Giant cross-Kerr nonlinearity in carbon nanotube quantum dots with spin-orbit coupling

We investigate the nonlinear interaction between two weak optical fields in carbon nanotube quantum dots based on electromagnetically induced transparency and spin-orbit coupling. Our results show, owing to the energy differences produced by strong spin-orbit coupling, that a giant cross-Kerr nonlinearity can be achieved with group-velocity matching, while the probe- and signal-fields absorptions are suppressed simultaneously. We demonstrate that such enhanced nonlinear optical effects can be employed to implement controlled-phase gate between pairs of single-photon pulses with high fidelity and to generate entanglement of coherent Schrodinger-cat states.