We systematically investigate the transport and photoluminescence measurements of a high-mobility two-dimensional electron gas in a GaAs/AlGaAs quantum well under magnetic fields $B$. By tuning the laser excitation power $P_{\mathrm{ex}}$, transitional patterns of the singlet and triplet (negative charged) trions occur in the high-$B$ regime: The two branches of singlet trions $X_s^{-}$ dominate at low $P_{\mathrm{ex}}$ $(<1$ $\mathrm{W}/{\mathrm{mm}}^2)$, and six more triplet $X_t^{-}$ branches emerge at high $P_{\mathrm{ex}}$ $(\sim 1-10$ $\mathrm{W}/{\mathrm{mm}}^2)$. At extremely high laser $P_{\mathrm{ex}}$ $(>100$ $\mathrm{W}/{\mathrm{mm}}^2)$ and at fixed $B$ fields, robust Fano resonance features are accompanied by the Gaussian resonance centered at $X_s^{-}$, which illustrates dark and bright trions. Therefore, a very high laser excitation (or electromagnetic field) becomes an efficient tool to probe dark trions. In addition, discontinuity and splitting features occur at fillings $\nu =2,4,6$, and the abrupt drops at high odd fillings factors ($\nu \sim 5,7,9$, etc.) originate from spin-resolved many-body interactions.

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• Excitons
• Trions
• Quantum wells
• Photoluminescence