Optically tunable nuclear magnetic resonance in a single quantum dot

We report optically detected nuclear magnetic resonance (ODNMR) measurements on small ensembles of nuclear spins in single GaAs quantum dots. Using ODNMR we make direct measurements of the inhomogeneous Knight field from a photoexcited electron which acts on the nuclei in the dot. The resulting shifts of the NMR peak can be optically controlled by varying the electron occupancy and its spin orientation, and lead to strongly asymmetric line shapes at high optical excitation. The all-optical control of the NMR line shape will enable position-selective control of small groups of nuclear spins inside a dot.

Figure 1

(Color online) (a) Diagram of the ODNMR experiment, depicting optical excitation and PL collection in the Faraday geometry, and the in-plane $B$-field $B_{\text{rf}}$ oscillating at a radio frequency. (b) PL spectra of the neutral exciton in a GaAs dot with and without rf excitation (squares and circles, respectively) at $B_{ext}=2\text{T}$. Lines show results of the peak fitting.

Figure 2

(Color online) Symbols show NMR spectra $E_{XZ}\left(f_{\text{rf}}\right)$ measured at moderate optical power of $0.5\mu \text{W}$ at $B_{ext}=2\text{T}$ for (a) ${}^{75}\text{A}\text{s}$, (b) ${}^{69}\text{G}\text{a}$, and (c) ${}^{71}\text{G}\text{a}$. Data and fitting (solid lines) for ${\sigma }^{+(-)}$ excitation are shown at the top (bottom) of each plot. Vertical lines mark positions of the NMR peaks. (d) Shift of the resonance frequency for ${}^{69}\text{G}\text{a}$ as a function of the rotation angle of the $\lambda /4$ plate in the laser excitation path.

Figure 3

(Color online) Symbols in (a) and (b) show NMR spectra $\Delta E_{XZ}\left(f_{\text{rf}}\right)$ for ${}^{71}\text{G}\text{a}$ measured at $B_{ext}=1.99\text{T}$. (a) Data for powers 0.19, 0.56, 1.4, and $3.5\mu \text{W}$ of ${\sigma }^{+}$-polarized light. (b) Data for ${\sigma }^{+}$- and ${\sigma }^{-}$-polarized light with power $3.5\mu \text{W}$. Lines show fitting obtained using Eq. (2) for a dot with the height of 4 nm and diameter 40 nm for $\rho =0.3$ and $F$ of 0.05, 0.14, 0.32, and 0.54 in (a) and $F=0.54$ in (b). Arrows and dotted vertical lines in (a) and (b) indicate peak position of the NMR spectra measured in the dark for $B_e=0$ (Ref. 26). (c) Power dependence of $F$ obtained from the fitting.

Figure 4

(Color online) The Knight shift of ${}^{71}\text{G}\text{a}$ as a function of the in-plane distance $r$ (a) and vertical coordinate $z$ (b) from the maximum of the electron wave function for the case $\rho F=0.2$. (c) The distribution of the Knight shift in the ${}^{71}\text{G}\text{a}$ nuclear-spin ensemble in the dot of 4 nm height and 40 nm diameter. The scale for $\Delta f$ is shown opposite. The graph depicts a vertical cross section through the middle of the dot (the dot boundaries are shown by black lines). (d) NMR curves calculated for ${}^{71}\text{G}\text{a}$ in the dot using Eq. (2) for different magnitudes of $\rho F$. (e) NMR curves calculated for $\rho F=0.5$ for a monolayer of ${}^{71}\text{G}\text{a}$ displaced vertically from the center of the dot by 2, 6, 9, and 11 ML.