  We have studied emission properties of high-density excitons in single-walled
carbon nanotubes through nonlinear photoluminescence excitation spectroscopy.
As the excitation intensity was increased, all emission peaks arising from
different chiralities showed clear saturation in intensity. Each peak exhibited
a saturation value that was independent of the excitation wavelength,
indicating that there is an upper limit on the exciton density for each
nanotube species. We developed a theoretical model based on exciton diffusion
and exciton-exciton annihilation that successfully reproduced the saturation
behavior, allowing us to estimate exciton densities. These estimated densities
were found to be still substantially smaller than the expected Mott density
even in the saturation regime, in contrast to conventional semiconductor
quantum wires.
