Interacting many-body systems in quantum wells: Evidence for exciton-trion-electron correlations

We report on the nonlinear optical dynamical properties of excitonic complexes in CdTe modulation-doped quantum wells, due to many-body interactions among excitons, trions, and electrons. These were studied by time and spectrally resolved pump–probe experiments. The results reveal that the nonlinearities induced by trions differ from those induced by excitons, and in addition they are mutually correlated. We propose that the main source of these subtle differences comes from the Pauli exclusion-principle through phase-space filling and short-range fermion exchange.

Figure 1

Measured (square symbol) and calculated (solid line) reflectivity spectra of the sample at $5\mathrm{K}$.

Figure 2

Differential reflectivity spectra obtained by pumping at the exciton resonance, at zero delay time between pump and probe pulses: (a) at temperatures of $5\mathrm{K}$ and excitation energies $E_P=1626.65\text{meV}$, at $10\mathrm{K}$ and $E_P=1626.4\text{meV}$ and at $20\mathrm{K}{E}_P=1626.0\text{meV}$ and, (b) at $5\mathrm{K}$, $E_P=1626.65\text{meV}$ and exciton densities of about: $8\times {10}^9{\text{cm}}^{-2}$, $1.5\times {10}^{10}{\text{cm}}^{-2}$, and $3\times {10}^{10}{\text{cm}}^{-2}$. Inset in (a): Time evolution of the nonlinear trion signal, obtained by pumping at the exciton resonance, at $5\mathrm{K}$ and exciton density of $3\times {10}^{10}{\text{cm}}^{-2}$. Inset in (b): Schematics of the trion transition. $E_{\text{Trion}}\left(k\right)$ and $E_{\text{electron}}\left(k\right)$ represent the trion and electron band dispersion, respectively. $f_{\text{electron}}$ represent the electron distribution.

Figure 3

Differential reflectivity spectra obtained by pumping at the trion resonance and with a trion density of about $2\times {10}^{10}{\text{cm}}^{-2}$: (a) at $5\mathrm{K}$, $E_P=1623.35\text{meV}$, and at different delay times and (b) at temperatures of $5\mathrm{K}$ $\left(E_P=1623.35\text{meV}\right)$, $10\mathrm{K}$ $\left(E_P=1623.4\text{meV}\right)$ and $20\mathrm{K}$ $\left(E_P=1623.4\text{meV}\right)$, at zero delay time.

Figure 4

(a) Integrated induced absorption signal of excitons and (b) integrated bleaching signal of trions, as a function of delay time for several excitation powers at the trion resonance, at $5\mathrm{K}$.