Electron correlation effects on the femtosecond dephasing dynamics of e ₂₂ excitons in (6,5) carbon nanotubes

Highly nonlinear pump fluence dependence was observed in the ultrafast one-color pump - probe responses excited by 38 fs pulses resonant with the E₂₂ transition in a room-temperature solution of (6,5) carbon nanotubes. The differential probe transmission (Î"T/T) at the peak of the pump - probe response (π = 20 fs) was measured for pump fluences from ̃10¹³ to 10¹⁷ photons/pulse cm². The onset of saturation is observed at ̃2 - 10¹⁵ photons/pulse cm ² (̃8 - 10⁵ excitons/cm). At pump fluences >4 - 10¹⁶ photons/pulse cm² (̃1.6 - 10⁶ excitons/cm), Î"T/T decreases as the pump fluence increases. Analogous signal saturation behavior was observed for all measured probe delays. Despite the high exciton density at saturation, no change in the E₂₂ population decay rate was observed at short times (<300 fs). The pump probe signal was modeled by a third-order perturbation theory treatment that includes the effects of inhomogeneous broadening. The observed Î"T/T signal is well-fit by a pump-fluence-dependent dephasing rate linearly dependent on the number of excitons created by the pump pulse. Therefore, the observed nonlinear pump intensity dependence is attributed to the effects of quasi-elastic exciton - exciton interactions on the dephasing rates of single carbon nanotubes. The low fluence total dephasing time is 36 fs, corresponding to a homogeneous width of 36 meV (290 cm^{- 1}), and the derived E₂₂ inhomogeneous width is 68 meV (545 cm^{- 1}). These results are contrasted with photon-echo-derived parameters for the E₁₁ transition.