  Theory predicts peculiar features for excited-state dynamics in one dimension
(1D) that are difficult to be observed experimentally. Single-walled carbon
nanotubes (SWNTs) are an excellent approximation to 1D quantum confinement, due
to their very high aspect ratio and low density of defects. Here we use
ultrafast optical spectroscopy to probe photogenerated charge-carriers in (6,5)
semiconducting SWNTs. We identify the transient energy shift of the highly
polarizable S33 transition as a sensitive fingerprint of charge-carriers in
SWNTs. By measuring the coherent phonon amplitude profile we obtain a precise
estimate of the Stark-shift and discuss the binding energy of the S33 excitonic
transition. From this, we infer that charge-carriers are formed instantaneously
with sizable quantum yield even upon pumping the first exciton, S11. The decay
of the photogenerated charge-carrier population is well described by a model
for geminate recombination in 1D, suggesting an initial charge carrier
separation of the same order of the exciton correlation length.
