Slow-light solitons in coupled asymmetric quantum wells via interband transitions

We investigate the formation and propagation of optical solitons in an asymmetric double quantum-well structure. Using a standard method of multiple scales we derive a nonlinear Schr\"odinger (NLS) equation with some high-order correction terms that describe effects of linear and differential absorption, nonlinear dispersion, delay response of nonlinear refractive index, and third-order dispersion of a probe field. We show that in order to make slowly varying envelope approximation be valid an excitation scheme of interband transition should be adopted. We also show that for realistic quantum-well parameters the probe field with time length of picosecond or shorter must be used to make dispersion and nonlinear lengths of the system be smaller than absorption length, only by which a shape-preserving propagation of optical solitons is available. In addition, we clarify validity domains for the perturbed NLS equation as well as the high-order NLS equation and provide various optical soliton solutions in different regimes both analytically and numerically. We demonstrate that the solitons obtained have ultraslow propagating velocity and can be generated under very low input light intensity.