Anomalous variations of spectral linewidth in internal excitonic quantum transitions of ultrafast resonantly excited single-walled carbon nanotubes

How the exciton fine structure and spectral linewidth in single-walled carbon nanotubes (SWNTs) evolve after ultrafast photoexcitation is critical for both understanding the fundamental optoelectronic properties and the development of nanophotonic functional devices. Yet, studies so far have mostly detected a subset of excitons near the Brillouin-zone center due to symmetry and momentum restrictions of the interband optical probes used, such as photoluminescence and absorption. Here we use ultrafast terahertz spectroscopy to probe the excitonic spectral linewidth associated with internal quantum transition across the entire momentum $K$ space in resonantly excited semiconducting SWNTs. The lowest-lying intraexcitonic transition surprisingly sharpens at both high pump fluence and initial times immediately following the photoexcitation. We attribute these anomalous variations in the spectral linewidth to the role of the dark state $1s(g)$ that influences the lifetime broadening of the bright state $1s(u)$, consistent with the temperature-dependent dephasing time with a crossover temperature set by the internal quantum level spacing of excitons.