Asymptotic exchange coupling of quasi-one-dimensional excitons in carbon nanotubes

An analytical expression is obtained for the biexciton binding energy as a function of the interexciton distance and binding energy of constituent quasi-one-dimensional excitons in carbon nanotubes. This allows one to trace biexciton energy variation and relevant nonlinear absorption under external conditions whereby the exciton binding energy varies. The nonlinear absorption line shapes calculated exhibit characteristic asymmetric (Rabi) splitting as the exciton energy is tuned to the nearest interband plasmon resonance. These results are useful for tunable optoelectronic device applications of optically excited semiconducting carbon nanotubes, including the strong excitation regime with optical nonlinearities.