Single-Shot Readout of Electron Spin States in a Quantum Dot Using Spin-Dependent Tunnel Rates

We present a method for reading out the spin state of electrons in a quantum dot that is robust against charge noise and can be used even when the electron temperature exceeds the energy splitting between the states. The spin states are first correlated to different charge states using a spin dependence of the tunnel rates. A subsequent fast measurement of the charge on the dot then reveals the original spin state. We experimentally demonstrate the method by performing readout of the two-electron spin states, achieving a single-shot visibility of more than 80%. We find very long triplet-to-singlet relaxation times (up to several milliseconds), with a strong dependence on the in-plane magnetic field.

Figure 1

(a),(b) Energy diagrams explaining two schemes for spin-to-charge conversion. (a) Energy-selective readout. Tunneling is energetically allowed from $|\mathrm{ES}⟩$ (left diagram), but not from $|\mathrm{GS}⟩$ (right diagram). (b) Tunnel-rate-selective readout. One electron is allowed to tunnel off the dot, regardless of the spin state, but the tunnel rate depends strongly on the spin state: ${\Gamma }_{\mathrm{ES}}\gg {\Gamma }_{\mathrm{GS}}$. If a charge measurement after a time $\tau$, where ${\Gamma }_{\mathrm{GS}}^{-1}\gg \tau \gg {\Gamma }_{\mathrm{ES}}^{-1}$, indicates that one electron has (not) tunneled, the state is declared ${}^{\prime }\mathrm{ES}^{\prime }$ (${}^{\prime }\mathrm{GS}^{\prime }$). (c) Visibility of the TR-RO as a function of the spin relaxation time $T_1$ and the ratio ${\Gamma }_{\mathrm{ES}}/{\Gamma }_{\mathrm{GS}}$, for ${\Gamma }_{\mathrm{GS}}=2.5\mathrm{kHz}$. The diamond corresponds to the readout parameters of Fig. 2e. Inset: definition of the error rates $\alpha$ and $\beta$. If the initial state is $|\mathrm{GS}⟩$, there is a probability $\alpha$ that the measurement gives the wrong outcome, i.e., ${}^{\prime }\mathrm{ES}^{\prime }$ ($\beta$ is defined similarly).

Figure 2

Single-shot readout of $N=2$ spin states. (a) Scanning electron micrograph of a device as used in the experiments. (b) Pulse waveform applied to gate $P$. (c) Response of the QPC current to the waveform of (b). Energy diagrams indicate the positions of the levels during the three stages. In the final stage, spin is converted to charge information due to the difference in tunnel rates for states $|S⟩$ and $|T⟩$. (d) Real-time traces of $\Delta I_{\mathrm{QPC}}$ during the last part of the waveform (dashed box in the inset), for $t_{\mathrm{wait}}=0.8\mathrm{ms}$. At the vertical dashed line, $N$ is determined by comparison with a threshold (horizontal dashed line in bottom trace) and the spin state is declared ${}^{\prime }T^{\prime }$ or ${}^{\prime }S^{\prime }$ accordingly. (e) Fraction of ${}^{\prime }T^{\prime }$ as a function of waiting time at $B_{\parallel }=0.02\mathrm{T}$, showing a single-exponential decay with a time constant $T_1$ of 2.58 ms.

Figure 3

Triplet-to-singlet relaxation as a function of $B_{\parallel }$. (a) Normalized fraction of ${}^{\prime }T^{\prime }$ vs $t_{\mathrm{wait}}$ for different values of $B_{\parallel }$. (b) Triplet-to-singlet relaxation rate $1/T_1$ as a function of $B_{\parallel }$. The red line is a second-order polynomial fit to the data (see text). For comparison, lines with linear, quadratic, and cubic $B_{\parallel }$ dependences are shown.

Figure 4

Single-shot readout of nearly degenerate states. (a) Singlet-triplet energy difference $E_{ST}$ as a function of magnetic field $B$, applied under a 45° angle with the 2DEG. Inset: zoom in of the region inside the dashed square. For $B>3.9\mathrm{T}$, $E_{ST}$ is smaller than the effective electron temperature. (b) Single-shot readout at $B=4.15\mathrm{T}$. This field value is indicated as “$\mathbf{b}$” in the inset of (a).