We performed pump-probe time-resolved absorption measurements on a modulation p-doped (Cd,Mn)Te quantum well. The density of the 2D hole gas was controlled, in the 10$\text{}^{10}$ cm$\text{}^{-2}$ range, by additional cw illumination. Interactions between photocreated neutral (X) and charged (X$\text{}^{+}$) excitons and the 2D hole gas were analyzed. We found that the strongest effect is the influence of the carriers on both X and X$\text{}^{+}$ optical resonances. Neutral and charged excitons are screened by holes, which results in the decrease in their intensities. We conclude from polarization resolved experiments that this screening is spin-dependent: it is more efficient between holes with opposite spins. Binding holes into the charged excitons reduces the screening of the neutral excitons and leads to an enhancement of the neutral exciton intensity. We also analyzed weaker effects, due to exciton-exciton interaction, at a constant hole density. We found that the reduction of the neutral exciton intensity due to two different mechanisms (phase-space filling and biexciton formation) is almost equal. We observed a spin-dependent blue shift of the neutral exciton line in the presence of a population of neutral excitons created by the pump pulse. Due to the attractive interaction between excitons with opposite spins, the corresponding shift of the neutral exciton is smaller than that observed due to the interaction between excitons with the same spins.
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