Coherent spin dynamics of an interwell excitonic gas in $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ coupled quantum wells

The spin dynamics of an interwell exciton gas has been investigated in $n\text{−}i\text{−}n$ $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ coupled quantum wells. The time evolution kinetics of the interwell exciton photoluminescence has been measured under resonant excitation of the $1s$ heavy-hole intrawell exciton, using a pulsed tunable laser. The formation of a collective exciton phase in time and the temperature dependence of its spin relaxation rate have been studied. The spin relaxation rate of the interwell excitons is strongly reduced in the collective phase. This observation provides evidence for the coherence of the interwell exciton collective phase at temperatures below a critical $T_c$. A theoretical analysis of the interwell exciton spin-flip dynamics has been developed.

Figure 1

(a) Streak camera image of the PL signal as result of excitation of the sample by a short circularly polarized $\left({\sigma }^{+}\right)$ laser pulse (about $1\mathrm{ps}$ duration). The brightness corresponds to the PL intensity. The horizontal axis gives energy, the vertical axis gives time. (b) Horizontal cut through the image [as indicated by the corresponding line in (a)] gives the PL spectrum at a fixed time. (c) Vertical cut [as shown by the vertical line in (a)] gives the PL kinetics at a fixed wavelength. Arrows indicate signal from the DE ($1s$ HH) and the IE. The image was obtained for a bias voltage $U=0.65\mathrm{V}$ at $T=1.85\mathrm{K}$ and an excitation power of about $30\mathrm{kW}∕{\mathrm{cm}}^2$.

Figure 2

Circular polarization resolved decay curves of the IE PL (${\sigma }^{+}$, squares; ${\sigma }^{-}$, circles; corresponding to detection co- and cross-polarized with the laser excitation, respectively) and its circular polarization degree (triangles) measured at different temperatures within the vertical gray line in Fig. 1, corresponding to a spectral window of $1\mathrm{meV}$ for $U=0.6\mathrm{V}$ and an excitation power of about $30\mathrm{kW}∕{\mathrm{cm}}^2$. Solid curves are biexponential fits to the circular polarization degree.

Figure 3

Temperature dependence of spin relaxation times. Note the break in the $y$ axis. The circles give the fast, ${\tau }_1$, and the slow, ${\tau }_2$, relaxation times at bias $U=0.6\mathrm{V}$, and the squares give the ${\tau }_1$ and ${\tau }_2$ times at $U=0.55\mathrm{V}$, both at an excitation power of about $30\mathrm{kW}∕{\mathrm{cm}}^2$. The arrow indicates the temperature where a strong change of the spin relaxation rate ${\tau }_2^{-1}$ occurs.

Figure 4

Temperature dependence of the spin relaxation time ${\tau }_2$ at different excitation powers and at $U=0.6\mathrm{V}$. Open circles correspond to an excitation power of about $30\mathrm{kW}∕{\mathrm{cm}}^2$ leading to an IE concentration $n_{\mathit{ex}}\sim 3\times {10}^{10}{\mathrm{cm}}^{-2}$. Squares and triangles correspond to excitation powers of about 20 and $45\mathrm{kW}∕{\mathrm{cm}}^2$, respectively. The arrows indicate the temperature region where a strong change of the spin relaxation rate occurs. Lines are guides to the eye.

Figure 5

Bias dependencies of the spin relaxation times at $T=2\mathrm{K}$ and an excitation power of about $30\mathrm{kW}∕{\mathrm{cm}}^2$. Circles correspond to the slow ${\tau }_2$ relaxation times, open squares to the fast ${\tau }_1$. Full squares give the spin relaxation times $\tau$ for high bias where a monoexponential decay of the circular polarization degree is observed. The dashed line indicates the boundary between the biexponential and the monoexponential spin relaxation ranges.

Figure 6

Circularly polarized IE PL decay curves (${\sigma }^{+}$, squares; ${\sigma }^{-}$, circles) as well as the corresponding circular polarization degree $\gamma$ (triangles) measured at different biases. The signal has been integrated over the vertical gray line in Fig. 1 covering an energy window of $1\mathrm{meV}$. Solid curves correspond to theoretical calculations according to expressions (14, 15). $T=2\mathrm{K}$.