Heralded preparation of spin qubits in droplet-etched GaAs quantum dots using quasiresonant excitation

We present a comprehensive study on heralded spin preparation employing excited state resonances of droplet-etched GaAs quantum dots. This achievement will facilitate future investigations of spin qubit based quantum memories using the GaAs quantum dot material platform. By observation of excitation spectra for a range of fundamental excitonic transitions, the properties of different quantum dot energy levels, i.e., shells, are revealed. The innovative use of polarization-resolved excitation and detection in the context of quasiresonant excitation spectroscopy of quantum dots greatly simplifies the determination of the spin preparation fidelities—irrespective of the relative orientations of laboratory and quantum dot polarization eigenbases. By employing this method, spin preparation fidelities of quantum dot ground states of up to 85% are found. Additionally, the characteristic nonradiative decay time is investigated as a function of ground state, excitation resonance, and excitation power level, yielding decay times as low as 29 ps for $s-p$ shell exited state transitions. Finally, by time-resolved correlation spectroscopy it is demonstrated that the employed excitation scheme has a significant impact on the electronic environment of quantum dot transitions and their apparent brightness.

Figure 1

(a) Typical spectrum of a single GaAs QD using above-band excitation. Selected fundamental emission lines (cf. Table 1) are annotated. (b) and (c)–(e) ${\text{X}}_S^0$ two-photon auto- and cross-correlation traces, respectively, as a function of the time delay $\tau$ between detection events. Recorded (modeled) correlation curves using above-band (AB) and quasiresonant (QR, ${\mathrm{\Delta }}_{\text{ex}}=10.08$ meV, cf. Fig. 2) excitation are drawn in black (red) and blue (green), respectively. The full QR data set is shown in Fig. S4 [27]. Cross correlations (c)–(e) are recorded between ${\text{X}}_S^0$ and ${\text{X}}_S^{+}, {\text{X}}_S^{-}+{\text{XX}}_S^0$, as well as ${\text{XXX}}_S^0$, respectively. Modeling of the correlation traces is performed using Eqs. (1, 2, 3, 4) and the extracted parameter values are summarized in Table 2. The characteristic correlation timescales $T_{\text{corr}}$ are annotated in the graphs.

Figure 2

Combined PLE (blue) and PL (black) spectra of selected $s$-shell transitions (cf. Table 1) obtained by integration over $s$-shell emission lines as a function of the relative energy between excitation laser and ${\text{X}}_S^0$ emission energy ${\mathrm{\Delta }}_{\text{ex}}$. Different resonances and excitation shells are annotated, for details see Table 3 and text. Above-band spectra are recorded at ${\text{X}}_S^0$ saturation excitation power of $1.5\mu \mathrm{W}$, while the PLE spectra are recorded by employing $1.2\mu \mathrm{W}$ quasiresonant laser excitation.

Figure 3

Quasiresonant pump-probe correlation measurements of fundamental QD transitions ${\text{X}}_S^0, {\text{X}}_S^{+}$, and ${\text{X}}_S^{-}$ at their respective excitation resonances (a) at excitation saturation and (b) far below saturation power $P_{\text{sat}}$. The curves are modeled according to Eq. (5) with $T_{\text{NR}}$ as the only free parameter. Specific resonances, excitation conditions, and estimated $T_{\text{NR}}$ values are summarized in last two columns of Table 3. Inset: Schematic illustration of the three-level system between initial state $|0\rangle$, excitonic $s$-shell state $|X_S\rangle$, and excited state resonance $|R^{X_S}\rangle$ in the context of quasiresonant pump-probe investigations. The relevant timescales of the pump $T_P$, the nonradiative decay (NR) to the $s$-shell $T_{\text{NR}}$, and optical decay of $X_S$ are indicated in brackets.

Figure 4

Polarization-resolved PL spectra of ${\text{X}}_S^{-}+{\text{XX}}_S^0, {\text{X}}_S^{+}$, and ${\text{X}}_S^0$ without applied external magnetic field (a) and with a field of 0.2 T in Faraday configuration (b), respectively. The spectra are recorded using above-band excitation at $P\simeq P_{\text{sat}}/2$. The raw spectra are shown in the upper panels, while in the lower ones the degree of polarization (PolDeg, see text) between orthogonal bases are depicted.

Figure 5

Exemplary polarization-resolved PLE spectra and polarization degrees (PolDeg) in 18 different combinations of excitation and detection polarization bases (I,J) of the ${\text{X}}_S^{-}+{\text{XX}}_S^0$ emission lines. The data corresponds to the third run of Fig. 6. The first (I) and second (J) bases are of the excitation and detection, respectively. Upper panels: Combinations with excitation polarization bases (a) H/V, (b) D/A, and (c) R/L. The respective excitation PolDegs are shown in the lower panels. Additionally, total PolDegs of each excitation axes $\langle \parallel \text{I-J}\parallel \rangle$ according to Eq. (6) are drawn. Resonances corresponding to Table 3 are annotated.

Figure 6

Spin preparation fidelity $f_{\text{SpinPrep}}\equiv \parallel {\text{PolDeg}}_{\text{ex}}\parallel$ [cf. Eq. (8)] spectra for QD $s$-shell transitions ${\text{X}}_S^0, {\text{X}}_S^{+}, {\text{X}}_S^{-}+{\text{XX}}_S^0$, and multiple experimental runs, more details are given in the text. Resonances of Table 3 are annotated by labels and gray dashed guidelines. The 80% spin preparation fidelity threshold is indicated in green.

Figure 7

Simplified schematic drawing of the experimental setup. The following abbreviations are used: Beam splitter (BS), superconducting single photon nanowire detectors (SSPDs), and charge coupled device (CCD).