Robust Single-Shot Spin Measurement with 99.5% Fidelity in a Quantum Dot Array

We demonstrate a new method for projective single-shot measurement of two electron spin states (singlet versus triplet) in an array of gate-defined lateral quantum dots in GaAs. The measurement has very high fidelity and is robust with respect to electric and magnetic fluctuations in the environment. It exploits a long-lived metastable charge state, which increases both the contrast and the duration of the charge signal distinguishing the two measurement outcomes. This method allows us to evaluate the charge measurement error and the spin-to-charge conversion error separately. We specify conditions under which this method can be used, and project its general applicability to scalable quantum dot arrays in GaAs or silicon.

Figure 1

(a) SEM micrograph of a device similar to the one measured. An array of quantum dots is fabricated with the proximal charge sensor and a top cobalt micromagnet layer (orange-shaded area). The dot $Q1$ (dashed white circle) is idle and singly occupied throughout the measurement, while the spin pair in $Q2$ and $Q3$ (filled white circles) is measured. The fourth dot is not used. (b) Charge stability diagram around the (111)-(102) transition, taken with the application of the $I/O/M$ pulse cycles shown in the inset. The positions of the initialization ($I$), operation ($O$), and measurement ($M$, $R$) configurations are denoted by circles along with the detuning axis $ϵ$. The main panel shows $V_{\mathrm{CDS}}=V_M-V_{\mathrm{ref}}$, the difference of the charge sensor signal before ($V_{\mathrm{ref}}$) and after ($V_M$) pulsing to $O$ to cancel out the slow drift and the smooth landscape of the background signal. (c) Energy spectrum (solid lines) as a function of $ϵ$ for the states labeled according to their charge and spin. The dotted arrows show transitions upon gate pulses and the system can make relaxations (solid arrows) with the corresponding rates labeled during each step. (d) Energy configurations in each pulse step.

Figure 2

(a),(b) Histograms of the single-shot signals in configuration (a) R [(111) readout; $V_S=158.5\mathrm{mV}$, $V_T=171.7\mathrm{mV}$] and (b) $M$ [(112) readout; $V_S=157.9\mathrm{mV}$, $V_T=177.7\mathrm{mV}$]. Thin solid lines show Gaussian distributions for $S$ and $T_0$ that would have been observed if no relaxation occurred. Dashed vertical lines show the threshold voltages. (c)–(e) Waiting time dependence of the mean signal $V_M$ at (c) $R$, (d) $M$, and (e) $I$. The values of $V_M$ differ from those in (a) and (b) due to the change of the charge sensor condition. The curves are fits to $A+B\exp (-t/T)$ with the corresponding relaxation time $T$ given in each panel.

Figure 3

(a) Schematics of the transition through the singlet $S\text{−}{S}_3$ (black lines) anticrossing. The blue horizontal line is the energy of the (111) triplet $T_0$. Notation similar to Fig. 1 is used. (b) Signal oscillation observed in the $I\to O\to M$ cycle. (c) The probability $p_n$ as a function of the pulse ramp time $\mathrm{\Delta }t$. A solid line is the fit according to Eq. (1) written in form $\exp (-\mathrm{\Delta }t/t_0)$, which gives $t_0=1.16\mathrm{ns}$. The inset shows the random fluctuation of $\omega$ in the course of measurement. (d) The values of the phase shift ${\varphi }_{\text{fit}}$ obtained from the fit with Eq. (2) versus the values ${\varphi }_{\text{calc}}$ calculated from $p_n$, $\mathrm{\Gamma }$, $\omega$, and $\mathrm{\Delta }t$ using the theoretical model (see Supplemental Material [33]).