Dynamic Nuclear Polarization with Single Electron Spins

We polarize nuclear spins in a GaAs double quantum dot by controlling two-electron spin states near the anticrossing of the singlet ($S$) and $m_S=+1$ triplet ($T_{+}$) using pulsed gates. An initialized $S$ state is cyclically brought into resonance with the $T_{+}$ state, where hyperfine fields drive rapid rotations between $S$ and $T_{+}$, “flipping” an electron spin and “flopping” a nuclear spin. The resulting Overhauser field approaches 80 mT, in agreement with a simple rate-equation model. A self-limiting pulse sequence is developed that allows the steady-state nuclear polarization to be set using a gate voltage.

Figure 1

(a) SEM image of a device similar to the one used in this experiment. A QPC with conductance, $g_S$, senses charge on the double dot. (b) Energy levels near the (1,1)-(0,2) charge transition. (c) $g_S$ measured as a function of $V_L$ and $V_R$. A pulse sequence used to polarize nuclei is superimposed on the charge stability diagram (see text). The bright signal at point $M$ that runs parallel to the $ϵ=0$ line is a result of Pauli-blocked $(1,1)\to (0,2)$ charge transitions and reflects $S\mathrm{\text{−}}{T}_{+}$ mixing at point $S$. (d) $P_S({\tau }_S=200\mathrm{ns})$ as a function of ${ϵ}_S$ and $B_0$. The field dependent “spin funnel” corresponds to the $S\mathrm{\text{−}}{T}_{+}$ anticrossing position, ${ϵ}_S={ϵ}^{*}$.

Figure 2

(a) Probabilistic nuclear polarization sequence. (b) Adiabatic nuclear polarization sequence (see text).

Figure 3

(a) $P_S$ as a function of applied field $B_0$ and ${ϵ}_S$. (b) Dependence of the $S\mathrm{\text{−}}{T}_{+}$ anticrossing position on measurement duration ${\tau }_M$, with $B_0=24\mathrm{mT}$. A decrease in ${\tau }_M$ increases the polarization rate, shifting the $S\mathrm{\text{−}}{T}_{+}$ resonance condition to more positive ${ϵ}_S$. (c) Schematic diagram illustrating the effect of nuclear polarization on the spin funnel. $B_{\mathrm{nuc}}$ is extracted by measuring the shift in the $S\mathrm{\text{−}}{T}_{+}$ position relative to the position without polarization. (d) $B_{\mathrm{nuc}}$ as a function of cycle frequency, $f$, measured sweeping ${ϵ}_S$ to increasing values (“with”) and decreasing values (“against”). Solid lines are predictions from a nonlinear diffusion model (see text).

Figure 4

(a) Self-limiting adiabatic polarization sequence. Left: Starting with $B_{\mathrm{nuc}}=0$, the sequence polarizes nuclear spins and $B_{\mathrm{nuc}}$ increases, shifting the $S\mathrm{\text{−}}{T}_{+}$ resonance to more positive $ϵ$. Right: Steady state is reached when ${ϵ}^{*}={ϵ}_F$. Dashed gray lines show the energy level configuration before nuclear polarization. (b) Calibration spin funnel acquired using the pulse sequence [Fig. 1c]. (c) $P_S$ as a function of ${ϵ}_F$ measured with the adiabatic polarization sequence applied. The complete pulse sequence consists of three adiabatic polarization cycles (a single adiabatic polarization cycle is shown in the inset) followed by one measurement cycle [shown in Fig. 1c]. The combined pulse sequence length is $\sim 6.4\mu \mathrm{s}$. Steady state hyperfine field $B_{\mathrm{nuc}}$ changes from 4 to 18 mT as set-point ${ϵ}_F$ is moved from $-2\mathrm{mV}$ to $-1.3\mathrm{mV}$.