Pulsed Nuclear Pumping and Spin Diffusion in a Single Charged Quantum Dot

We report the observation of a feedback process between the nuclear spins in a single charged quantum dot under coherently pulsed optical excitation and its trion transition. The optical pulse sequence intersperses resonant narrow-band pumping for spin initialization with off-resonant ultrafast pulses for coherent electron-spin rotation. A hysteretic sawtooth pattern in the free-induction decay of the single electron spin is observed; a mathematical model indicates a competition between optical nuclear pumping and nuclear spin-diffusion. This effect allows dynamic tuning of the electron Larmor frequency to a value determined by the pulse timing, potentially allowing more complex coherent control operations.

Figure 1

(a) Sample geometry showing a single QD and a transverse magnetic field. (b) Level structure and optical interactions. ${\Omega }_{\mathrm{p}}$ (green) labels the cw optical pump, ${\Omega }_{\mathrm{eff}}$ (red) labels the pulsed coherent rotation. Wavy lines indicate spontaneous emission; the photons collected for measurement are indicated by the dashed box. (c) Periodic optical FID pulse sequence, and resulting average electron polarization. Optical pumping increases the polarization for a duration $T=26\mathrm{ns}$. The saturation polarization, ($T\to \infty$, dashed line) is $S_{\mathrm{p}}^z$; in time $T$ only $S_{\mathrm{f}}^z$ is reached. After pumping and a short delay, a picosecond pulse (red [medium gray]) nearly instantaneously rotates the electron spin to the equator of the Bloch sphere ($⟨S^z⟩=0$); a time $\tau$ later a second pulse rotates the spin to achieve electron polarization $S_{\mathrm{i}}^z$. The theoretical count rate $C(\omega ,\tau )$ of Eq. (1) is found as $S_{\mathrm{f}}^z-S_{\mathrm{i}}^z$ in steady-state conditions.

Figure 2

(a) Experimental FID count rate as a function of two-pulse time delay $\tau$. (b) Experimental FID fringe count rate as $\tau$ is continuously scanned longer and then shorter, showing clear hysteresis.

Figure 3

Count rate $C(\omega ,\tau )$ as a function of Overhauser shift $\omega$ and two-pulse delay $\tau$. The green (light gray) areas indicate where a higher count rate is expected. Oscillations in the horizontal directions at frequency ${\omega }_0+\omega$ are due to Ramsey interference; the Gaussian envelope in the vertical direction is due to the reduction of optical pumping with detuning. The superimposed black lines indicate stable points where $\partial \omega /\partial t=0$ according to Eq. (3). Superimposed on these lines are the solutions to this equation which result as $\tau$ is scanned longer (yellow [light gray] line) and shorter (white line).

Figure 4

(Top) The modeled count rate or FID amplitude $C({\omega }_{\mathrm{f}},\tau )$. The blue (dark gray) lines and the red (light gray) lines correspond to scanning $\tau$ longer and shorter, respectively. The dotted line is the expected FID in the absence of nuclear effects. (Bottom) The Overhauser shift ${\omega }_{\mathrm{f}}$ predicted by the model, repeated from Fig. 3.