Coherent magneto-optical activity in a single chiral carbon nanotube

We propose a theoretical framework and dynamical model for description of the natural optical activity and Faraday rotation in an individual chiral singlewalled carbon nanotube in the highly nonlinear coherent regime. The model is based on a discrete-level representation of the optically active states near the band edge. Chirality is modeled by a system Hamiltonian in a four-level basis corresponding to energy-level configurations, specific for each handedness, that are mirror reflections of each other. The axial magnetic field is introduced through the Aharonov-Bohm and Zeeman energy-level shifts. The time evolution of the quantum system, describing a single nanotube with defined chirality, under un ultrashort polarised pulse excitation is studied using the coupled coherent vector Maxwell-pseudospin equations [Ref.[34]]. We provide an estimate for the dielectric response function and the optical dipole matrix element for transitions excited by circularly polarised light in a single nanotube and calculate the magnitude of the circular dichroism and the specific rotatory power in the absence and in the presence of an axial magnetic field. Giant natural gyrotropy (polarisation rotatory power ~ 3000.=mm (B = 0), superior to the one of the crystal birefringent materials, liquid crystals and comparable, or exceeding the one of the artificially made helical photonic structures, is numerically demonstrated for the specific case of a (5;4) nanotube. A quantitative estimate of the coherent nonlinear magneto-chiral optical effect in an axial magnetic field is given (~ 30000.=mm at B = 8 T). The model provides a framework for investigation of chirality and magnetic field dependence of the ultrafast nonlinear optical response of a single carbon nanotube.