Electrical readout of spins in the absence of spin blockade

TL;DR

This paper tackles the challenge of reading out two-spin states when spin blockade (SB) is lifted by mechanisms such as strong spin-orbit coupling (SOC) or low-lying orbital states. It introduces a dispersive readout approach that uses the detuning-dependent polarizability of the two-spin system, yielding a state-dependent quantum capacitance detectable via a microwave resonator. The authors demonstrate this method in a silicon hole quantum dot–boron acceptor hybrid, showing SOC- and orbitally-induced SB lifting and performing selective spin readout at distinct detuning points without requiring diabatic passages. They also quantify detuning-controlled spin relaxation times ($T_1$) and discuss tri-state readout capabilities, leakage detection, and applicability to silicon-based QD–acceptor platforms, potentially enabling high-fidelity, scalable two-spin readout in systems with strong SOC or significant orbital structure.

Abstract

In semiconductor nanostructures, spin blockade (SB) is the most scalable mechanism for electrical spin readout, requiring only two bound spins for its implementation. In conjunction with charge sensing techniques, SB has led to high-fidelity readout of spins in semiconductor-based quantum processors. However, various mechanisms may lift SB, such as strong spin-orbit coupling (SOC) or low-lying excited states, hence posing challenges to perform spin readout at scale and with high fidelity in such systems. Here, we present a method, based on the dependence of the two-spin system polarizability on energy detuning, to perform spin state readout even when SB lifting mechanisms are dominant. It leverages SB lifting as a resource to detect selectively different spin measurement outcomes. We demonstrate the method using a hybrid system formed by a quantum dot (QD) and a Boron acceptor in a silicon p-type transistor and show spin-selective readout of different spin states under SB lifting conditions due to (i) SOC and (ii) low-lying orbital states in the QD. We further use the method to determine the detuning-dependent spin relaxation time of 0.1 - 8 $μ$s. Our method should help perform projective spin measurements with high spin-to-charge conversion fidelity in systems subject to strong SOC, will facilitate state leakage detection and enable complete readout of two-spin states.

Figures (5)

• Figure 1: Spin readout using spin-blockade: (a) Anti-symmetric spins allow for the movement of spins, while (b,c) symmetric spins are blockaded, allowing for the two-particle spin states to be distinguished. At increased detuning, SB can be lifted in the presence of either large spin-orbit interaction (b) or the presence of low-lying excited orbital states of energy $\delta_o$ (c).
• Figure 2: Device description and readout concept: (a) Schematic of silicon nanowire transistor (top-view), labelled with Source (S), Drain (D) and top-gate (G) contacts, embedded in an LCR resonator for charge readout. (b) Schematic side-view of Si-nanowire with gate stack including gate metal (red), gate oxide (grey), channel (transparent blue), buried oxide (BOX in black) and intrinsic silicon substrate (Si-i, also blue). The corner QD and Boron atom where holes are confined are marked in yellow. (c) Charge stability diagram showing the capacitive signal measured in the V$_\text{g}$-V$_\text{bg}$ space near the boron-dot transition (positive slope). A boron-reservoir transition is also visible (negative slope). The charge occupation are annotated in the plot. The approximate location of the dot-reservoir transition is indicated in red dashed lines. Location of Load, Wait and Read voltages for readout measurements are marked in red. (d) Magneto-spectroscopy measurement near the point labelled R in the stability diagram. The dotted line shows the location of the T$^-_{1,1}$/S$_{2,0}$ anticrossing. (e) Simulated magneto-spectroscopy of the same transition. The insert shows a simulation of the same transition with $\Delta_\text{sf}$ = 0, showing the emergence of SB. (f,h) Energy level diagram at two magnetic fields. (g,i) Capacitive signal of the lowest two states ($\uparrow_B,\downarrow_D$) and ($\downarrow_B,\downarrow_D$) at two magnetic fields. In each case the excited state is plotted in dashed lines.
• Figure 3: Readout protocol with spin-orbit coupling: (a) Schematic of pulsing scheme. The state is initialised by randomly unloading a spin from the Boron atom starting from a (2,$\downarrow$) configuration resulting in either a ($\downarrow_B,\downarrow_D$), or a ($\uparrow_B,\downarrow_D$) The measurement is performed either at R$_A$ [triggered by the ($\uparrow_B,\downarrow_D$) state] or at R$_P$ [triggered by the ($\downarrow_B,\downarrow_D$) state]. (b) Energy level diagram showing the load (L) and read points for the two states (R$_A$, R$_P$). The black dashed line denotes the Boron-reservoir transition between the (2,1) and the (1,1) charge states. (c) Schematic of pulse sequence for spin readout. States are initialised at L, and then pulsed to either R$_A$ or R$_P$ (blue or red lines). The black dashed lines indicates the control pulse where the state is initialised in the (1,1) region. The time at which data acquisition is started is indicated. (d) Capacitive signal as a function of measurement time and detuning showing two signal arising from the ($\downarrow_B,\downarrow_D$) and ($\uparrow_B,\downarrow_D$) states. R$_A$ and R$_P$ are indicated with dashed lines. Measurements carried out at $B = 1$ T. (e,f) Line-cuts of d at detuning of R$_A$ and R$_P$ showing the capacitive signal (normalised to the peak value of each trace) against time. Dashed lines are given as a guide to the eye. The black lines are the signals recorded from the control measurement.
• Figure 4: $T_1$ characterisation: Measurements carried out at $B = 700$ mT. (a-c) Schematic of the measurement protocol: The state is initialised as described in Figure \ref{['fig:readout-proof-of-principle']}. This is followed by a Wait (W($\varepsilon$)) period of variable time and pulse depth in which ($\uparrow_B,\downarrow_D$) may relax into T$^-_{1,1}$. Finally the state is read out at the spin anti-parallel readout point (R$_A$). The location of W($\varepsilon$) is varied to characterise $T_1$ as a function of $\varepsilon$. The time at which data acquisition is started is indicated. (d) Example capactive signal [a proxy for the ($\uparrow_B,\downarrow_D$) population] against t$_{\text{w}}$ at $\varepsilon$ = -92 $\mu$eV = -1.12 $\Delta_c$ (red dot panel e). The data is taken from the maximum signal of line traces similar to that in Figure \ref{['fig:readout-proof-of-principle']}d. The data is fitted using an exponential decay to extract T$_1$ (730 $\pm$ 80 ns in this case). (e) $T_1$ against detuning of the wait location W($\varepsilon$) showing an exponential dependence (black dashed line) with detuning. The location of R$_A$ is marked in blue. The data in panel d is marked with a red dot.
• Figure 5: Readout utilising orbital states: (a) Stability diagram of ICT B showing the nominal charge occupation. The readout location is highlighted. (b,c) Magneto-spectroscopy and simulation at the point marked R in a. (d,f) Energy level diagrams showing the energy levels of the transition at two magnetic fields. (e,g) Capacitive signals from the ($\uparrow_B,\downarrow_D$)/S$_{0,2}$ (blue) and T$^-_{1,1}$/T$^-_{0,2}$ (red) anticrossings marking the two readout locations. In each case the excited state is marked in dashed lines. (h,i) Capacitive signal measured, used to distinguish ($\uparrow_B,\downarrow_D$) and T$^-_{1,1}$ states utilising the orbital T$^-_{1,1}$/T$^-_{0,2}$ transition (low magnetic field) or the ($\uparrow_B,\downarrow_D$)/S$_{0,2}$ transition (high magnetic field) as readout points. The response is normalised to the maximum of each linetrace.