Dynamics of optically induced nuclear spin polarization in individual $\text{InP}/{\text{Ga}}_x{\text{In}}_{1-x}\text{P}$ quantum dots

We report on dynamics of optically induced nuclear spin polarization in individual InP/GaInP quantum dots at $T=4.2\text{K}$. Dots with different charge states arising from residual doping in a nominally undoped sample have been studied. In the same sample, we find strong dot-to-dot variation in the nuclear spin decay times in the dark from $\sim 85$ to $\sim 6000\text{s}$. The longest decay times measured are comparable to those previously measured in bulk InP and correspond to almost complete suppression of nuclear spin diffusion out of the dot. In the negatively charged dots, the spin decay times exceed 300 s (with the slowest decay of $\sim 6000\text{s}$), about ${10}^5$ times longer than those reported previously in electron charged dots in gated structures. We discuss possible mechanisms responsible for suppression of nuclear spin diffusion, including inhomogeneous quadrupolar shifts and stabilizing effect of the hyperfine interaction with the electron confined in the dot.

Figure 1

(Color online) Results of the optical spin pumping experiments on quantum dots with different charging. (a) Normalized PL intensity as a function of pump power of the trion transitions in negatively $\left(X^{-}\right)$ charged dot (N1), positively $\left(X^{+}\right)$ charged dot (N2), and exciton $\left(X^0\right)$ and biexciton $\left(X{X}^0\right)$ transitions in a neutral dot (N3). (b) Overhauser splitting (OHS) and corresponding nuclear field as a function of the power of ${\sigma }^{+}$ excitation at $B_z=2.5\text{T}$ for the dots shown on panel (a). [(c) and (d)] Nuclear polarization $\left|B_N\right|$ as a function of magnetic field $B_z$ under ${\sigma }^{+}$- (squares) and ${\sigma }^{-}$- (circles) polarized excitation at $P_{exc}=70\mu \text{W}$ in (c) negatively and (d) positively charged dots N4 and N2, respectively. In both cases $B_N<0$ $\left(B_N>0\right)$ when excited with ${\sigma }^{+}$ $\left({\sigma }^{-}\right)$-polarized laser.

Figure 2

(Color online) (a) Time diagram of the measurement of the nuclear polarization buildup dynamics in a single dot. In this experiment $t_{pump}$ is varied as an independent variable while $t_{erase}=8t_{pump}$, $t_{det}=t_{pump}/4$, and excitation power of both pulses is $\approx 70\mu \text{W}$. [(c) and (d)] Overhauser field $B_N$ buildup dynamics in the negatively charged dot $X^{-}$ N4 at $B_z=0$ (circles), 0.4 T (triangles), and 2 T (squares). Open (solid) symbols correspond to ${\sigma }^{-}$ erase/${\sigma }^{+}$ pump (${\sigma }^{+}$ erase/${\sigma }^{-}$ pump) experiments. Dashed arrow shows initial increase in $B_N$ not resolved in the experiment.

Figure 3

(Color online) Magnetic field dependence of the nuclear spin buildup time under ${\sigma }^{+}$-polarized optical pumping (open symbols) and of the spin decay time in the dark condition (solid symbols) in a negatively charged dot $X^{-}$ N4 (HD sample).

Figure 4

(Color online) Nuclear spin decay dynamics. Inset shows a diagram of the cycle in the pump-probe experiment. The power of the pump has been chosen at a level corresponding to the maximum PL intensity $P_{exc}\sim P_{exc}^{sat}$ with an exception for the neutral dot $X^0$, where high power pump $P_{exc}\sim 15P_{exc}^{sat}$ has been used. (a) Decay of nuclear spin polarization in a negatively charged dot ($X^{-}$ N4, HD sample) at $B_z=8\text{T}$. Squares and circles show data measured with ${\sigma }^{-}$- and ${\sigma }^{+}$-polarized pumps, respectively. For delays $t_{delay}>100\text{s}$ large fluctuations of $B_N$ in $X^{-}$ N4 can be seen, demonstrating that nuclear spin decay is a random discrete process. Solid lines show an exponential function with ${\tau }_{dec}\approx 250\text{s}$. (b) Nuclear spin decay in positively charged dots ($X^{+}$ N2 and N5, LD sample) at $B_z=4.1\text{T}$. Exponential fit with ${\tau }_{dec}\approx 4200\text{s}$ (85 s) is shown with the dashed (solid) line for dot N2 (N5). (c) Nuclear spin relaxation in a negatively charged dot ($X^{-}$ N1, LD sample) and in a neutral dot ($X^0$ N3, LD sample) at $B_z=4.1\text{T}$. Exponential fit with ${\tau }_{dec}\approx 5800\text{s}$ (350 s) is shown with the dashed (solid) line for dot $X^{-}$ N1 ($X^0$ N3).

Figure 5

(Color online) (a) Schematic representation of the effect of a trapped electron on nuclear spin on the dot: inhomogeneous Knight field causes energy splitting mismatch between different nuclei, leading to suppression of nuclear spin diffusion out of the dot. (b) Magnetic field dependence of the nuclear polarization $\left|B_N\right|$ on the negatively charged dot N4 under ${\sigma }^{+}$ (squares) and ${\sigma }^{-}$ (circles) excitations. The observed minima of nuclear polarization correspond to the situation when the external field $B_z$ compensates electron Knight field $\pm B_e$ induced by ${\sigma }^{\pm }$ excitation, resulting in partial depolarization of nuclei. The value of $⟨B_e⟩\approx 3\text{mT}$ is estimated from splitting between the minima. [(c) and (d)] PL spectrum from the aperture containing two positively charged dots ($X^{+}$ N2 and N5) (c) at a low excitation power $10\mu \text{W}$ and (d) its time dependence under high power $\left(200\mu \text{W}\right)$ excitation. Dot N2 and additional spectral features observed at high power demonstrate a large random spectral drift while PL from the dot N5 is stable in time.

Figure 6

(Color online) (a) Photoluminescence spectra of a neutral exciton $X^0$ (dot N3) measured in ${\sigma }^{+}$ and ${\sigma }^{-}$ circular polarizations in Faraday $\left(B\parallel Oz\right)$ geometry (${\sigma }^{-}$-polarized excitation) and in orthogonal ${\pi }_1$, ${\pi }_2$ linear polarizations in Voigt $\left(B\perp Oz\right)$ geometry (linearly polarized excitation). Low energy parts of the spectra in Faraday geometry separated by vertical line are multiplied by 10. (b) Energies of PL lines deduced from spectra in panel (a) as a function of magnetic field. Exciton components originating from bright $J_z=\pm 1$ (dark $J_z=\pm 2$) states are shown with squares (triangles). Solid lines show approximation (see explanation in text). [(c) and (d)] Hanle effect measurements for various charged dots. Circular polarization degree of PL under circularly polarized excitation is shown as a function of in-plane magnetic field $B_x$ for (c) positively and (d) negatively charged dots. Solid lines show best fit with Lorenz function. The products of depolarization times and $g$ factors are found from the fitting: $gT=350\text{ps}$ ($X^{+}$ N2, LD sample), 280 ps ($X^{+}$ N5, LD sample), 2.3 ns ($X^{-}$ N1, LD sample), and 1.1 ns ($X^{-}$ N4, HD sample).