Dynamics of Coherent and Incoherent Spin Polarizations in Ensembles of Quantum Dots

The temperature dependence of spin coherence in InGaAs quantum dots is obtained from quantum beats observed in polarization-resolved pump-probe experiments. Within the same sample we clearly distinguish between coherent spin dynamics leading to quantum beats and incoherent long-lived spin-memory effects. Analysis of the coherent data using a theoretical model reveals $\approx 10$ times greater stability of the spin coherence at high temperature compared to that found previously for exciton states in four-wave-mixing experiments by Borri et al. [Phys. Rev. Lett. 87, 157401 (2001)]. The data on incoherent polarization reveal a new form of spin memory based on charged quantum dots.

Figure 1

(a) Schematic diagram of QD exciton states in the case of confining potential of high (left) and low (right) symmetry. $|0\rangle$, $|\uparrow \rangle$, and $|\downarrow \rangle$ denote the initial photon and spin-up and -down exciton states, respectively. In the low symmetry case, mixing of the otherwise degenerate $|\uparrow \rangle$ and $|\downarrow \rangle$ states is observed. Fine structure splitting of the new linearly polarized eigenstates is denoted $E_{\mathrm{F}\mathrm{S}}$. $E_{\mathrm{e}\mathrm{x}}$ denotes the exciton energy. (b) Schematic diagram of the excitation by $\sigma$-polarized light of dot 1 (2) charged with spin-up (-down) electron. Dot 1 (2) can absorb ${\sigma }^{+}({\sigma }^{-})$ light only.

Figure 2

(a) Dependence of the differential transmission on the pump-probe delay measured at $T=7\mathrm{K}$ for ${\sigma }^{+}$-polarized pump and ${\sigma }^{+}$- or ${\sigma }^{-}$-polarized probe (gray and black lines, respectively). Both $\approx 100\mathrm{f}\mathrm{s}$ pulses are tuned to the QD ground state. (b) Temporal dependence of the degree of ${\sigma }^{+}$ circular polarization after excitation of the sample with a ${\sigma }^{+}$-polarized pulse at $T=7K$.

Figure 3

Dependence of the differential transmission on the pump-probe delay measured at (a) $T=35\mathrm{K}$, (b) $T=50\mathrm{K}$, (c) $T=80\mathrm{K}$, and (d) $T=110\mathrm{K}$ for ${\sigma }^{+}$-polarized pump and ${\sigma }^{\pm }$-polarized probe. The inset in (c) shows the temporal dependence of the degree of circular polarization in the sample at $T=80\mathrm{K}$.

Figure 4

Temperature dependence of $T_{\mathrm{c}\mathrm{o}\mathrm{h}}$ (circles), ${\tau }_{\mathrm{c}\mathrm{h}X}$ (squares), and ${\tau }_X$ (triangles). Inset shows logarithm of $T_{\mathrm{c}\mathrm{o}\mathrm{h}}$ versus $1/T$. The fit is a linear function with slope of $\approx 260\mathrm{K}$ (22.5 meV).