Local Manipulation of Nuclear Spin in a Semiconductor Quantum Well

The shaping of nuclear spin polarization profiles and the induction of nuclear resonances are demonstrated within a parabolic quantum well using an externally applied gate voltage. Voltage control of the electron and hole wave functions results in nanometer-scale sheets of polarized nuclei positioned along the growth direction of the well. Applying rf voltages across the gates induces resonant spin transitions of selected isotopes. This depolarizing effect depends strongly on the separation of electrons and holes, suggesting that a highly localized mechanism accounts for the observed behavior.

Figure 1

(a) Sample orientation with respect to laser excitation and applied magnetic field $B_0$. Sample normal is tilted away from the laser propagation direction by an angle $\alpha =20°$. A gold pad is annealed to contact the back gate; a semitransparent layer of gold acts as the front gate. (b) Landé $g$ factor (left axis) plotted versus bias voltage $U_g$ in black and central position $z_0$ of the electron wave function (right axis) plotted versus $U_g$ in red.

Figure 2

(a) Electron wave function shown schematically, centered at different polarizing positions $z_c$ (3.3, 7.1, and 10.4 nm). (b) Corresponding nuclear polarization distributions created at $B_0=3.98\mathrm{T}$, by polarizing nuclei for 20 min at position $z_c$ (blue lines). Nuclear polarization is measured as a frequency shift $\Delta {\nu }_L$ and is plotted as a function of $z_0$ (solid points). Red curves are Gaussian fits to the data. Centers of the Gaussian fits are 3, 6, and 13 nm, respectively.

Figure 3

(a) Upper curve: ${\theta }_F$ as a function of $\Delta t$ with no applied rf voltage (offset 1 mrad for clarity), $B_0=6\mathrm{T}$, $U_g=-0.1\mathrm{V}$ [fit by Eq. (1) red]. Lower curve: ${\theta }_F$ as a function of $\Delta t$ at the same $B_0$ and $U_g$ with an off-resonant rf voltage of $0.785{\mathrm{V}}_{\mathrm{r}\mathrm{m}\mathrm{s}}$ at 28.5 MHz corresponding to a peak-to-peak oscillation of $z_0$ of $\sim 4\mathrm{n}\mathrm{m}$ [fit by Eq. (2) red]. (b) Maximum ($z_{\max }$) and minimum ($z_{\min }$) wave function positions plotted as a function of $U_g$ for different rms rf voltages. Square (circular) data points represent the upper (lower) bound of wave function displacement $z_{\max }$ ($z_{\min }$). Solid lines are fits to $z_{\max }$ and $z_{\min }$. Nuclear polarization is constant in (a) and (b); observed effects are explained by electron dynamics alone.

Figure 4

(a) ${\theta }_F$ as a function of time delay $\Delta t$. Red “×” indicates $\Delta t=300\mathrm{p}\mathrm{s}$ used for scan (b) showing ${\theta }_F$ as a function of applied gate frequency $f_g$ [(a),(b): $B_0=5.46\mathrm{T}$, rf voltage is $0.14{\mathrm{V}}_{\mathrm{r}\mathrm{m}\mathrm{s}}$]. Dotted, dashed, long-dashed, and solid vertical lines indicate literature values for $\frac{1}{2}{f}_{\mathrm{N}\mathrm{M}\mathrm{R}}$, $\frac{2}{3}{f}_{\mathrm{N}\mathrm{M}\mathrm{R}}$, $f_{\mathrm{N}\mathrm{M}\mathrm{R}}$, and $2f_{\mathrm{N}\mathrm{M}\mathrm{R}}$, respectively, for each color-coded isotope. (c) Larmor frequency shift $\Delta {\nu }_L$ for different laser powers during rf irradiation [(c),(d): $B_0=3.98\mathrm{T}$, rf voltage is $0.286{\mathrm{V}}_{\mathrm{r}\mathrm{m}\mathrm{s}}$, at 29.113 MHz for 20 s, depolarizing ${}^{75}\mathrm{A}\mathrm{s}$]. (d) $\Delta {\nu }_L$ as a function of transient offset voltage where the rf modulation is applied. Bias voltage $U_g$ is always reset to 0.0 V when measuring $\Delta {\nu }_L$.