Figure 1

(a) Schematic energy diagram of the device, containing two layers of self-assembled indium gallium arsenide QDs, separated by a 9 nm gallium aresenide tunnel barrier and embedded in a gallium aresenide Schottky diode. (b) Ground and lowest-lying optically excited states in the (1,1) regime. Blue arrows indicate electron spins in the bottom QD, red single (double) arrows indicate electron (hole) spins in the top QD. (c) Schematic energy diagram of the ground and optically excited states versus $V$. A magnetic field in Faraday geometry induces Zeeman splittings proportional to the $g$ factors shown, with $g_e^r$ ($g_e^b$) denoting the electronic $g$ factor in the red (blue) QD, and $g_h^r$ the hole $g$ factor in the red QD. The dotted red line indicates the sweet spot, where $d{E}_{ST}/dV=0$. Inset: Circularly polarized dipole-allowed optical transitions between the states shown in (b). (d) Differential reflection (dR) measurement of the trion transitions in the red QD of CQD1 versus $V$ at $B=0.2\mathrm{T}$, measured around saturation power (laser Rabi frequency $\Omega =0.8\mu \mathrm{eV}$) in the presence of a weak nonresonant (850 nm) laser. Blue (green) dashed lines indicate the $S-R_{+}$ ($T_0-R_{+}$) transition energies, extracted from two-laser repump measurements [23], and the dotted red line indicates the sweet spot. The unmarked diagonal feature in the top right-hand corner is due to indirect transitions involving the (1,2) charging ground state. Inset: $E_{ST}$ versus $V$, including a parabolic fit (red line).Reuse & Permissions

Figure 2

Coherent population trapping with an $ST$ qubit (CQD1). (a) CPT measured in dR versus pump and probe laser detuning at $\Delta V=-13\mathrm{mV}$ and $B=0.2\mathrm{T}$. The probe laser (${\Omega }_S=0.34\mu \mathrm{eV}$; incident on the $S-R_{+}$ transition) and the pump laser (${\Omega }_{T_0}=0.83\mu \mathrm{eV}$; incident on the $T_0-R_{+}$ transition) have orthogonal linear polarization. Inset: Schematic diagram of the right-hand circularly polarized lambda scheme. (b) dR (blue dots) versus probe detuning at $B=0.2\mathrm{T}$ and ${\Omega }_{T_0}=0.77\mu \mathrm{eV}$, in the presence of a weak nonresonant (850 nm) laser that reduces the charge fluctuations. A numerical fit (red line) to an eight-level model [23] gives the $T_2^{*}$ time indicated. (c) Same as in (b), but with ${\Omega }_{T_0}=0.58\mu \mathrm{eV}$ and $\Delta V=-23\mathrm{mV}$. (d) Same as in (b), but at $B=0\mathrm{T}$. (e) Same as in (b), but at $\Delta V=-13\mathrm{mV}$ and without the nonresonant laser.Reuse & Permissions

Figure 3

Quantitative analysis of the $T_2^{*}$ decoherence time in CQD1 at 0.2 T. (a) dR spectra (blue dots) far away from the sweet spot ($\Delta V=-23\mathrm{mV}$) for two different pump Rabi frequencies ${\Omega }_{T_0}$ (indicated in gray). Numerical fits [23] to the data are shown in red. Traces are offset vertically for clarity. (b) dR spectra and fits closer to the sweet spot ($\Delta V=-8\mathrm{mV}$). (c) Close-up of the upper trace in (a). The spectrum is fitted with different values of $\Delta V$ while keeping $T_2^{\mathrm{tunnel}}=250\mathrm{ns}$ constant. From dark gray to red to black: $\Delta V=-43$, $-23$, $-13\mathrm{mV}$, corresponding to the $T_2^{*}$ values indicated in the figure. (d) Close-up of the upper trace in (b), fitted with $\Delta V=-22$, $-12$, $-8$, 0 mV.Reuse & Permissions

Figure 4

Suppressed decoherence close to the sweet spot in CQD2. (a) dR spectra (blue dots) with ${\Omega }_{T_0}=0.46\mu \mathrm{eV}$ at $B=0.2\mathrm{T}$. Because of sample drifts, tuning the gate voltage exactly to the sweet spot is challenging, so we estimate that $\Delta V=0\pm 2\mathrm{mV}$. (b) Close-up of (a). The numerical fits [23] correspond to the $T_2^{*}$ values indicated in the figure, with $T_2^{*}=200\mathrm{ns}$ fitting best. (c) CPT spectrum for very low pump and probe power (${\Omega }_S\approx {\Omega }_{T_0}=0.12\mu \mathrm{eV}$). In this regime, the CPT dip has a full width at half maximum of only $\sim 10\mathrm{MHz}$.Reuse & Permissions