The Realization Of Vector Thirring Model And Its Characteristics Via Electromagnetically Induced Transparency

We propose a scheme to construct a vectorial Thirring model via electromagnetically induced transparency (EIT). The system we consider is a cold, resonant atomic gas with a six level configuration and interacting with probe and control fields. We show that under EIT conditions the probe field envelope obeys a coupled nonlinear Schr?dinger equations, which becomes a Thirring model when the system parameters are suitably chosen, and these coefficients of nonlinearity terms are tunable by the detunings at will. In the (1+1)-dimensional Thirring model, various soliton pairs are presented, which display many in-teresting characteristics, including the controllable soliton in one solution of soliton pair, that is, one soliton can be adjusted by the propagation constant of another equations in which its soliton solution remains unchanged, the different type of soliton pair solutions found in the same coupled equations, and the stable dark-multi-dark soliton pair that are more stable than dark-dark soliton pair. In addition, we also find the (2+1)-dimensional bright-dark and dark-dark soliton pairs in this model. Comparing with the previous study, the present scheme uses only a single atomic species and two beams of laser field, hence is easy for the physical realization; On the other hand, there are more abundant soliton pairs, including bright-bright,bright-dark, and dark-dark.