Electrical driving of hole spin states in planar silicon MOS device by g-matrix modulation

Abstract

Hole spins in group IV quantum dots are a highly promising way to develop CMOS compatible spin qubits owing to their inherent spin-orbit coupling, which enables fast, coherent, and electrical spin control. However, spin-orbit coupling not only enables multiple spin-control mechanisms, but also exposes the qubits to charge noise. In this work, we perform a systematic study of the spin control mechanism in a planar silicon hole quantum dot. We use g-matrix formalism to discern contributions from the various spin driving mechanisms and identify regions where spins are less sensitive to charge noise. By mapping out the dependence of the Rabi frequency on the magnetic field orientation, we observe the largest Rabi frequency in the in-plane direction and the smallest Rabi frequency close to the out-of-plane direction. These results enhance the understanding of how different mechanisms contribute to spin driving within an industrially relevant architecture and aid in establishing the operating conditions for the rapid and coherent manipulation of hole qubits.

Figures (8)

• Figure 1: Device operating point and latched readout. (a) A schematic of the device showing the layout of gates and the position of the quantum dot. Hole quantum dots are formed under gates P1 and P2. The difference in tunneling rates from reservoir to the dots (fast and slow) enables latched readout. (b) Charge stability diagram of the (2,8)$\leftrightarrow$(1,9) transition. The labels indicate the numbers of holes in the P1 and P2 quantum dots. The color axis represents the electrical current $I$ through the sensor. The pulse sequence used for spin control and readout is shown in the figure. The pulse starts from the initialization point (I) in (2,8), followed by the separation point (S) which pushes the spin into (1,9). For readout, the pulse first goes to the projection point, and then go to the latched readout point (R). (c) A schematic showing the pulse sequence used for spin manipulation. The figure also shows how the spins in quantum dots evolve during the pulse sequence. Initialization (I) and readout (R) are performed in the (2,8) state and manipulation (S) happens in the (1,9) state. (d) Change in sensor current ($\mathrm{d}I$) due to the pulse sequence (described above) measured as a function of microwave frequency and the magnetic field magnitude along the x-direction (shown in inset). The region where the spin resonance condition is satisfied results in enhancement of current (red line). The slope of the line gives the $g$-factor of one of the quantum dots.
• Figure 2: Mapping of $g$-factor anisotropy at two different P1 voltages. $g$-factor ($|g^*|$) measured for different orientation (defined by $\theta$ and $\phi$) of the magnetic field around the sample x (a), y (b), and z (c) axes. The magnetic field was kept at a constant magnitude of $0.130T$. Different colors indicate different P1 voltage pulses at which the experiment was performed. The markers are experimental data, and the solid line is fit to the Eq. \ref{['equation_1_g-TMR']}. The schematic below each polar plot defines the plane of rotation for which the experiment is being done. (d) Angular dependence of $\beta_{||}$ as a function of angle. The green line marks the "sweet lines", corresponding to the region where $\beta_{||}=0$.
• Figure 3: Coherent spin manipulation and anisotropy in Rabi frequency. (a) Rabi oscillations for different levels of driving power. The markers are experimental data and the solid lines are the fits to the equation $A\sin (2\pi f_\mathrm{Rabi}\tau) e^{-\frac{\tau}{d_1}}$. Rabi frequencies are $101MHz$ and $72MHz$ for microwave power of $0dBm$ and $-3dBm$ respectively. Magnetic field of magnitude $0.135T$ is applied in the x-direction. The microwave frequency is $3.5GHz$. (b) Color plot of Rabi oscillations for a range of microwave power and burst time at the same microwave frequency and magnetic field magnitude as in (a). (c)-(d) Rabi frequency as a function of the magnetic field orientation at microwave power of $5dBm$. The blue markers are the data point and orange markers are fitted to Eq. \ref{['equation_5_g-TMR']}. The inset schematic shows the direction of the plane of rotation. The error bars for $\theta=22°$ and $30°$ in (d) are not obtained as the Rabi frequency values are calculated using FFT (Fast Fourier Transform) of the time domain data instead of curve fitting.
• Figure 4: Spin driving mechanism for Rabi drive. (a) $g$-TMR and (b) IZ contributions to Rabi frequency extracted from fitting. The "$\textcolor{crossCyan}{\times}$" is the chosen $\bm{B_\mathrm{SO}}$ direction where a minimum in Rabi frequency occurs. The "$\textcolor{blue}{\times}$" is same as "$\textcolor{crossCyan}{\times}$" rotated by $180°$. The continuous "$$" line includes all possible directions which are perpendicular to "$\textcolor{crossCyan}{\times}$"("$\textcolor{blue}{\times}$"). (c) Total Rabi frequency with enhanced coherence sweetlines ($\beta_{||}=0$) as dashed green lines reproduced from Fig. \ref{['figure_2_g-TMR']}. (d) Angle between the $g$-TMR and IZ components.
• Figure 5: Device operating point and latched readout. (a) SEM image of the device showing the layout of gates and the position of the quantum dot. Hole quantum dots are formed under gates P1 and P2. The difference in tunneling rates between the two dots (fast and slow) enables latched readout. (b) Charge stability diagram down to the last hole. The labels indicate the number of holes in the P1 and P2 quantum dots. The color axis represents the change in current through the sensor. The (2,8)$\leftrightarrow$(1,9) charge transition, marked with a white circle, corresponds to the operating regime. (c) (2,8)$\leftrightarrow$(1,9) charge transition regime. The pulse sequence starts with initialization (I) in (2,8) and then proceeds to S point which pushes the spin into a (1,1)-type configuration. For readout the pulse goes to PSB point (P) and then to R for latched readout. (d) Energy level diagram as a function of detuning $\epsilon$ illustrating the single spin states for the (2,8) $\rightarrow$(1,9) charge transition. Different colored arrow shows different possible single spin transitions.