  One- and two-photon luminescence excitation spectroscopy showed a series of
distinct excitonic states in single-walled carbon nanotubes. The energy
splitting between one- and two-photon-active exciton states of different
wavefunction symmetry is the fingerprint of excitonic interactions in carbon
nanotubes. We determine exciton binding energies of 0.3-0.4 eV for different
nanotubes with diameters between 0.7 and 0.9 nm. Our results, which are
supported by ab-initio calculations of the linear and non-linear optical
spectra, prove that the elementary optical excitations of carbon nanotubes are
strongly Coulomb-correlated, quasi-one dimensionally confined electron-hole
pairs, stable even at room temperature. This alters our microscopic
understanding of both the electronic structure and the Coulomb interactions in
carbon nanotubes, and has direct impact on the optical and transport properties
of novel nanotube devices.
