Fast preparation of a single-hole spin in an InAs/GaAs quantum dot in a Voigt-geometry magnetic field

The preparation of a coherent heavy-hole spin via ionization of a spin-polarized electron-hole pair in an InAs/GaAs quantum dot in a Voigt geometry magnetic field is experimentally investigated. For a dot with a typical bright-exciton fine-structure splitting of $17\mu \mathrm{eV}$, the fidelity of the spin preparation is limited to 0.75, with optimum preparation occurring when the effective fine structure of the bright exciton matches the in-plane hole Zeeman energy. In principle, higher fidelities can be achieved by minimizing the bright-exciton fine-structure splitting.

Figure 1

Energy-level diagram of neutral exciton and positive trion subsystems in a Voigt geometry magnetic field. The neutral exciton has two bright $m_J=\pm 1$ states $|b\rangle$ and two dark $m_J=\pm 2$ states $|d\rangle$ that are mixed by the magnetic field. The hole (trion) spin energy eigen states are aligned parallel $|h\rangle (|T\rangle )$ and antiparallel $|\overline{h}\rangle \left(\right|\overline{T}\rangle )$ to the magnetic field.

Figure 2

(a) Principle of operation. Preparation: (i) resonant excitation with ${\sigma }_{+}$-polarized $\pi$ pulse prepares a spin-polarized electron-hole pair in the dot; (ii) the electron tunnels to leave a hole with a net spin. Detection: (iii) resonant excitation of the hole-trion transition with a circularly polarized $\pi$ pulse creates a trion conditional on the spin state of the hole; (iv) eventually, all carriers tunnel from the dot leading to a change in photocurrent proportional to the occupation of the target hole-spin state when the detection pulse arrived.

Figure 3

(a) Photocurrent spectra of neutral exciton transition with and without application of a 4.7-T Voigt geometry magnetic field. At high magnetic field, an additional peak is observed due to mixing of the bright and dark excitons that activates the dark-exciton state. (b) Diamagnetic shift of neutral exciton transition with in-plane magnetic field $B$.

Figure 4

Larmor precession of heavy hole in 4.7-T magnetic field. Two-color photocurrent spectra are measured by tuning the detection pulse through the hole-trion transition for co (red) and cross-circularly (black) polarized excitation. The co- and cross-circular trion peaks oscillate in antiphase and are displayed for various values of the interpulse time delay over one 180-ps period of the Larmor precession.

Figure 5

(a–d) Larmor precession of hole-spin vs. magnetic field at $V_g=0.80\mathrm{V}$. (e–h) Larmor precession of hole-spin vs. gate voltage at $B=4.7\mathrm{T}$. (black/red) Sum/difference of amplitudes of trion peak for co- and cross-circular excitation conditions. (black) The sum is proportional to the total hole population. (red) The difference is proportional to the hole spin-$z$ component.

Figure 6

Electron-tunneling rate vs. applied magnetic field. The tunneling rate decreases, due to an effective increase in the barrier thickness, due to the Lorentz force experienced by carriers tunneling from the dot.

Figure 7

Magnetic field dependence of Larmor precession frequency of hole spin at $V_g=0.84\mathrm{V}$. An in-plane hole $g$ factor of $|g_{hx}|=0.079\pm 0.004$ is deduced.

Figure 8

Electric-field dependence of in-plane hole $g$ factor. The hole Zeeman energy is fitted to $E_{hZ}=(18.4\pm 0.2)+(4.1\pm 0.2)V_g\mu \mathrm{eV}$.

Figure 9

Magnetic- and electric-field dependence of maximum contrast of Larmor precession. Lines give calculation of contrast using measured parameters.

Figure 10

Calculations of contrast based on model as a function of (a) fine-structure splitting ${\delta }_1\left(\mu \mathrm{eV}\right)$ and (b) electron-tunneling time $t_e\left(\mathrm{ps}\right)$.