Pulsed-gate measurements of the singlet-triplet relaxation time in a two-electron double quantum dot

A pulsed-gate technique with charge sensing is used to measure the singlet-triplet relaxation time for nearly degenerate spin states in a two-electron double quantum dot. Transitions from the (1,1) charge occupancy state to the (0,2) state, measured as a function of pulse cycle duration and magnetic field, allow the (1,1) singlet-triplet relaxation time $(⩾70\mu \mathrm{s})$ and the (0,2) singlet-triplet splitting to be measured. This technique can be readily applied to read out a spin-qubit operating in a singlet-triplet basis.

Figure 1

(Color) (a) Scanning electron microscopy (SEM) image of a device identical in design to the one used in this experiment. Gates 2–6 and 12 define the double dot. (●) denotes an ohmic contact. (b) Large-scale plot of $d{G}_S∕d{V}_6$ as a function of $V_2$ and $V_6$. Charge states are labeled $(M,N)$, where $M\left(N\right)$ is the time-averaged number of electrons on the left (right) dot. (c) Zoom in near the (1,1) to (0,2) charge transition. (d) 25 mV pulses with a 50% duty cycle and $10\text{‐}\mu \mathrm{s}$ period are applied to the coax connected to gate 2. This results in two copies of the charge stability diagram shifted relative to one another by $\Delta \vec{V}$.

Figure 2

(Color) (a) Sensor conductance, $G_S$, as a function of $V_2$ and $V_6$ while applying the forward pulse sequence (see text) with $\tau =10\mu \mathrm{s}$ and $B_{\perp }=100\mathrm{mT}$. Spin-blocked transitions result in some (1,1) charge signal in the (0,2) pulse triangle (bounded by the red lines). Outside of the pulse triangle it is possible to access other charge states. This relaxes the spin blockade (see color-coded level diagrams). (b) Level diagram illustrating the possible transitions from (1,1) to (0,2). The black arrows indicate fast transitions; the gray arrows indicate spin-blocked transitions. (c) $G_S$ as a function of $V_2$ and $V_6$ while applying the reverse “control” pulse sequence with $\tau =10\mu \mathrm{s}$ and $B_{\perp }=100\mathrm{mT}$. The ${(0,2)}_S$ to ${(1,1)}_S$ transition is not spin blocked. As a result, there is no detectable pulse signal in the pulse triangle (bounded by the red lines). (d) Level diagram illustrating the (0,2) to (1,1) transition. A best-fit plane has been subtracted from the data in (a) and (c) to remove signal from direct gate to QPC coupling.

Figure 3

(Color online) Forward pulse sequence results with $\tau =10\mu \mathrm{s}$. (a)–(d) $G_s$ as a function of $V_2$ and $V_6$ for increasing $B_{\perp }$. $B_{\perp }$ reduces $J$. Eventually ${(0,2)}_T$ is lowered into the “$M$” pulse window [inset of (b)]. At this point, ${(1,1)}_T$ to ${(0,2)}_T$ transitions are energetically possible and the transition from the (1,1) to (0,2) charge state is no longer “spin blocked.” This cuts off the tip of the pulse triangle in (0,2) [see (b)]. A best-fit plane has been subtracted from the data in (a)–(d).

Figure 4

(Color online) Forward pulse sequence results with $B_{\perp }=100\mathrm{mT}$. (a)-(c) $G_S$ as a function of $V_2$ and $V_6$ for increasing pulse periods, $\tau$. For longer periods, singlet-triplet relaxation occurs and the (1,1) to (0,2) transition proceeds, reducing the signal in the (0,2) pulse triangle. (d) $G_s$ with $V_2=-403.0\mathrm{mV}$, $V_6=-523.8\mathrm{mV}$ [gate voltage position indicated by the black triangle in (c)] measured as a function of $\tau$. $G_s=10\times {10}^{-3}{e}^2∕h$ in the (0,2) charge state, while $G_s=20\times {10}^{-3}{e}^2∕h$ in the (1,1) charge state. For short $\tau$, the (1,1) to (0,2) transition is blocked approximately half of the time, resulting in a pulse signal of $15\times {10}^{-3}{e}^2∕h$ in the (0,2) pulse triangle. The (1,1) to (0,2) transition probability increases (sensor signal decreases) with $\tau$ due to spin relaxation with a characteristic time scale of $70\pm 10\mu \mathrm{s}$. A best-fit plane has been subtracted from the data in (a)–(c).