Nonlinear optical probe of indirect excitons

We propose the application of nonlinear optics for studies of spatially indirect excitons in coupled quantum wells. We demonstrate that despite their vanishing oscillator strength, indirect excitons can strongly contribute to the photoinduced reflectivity and Kerr rotation. This phenomenon is governed by the interaction between direct and indirect excitons. Both dark and bright states of indirect excitons can be probed by these nonlinear optical techniques.

Figure 1

Sketch of pump-probe experiment on CQWs sample. DX and IX optical transitions are shown. Both pump and probe frequencies are resonant with one of DX resonances.

Figure 2

Kerr rotation ($\delta {\theta }_{\xi }$) and photoinduced reflectivity ($\delta R_{\xi }$) spectra, calculated from Eq. (6) assuming different nonlinearities: DX energy shift ($\xi ={\omega }_0$, red solid line), DX transition saturation ($\xi ={\Gamma }_0$, blue dashed line), and DX nonradiative broadening ($\xi =\Gamma$, green dotted line).

Figure 3

(a) Parameters of the IX wave function obtained via variational procedure and the resulting in-plane radius. (b) Interaction constants computed by Monte Carlo method. DX-IX carrier exchange constant $V_{\text{exch}}^{\text{D-I}}$ (blue dotted-dashed line), IX-IX carrier exchange constant $V_{\mathrm{exch}}^{\mathrm{I}\text{−}\mathrm{I}}$ (red dashed line), and direct or exciton exchange interaction constant $V_{\mathrm{dir}}^{\mathrm{I}\text{−}\mathrm{I}}$ (red solid line). (c) PL shifts of IX and DX lines calculated from Eq. (15).

Figure 4

Exciton relaxation dynamics in CQWs after a short circularly polarized pump pulse: (a) the normalized exciton populations in equally pumped symmetric CQWs; (b) the same for the pumping of an “electron” QW in asymmetric CQWs; (c) the same for the pumping of a “hole” QW in asymmetric CQWs; (d) DX and IX bright exciton polarization degrees. For all panels, solid and dashed curves correspond to bright and dark states, respectively, blue and purple curves are related to DXs in electron and hole QWs, while red curves describe IXs. The parameters used in this calculation are ${\gamma }_h=(300$ ps${)}^{-1}$, ${\gamma }_e=(30$ ps${)}^{-1}$, ${\Gamma }_{\mathrm{NR}}^D\ll {\Gamma }_0^D=(100$ ps${)}^{-1}$, ${\Gamma }_{\mathrm{NR}}^I\ll {\Gamma }_0^I=(10$ ns${)}^{-1}$ [40], ${\gamma }_{es}=(1$ ns${)}^{-1}$, ${\gamma }_{hs}=(10$ ps${)}^{-1}$, ${\gamma }_{Xs}=(50$ ps${)}^{-1}$ [41].

Figure 5

Calculated dynamics of the photoinduced reflectivity (dashed curves) and Kerr rotation (solid curves) signals in CQWs after a short circularly polarized pump: (a) symmetric CQWs, both QWs are pumped, (b) asymmetric CQWs, electron QW pumping, (c) asymmetric CQWs, hole QW pumping. Blue and purple lines describe signals on electron and hole QWs resonant frequencies, respectively, black curves describe folded signals from both symmetric CQWs. Parameters of calculation are the same as in Fig. 4.