Hole spin mode locking and coherent dynamics in a largely inhomogeneous ensemble of $p$-doped InAs quantum dots

In this study, we evidence hole spin mode locking in a largely inhomogeneous $p$-doped InAs quantum dot (QD) ensemble, $\Delta g_x^h/g_x^h\approx 34\%$, which allows us to reveal a long spin coherence time of $T_2^h\approx 0.8\mu \mathrm{s}$. In addition, with a two-pump experiment, we demonstrate, in a low magnetic range 60–120 mT, the possibility to synchronize and tune a single subset of QDs through the distribution. Experiments are supported by an analysis within the density matrix approach.

Figure 1

(a) PCD signal at 2 K vs pump-probe delay for different $B_x$ values and an excitation density of 2 mW. (b) PCD signal at 788 mT: Data (open symbols) and theoretical curve (solid line; parameters: $g_x^e=-0.31$, $g_x^h=0.{41}^{}$, $T_{\Delta }^e=500\mathrm{ps}$, $\Delta g_x^e/g_x^e=9\%$, $\Delta g_x^h/g_x^h=34\%$, $T_2^h=800\mathrm{ns}$, and $\theta =0.9\pi$). The trion-spin and resident-hole spin contributions are shown by the dashed and dotted lines, respectively. (c) and (d) Field dependence of $1/T_h^{*}$ and ${\omega }_h$, and $1/T_e^{*}$ and ${\omega }_e$ (circle and square symbols, respectively). Solid lines are fits (see text). (e) Magnification of the $\mathrm{PCD}(t<0)$ at 788 mT: experimental data (open circles), and theoretical curves (lines) for different $T_2^h$.

Figure 2

(a) Amplitude of $\mathrm{PCD}(t<0)$ for a single-pump excitation and (b) replica amplitude for a double-pump excitation vs the pump-pulse Rabi angle. Experiment: solid symbols; theoretical curve: solid line. The fitting curves are obtained with a $\theta$ dispersion of 40$\%$ and 55$\%$, respectively (corresponding to slightly different experimental conditions). Insets: Theoretical curves without $\theta$ dispersion. Arrows in (a) and (b) indicate the excitation conditions for data shown in Figs. 1b and 3c, respectively.

Figure 3

(a) PCD signal at 2 K vs pump-probe delay for different values of $B_x$ and for a double-pump excitation. The density of excitation for each pump was $\approx$1 mW. The signal has been amplified (50×) at negative delays. (b) Upper panel: $\mathrm{PCD}(t<0)$ vs pump-probe delay in the low-field regime. Lower panel: $|g_x^h|$ distribution; vertical lines indicate the $|g_x^h|$ value of FSM associated with $B_x$ shown in the upper panel. (c) PCD vs delay at $B_x=731$ mT; experiment: solid symbols; theoretical curve: solid line; parameters are the same as in Fig. 1, with $\theta =0.4\pi$ for both pumps. Inset: Magnification of the replica and comparison between experiments and theoretical curves for different $T_2^h$.