Dynamic nuclear polarization in InGaAs/GaAs and GaAs/AlGaAs quantum dots under nonresonant ultralow-power optical excitation

We study experimentally the dependence of dynamic nuclear spin polarization on the power of nonresonant optical excitation in two types of individual neutral semiconductor quantum dots: InGaAs/GaAs and GaAs/AlGaAs. We show that the mechanism of nuclear spin pumping via second-order recombination of optically forbidden (“dark”) exciton states recently reported in InP/GaInP quantum dots [E. A. Chekhovich et al., Phys. Rev. B 83, 125318 (2011)] is relevant for material systems considered in this work. In the InGaAs/GaAs dots this nuclear spin polarization mechanism is particularly pronounced, resulting in Overhauser shifts up to $\sim$80 $\mu$eV achieved at ultralow optical excitation power, $\sim$1000 times smaller than the power required to saturate ground state excitons. The Overhauser shifts observed at ultralow power pumping in the interface GaAs/AlGaAs dots are generally found to be smaller (up to $\sim$40 $\mu$eV). Furthermore in GaAs/AlGaAs we observe dot-to-dot variation and even sign reversal of the Overhauser shift which is attributed to the dark-bright exciton mixing originating from electron-hole exchange interaction in dots with reduced symmetry. Nuclear spin polarization degrees reported in this work under ultralow-power optical pumping are comparable to those achieved by techniques such as resonant optical pumping or above-gap pumping with high-power circularly polarized light. Dynamic nuclear polarization via second-order recombination of “dark” excitons may become a useful tool in single quantum dot applications, where manipulation of the nuclear spin environment or electron spin is required.

Figure 1

Photoluminescence (PL) spectra of neutral InGaAs quantum dot A1 (a) and GaAs QD B1 (b) measured in external magnetic field applied along the sample growth axis $B_z=8$ T or $B_z=4$ T, respectively. Two spectra are shown for each quantum dot: at ultralow optical excitation power ($P_{\mathrm{exc}}=11$ nW for InGaAs and $P_{\mathrm{exc}}=3.5$ nW for GaAs) and at high power ($P_{\mathrm{exc}}=3$ $\mu$W for InGaAs and $P_{\mathrm{exc}}=0.3$ $\mu$W for GaAs). All spectra are normalized to have similar maximum intensities. In a neutral quantum dot heavy holes $\Uparrow$ ($\Downarrow$) and electrons $\uparrow$ ($\downarrow$) with spins parallel (antiparallel) to the external field can form optically allowed “bright” states ($|\Uparrow \downarrow \rangle$,$|\Downarrow \uparrow \rangle$) and forbidden “dark” states ($|\Uparrow \uparrow \rangle$,$|\Downarrow \downarrow \rangle$) with total spin projections $J_Z=\pm 1$ and $\pm 2$ respectively. At ultralow excitation powers all four (bright and dark) excitons are observed in PL. At high powers the PL of the dark states is saturated and only bright states are observed.

Figure 2

Magnetic field dependence of exciton PL energies in InGaAs QD A2 (a) and GaAs QD B1 (b). Open symbols represent bright states $|\Uparrow \downarrow \rangle$ (circles) and $|\Downarrow \uparrow \rangle$ (squares), while solid symbols correspond to the dark states $|\Uparrow \uparrow \rangle$ (circles) and $|\Downarrow \downarrow \rangle$ (squares). Lines show fitting using Eqs. (1), allowing electron and hole $g$ factors to be determined (see details in text).

Figure 3

Detection of nuclear spin polarization using PL in a single quantum dot. PL spectra of the InGaAs QD A1 measured at magnetic field $B_z=7$ T and excitation power $P_{\mathrm{exc}}=10$ nW are shown for ${\sigma }^{+}$ (open symbols) and ${\sigma }^{-}$ (solid symbols) polarized optical pumping. A logarithmic vertical scale is used to make all dark and bright exciton PL lines clearly visible in both spectra. At ${\sigma }^{-}$ polarized optical pumping nuclear spin polarization is close to zero, while ${\sigma }^{+}$ pumping induces significant negative nuclear spin polarization antiparallel to the external field (see Sec. 4b). This negative nuclear spin polarization shifts excitons with electron spin $\uparrow$ ($\downarrow$) to lower (higher) energies. We use the change in the energy splitting of the $|\Uparrow \downarrow \rangle$ and $|\Downarrow \uparrow \rangle$ PL peaks as the measure of the Overhauser shift $E_{\mathrm{OHS}}$.

Figure 4

(a) Results of power dependence measurements on InGaAs neutral QD A2 at $B_z=7$ T under ${\sigma }^{+}$ (open symbols) and ${\sigma }^{-}$ (solid symbols) optical pumping. PL intensities of all bright and dark exciton states are shown at the top of the graph (left scale). Overhauser shift $E_{\mathrm{OHS}}=-(\Delta E_{|\Uparrow \downarrow \rangle ,|\Downarrow \uparrow \rangle }-\Delta E_{|\Uparrow \downarrow \rangle ,|\Downarrow \uparrow \rangle }^{B_N=0})$ is shown at the bottom of the graph with diamonds (right scale). Additional scale on the right shows effective nuclear field $B_N$. The vertical dashed line at $P_{\mathrm{exc}}\sim 5$ $\mu$W shows an approximate boundary between two distinct nuclear spin pumping mechanisms: low-power DNP via second-order recombination of the dark excitons and high-power DNP due to spin transfer from spin polarized excitons/electrons (see explanation in the text). (b) Contour plot of the power dependence of $E_{\mathrm{OHS}}$ on $P_{\mathrm{exc}}$ and $B_z$ measured for QD A2 under ${\sigma }^{+}$ optical pumping. Low-power DNP is observed in a range of large magnetic fields with the maximum $|E_{\mathrm{OHS}}|$ achieved at $B_z=7$ T and $P_{\mathrm{exc}}\approx 100$ nW.

Figure 5

Energy level diagram of a neutral exciton in an InGaAs/GaAs QD at high magnetic field ($B_z\sim 7$ T). Vertical arrows show circularly polarized optical transitions due to recombination of the $|\Uparrow \downarrow \rangle$ and $|\Downarrow \uparrow \rangle$ bright excitons. Zigzag arrows show transitions between the dark ($|\Uparrow \uparrow \rangle$ and $|\Downarrow \downarrow \rangle$) and bright excitons induced by the electron-nuclear hyperfine interaction. Two second-order processes $K^{+}$ and $K^{-}$ are highlighted: each process starts from a QD populated by a dark exciton ($|\Uparrow \uparrow \rangle$ or $|\Downarrow \downarrow \rangle$ respectively) and changes total nuclear spin polarization on the dot by $+$1 or $-$1 respectively (see detailed explanation in Sec. 4b).

Figure 6

(a) Results of power dependence measurements on GaAs neutral QD B1 at $B_z=8$ T under ${\sigma }^{+}$ (open symbols) and ${\sigma }^{-}$ (solid symbols) optical pumping. PL intensities of all bright and dark exciton states are shown at the top of the graph (left scale). Overhauser shift $E_{\mathrm{OHS}}$ is shown at the bottom of the graph with diamonds (right scale). The additional scale on the right shows effective nuclear field $B_N$. (b) Contour plot of the power dependence of $E_{\mathrm{OHS}}$ on $P_{\mathrm{exc}}$ and $B_z$ measured for QD B1 under ${\sigma }^{+}$ optical pumping.

Figure 7

Results of power-dependence measurements on several individual neutral QDs from the same InGaAs and GaAs samples as reported in Figs. 4 and 6. (a)–(c) show the data for InGaAs QDs A1, A3, and A4 measured at $B_z=8$ T [compare to Fig. 4a]. (d),(e) show the data for GaAs QDs B2 and B3 measured at $B_z=6.4$ T and $B_z=8$ T respectively [compare to Fig. 6a].