We report on the observation of an excited $2s$ state of a trion in a 4.2 nm wide doped $\mathrm{GaAs}/{\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ quantum well using magneto-optical Kerr effect (MOKE) spectroscopy under out-of-plane magnetic fields up to 6 T. This resonance appears slightly below the $2s$ exciton in energy. Strikingly, the $2s$ trion is found to be bound only for magnetic fields larger than 1 T. The signature of the $2s$ trion is absent in the magnetoreflectance spectra, while it is detectable in the MOKE spectra signifying the importance of the powerful technique. Similar to the $1s$ states, the $2s$ trion shows an opposite degree of magnetic-field-induced polarization compared to its exciton counterpart, in agreement with our theoretical calculations. This transfer of oscillator strength between the complexes establishes an optical fingerprint of the $2s$ excited trion.

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• Magneto-optical Kerr effect
• Magneto-optics
• Trions
• Quantum many-body systems
• Quantum wells
• Two-dimensional electron system