High-Fidelity Single-Shot Singlet-Triplet Readout of Precision-Placed Donors in Silicon

In this work we perform direct single-shot readout of the singlet-triplet states in exchange coupled electrons confined to precision-placed donor atoms in silicon. Our method takes advantage of the large energy splitting given by the Pauli-spin blockaded (2,0) triplet states, from which we can achieve a single-shot readout fidelity of $98.4\pm 0.2\%$. We measure the triplet-minus relaxation time to be of the order 3 s at 2.5 T and observe its predicted decrease as a function of magnetic field, reaching 0.5 s at 1 T.

Figure 1

The $(1,1)\leftrightarrow (2,0)$ charge transition in a double donor dot. (a) A scanning tunneling micrograph of the predosed device showing the hydrogen resist (blue region) and silicon beneath (yellow overlay). Three gates $G_L$, $G_M$, and $G_R$ control the electrostatic environment of the donors dots. The single-electron transistor (SET) is tunnel coupled to source ($S$) and drain ($D$) and controlled predominantly by $G_{\mathrm{SET}}$. (b) Donor sites $L$ and $R$ are separated by $16\pm 1\mathrm{nm}$, and are equidistant at $19\pm 1\mathrm{nm}$ from a SET charge sensor, which also serves as an electron reservoir (red arrows). Insets are close-up images of $L$ and $R$ showing lithographic patches large enough for 2 and 1 $P$ atoms respectively. (c) A charge stability map showing the current through the SET as a function of voltages $\{V_{GL},V_{GR}\}$ near the (1,1)-(2,0) transition. Current peaks running at $\sim 45°$ show Coulomb blockade of the SET and breaks in these lines correspond to single electron transitions of $L$ and $R$. The solid white lines indicate the dot-SET ground-state transitions, whereas the area enclosed by the dashed white lines shows the region where $S(2,0)$ is the ground state and all $T(1,1)$ states are metastable. The detuning axis $\epsilon$ is shown by the white arrow. Singlet-triplet readout is performed at the point shown by the circle marker.

Figure 2

Single-shot singlet-triplet readout in precision-placed donor atoms. (a) The relevant chemical potentials of electrons at donor sites $L$ and $R$ with respect to the SET Fermi level (grey region) at the readout position. The movement of electrons is shown by the solid black arrows and the red arrow depicts the forbidden transition of the $T(1,1)$ state to the $T(2,0)$ configuration due to Pauli-spin blockade. (b) Example SET readout trace of singlet and triplet states. [(c) and (d)] Optimization of electrical readout visibility, ${\mathcal{V}}_{\mathrm{ER}}$. Green markers in (c) show the minimum voltage after the current amplifier during readout for 100,000 traces. Solid bars show a simulation of 10,000 readout traces with a singlet (red) and triplet (blue) ratio of $1:2$ as observed in the experiment. (d) The readout voltage threshold, $V_t$, is chosen to maximize ${\mathcal{V}}_{\mathrm{ER}}$ (green) based on individual readout fidelities for singlet (blue), $F_S$, and triplet (red), $F_T$, states. Shaded regions of each line indicate one standard deviation. [(e) and (f)] Optimization of state-to-charge conversion visibility, ${\mathcal{V}}_{\mathrm{STC}}$. (e) Experimentally obtained tunnel times (bars) for the relevant charge transitions and fits to exponential decays (lines). (f) State-to-charge conversion fidelities for triplet and singlet, $\alpha$ (blue) and $\beta$ (red), respectively. Optimum readout time $\mathrm{\Delta }t$ gives the maximum visibility ${\mathcal{V}}_{\mathrm{STC}}$ (green). Analysis of ST readout was performed at $B_z=2.5\mathrm{T}$, where $T_1$ of the $|T^{-}⟩$ state is of the order of seconds.

Figure 3

Field dependence of $|S(2,0)⟩\leftrightarrow |T^{-}⟩$ mixing and $|T^{-}⟩T_1$ relaxation. (a) The eigenspectrum of the two electron system at the (1,1)-(2,0) charge transition in a static magnetic field $B_z$. The detuning parameter $\epsilon$ corresponds to the black arrow shown in (c), and controls the exchange coupling, $J$, between the electrons. (b) A schematic of the two-level pulse scheme used to observe mixing between $|S(2,0)⟩\leftrightarrow |T^{-}(1,1)⟩$ states. (c) Pulsing schemes for results shown in [(d)–(f)]. (d) The triplet probability, $P_T$, as a function of static magnetic field $B_z$ and the wait position along the detuning axis, $\epsilon$. A peak at 45° for $\epsilon >0$ corresponds to the position in this parameter space where mixing between $|S(2,0)⟩\leftrightarrow |T^{-}(1,1)⟩$ can occur. A fainter peak running at $-45°$ in the data corresponds to $|S(2,0)⟩\leftrightarrow |T^{+}(1,1)⟩$ mixing for $\epsilon <0$. [(e) and (f)] Measurement of the $|T^{-}⟩T_1$ time. To initialize the $|T^{-}⟩$ state we wait at a position along $\epsilon$ shown by the square marker in (a) and (c) that follows the dotted red line in (d) for $\epsilon >0$ as a function of field, $B_z$. (e) Probability of the triplet state for $B_z=\{1.0,2.5\}\mathrm{T}$, as a function of the time spent at the star marker shown in (c). (f) Measurement of $T_1$ from $B_z=1.0\to 2.5\mathrm{T}$.