f_L = f_L(T) - f_L(30~\rm mK)$. The Larmor frequency is extracted by averaging Ramsey oscillations over 30 minutes and the inhomogeneous dephasing times extracted from the same measurement are analyzed in Appendix \ref{['app:T2']}. The dot-dashed line correspond to the fits discussed in section \ref{['sec:electric_fit']}. The dashed black line shows zero Larmor shift.
• Figure 2: Simulation of the device. a. Electric field map of the device. The white dashed lines delimitate the gates and the silicon channel, in between are the oxides and dielectrics. The solid white line depicts the hole wavefunction and the faded red lines delimit the 6-nm-thick shell where dipoles are placed. The colorbar is shared for both panels. b. (resp. c.) g-factor (resp. longitudinal spin electric susceptibility) as a function of the magnetic field orientation. The scattered points correspond to the experimental data, and the solid grey lines are the simulation results.
• Figure 3: Dipole model simulation. a. Histograms of $\delta f_L^{(N)}(T)$ normalized with respect to $\delta f_L^{(N)}(30~$mK$)$ for $5000$ different dipoles configurations with $N=460$ dipoles ($\rho = 3.54 \times 10^{18}$ cm$^{-3}$) and $|\boldsymbol{\mathbf{p}}| = 0.6~e\cdot$pm, at 50 mK (blue), 100 mK (purple) and 200 mK (red). The magnetic field orientation is fixed at $\theta=120~\rm deg$ . b. Dependence on $\theta$ of the average $\langle\delta f_L^{(N)}\rangle$ (top panel) and of the standard deviation $\sigma$ (bottom panel). The dashed black line shows zero Larmor shift. c. Simulated average Larmor frequency shift as a function of temperature for the four orientations highlighted by vertical colored dashed lines in panel b. The colored diamonds correspond to the experimental data shown in Fig. \ref{['fig1']}.
• Figure 4: Hahn Echo coherence times as a function of the magnetic field orientation. The solid line represent a fit to Eq. \ref{['eq:t2echo']}. The vertical dashed black lines represent the position of the thermal sweetspots expected from the measured values of $\beta_\parallel(T_3)$ and $\beta_\parallel(T_4)$.
• Figure 5: Temperature dependence of the coherence times for each orientation of the magnetic field on a log-log scale. The dashed line corresponds to fits to a $T^{-1/2}$ model. The black dotted line represents a $T^{-1}$ scaling for comparison.