We report on high frequency resolution coherent nonlinear optical spectroscopy on an ensemble of InGaN disks in GaN nanowires at 300 K. Sub-$mu$eV resonances in the inhomogeneously broadened third order ($chi^{(3)}$) absorption spectrum show asymmetric line shapes, where the degree of asymmetry depends on the wavelength of the excitation beams. Theory based on the Optical Bloch Equations (OBE) indicates that the lineshape asymmetry is a result of fast decoherence in the system and the narrow resonances originate from coherent population pulsations that are induced by decoherence in the system. Using the OBE, we estimate that the decoherence time of the optically induced dipole (formed between the unexcited ground state the excited electron-hole pair) at room temperature is 125 fs, corresponding to a linewidth of ~10 meV. The decay time of the excitation is ~5-10 ns, depending on the excitation energy. The lineshapes are well fit with the OBE indicating that the resonances are characterized by discrete levels with no evidence of many body physics.
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