  Through ultrafast pump-probe spectroscopy with intense pump pulses and a wide
continuum probe, we show that interband exciton peaks in single-walled carbon
nanotubes (SWNTs) are extremely stable under high laser excitations. Estimates
of the initial densities of excitons from the excitation conditions, combined
with recent theoretical calculations of exciton Bohr radii for SWNTs, suggest
that their positions do not change at all even near the Mott density. In
addition, we found that the presence of lowest-subband excitons broadens all
absorption peaks, including those in the second-subband range, which provides a
consistent explanation for the complex spectral dependence of pump-probe
signals reported for SWNTs.
