In this paper, we investigate the fast quantum control of Dirac equation dynamics by counter-diabatic driving, sharing the concept of shortcut to adiabaticity. We systematically calculate the counter-diabatic terms in different Dirac systems, like graphene and trapped ions. Specially, the fast and robust population inversion processes are achieved in Dirac system, taking into account the quantum simulation with trapped ions. In addition, the population transfer between two bands can be suppressed by counter-diabatic driving in graphene system, which might have potential applications in opt-electric devices.
We report that the transmitted evanescent light beam under total reflection will experience a lateral displacement
similarly to that of the reflected beam, called Goos-Haenchen (GH) effect. By a dielectric thin film coated onto the
dielectric surface, which is usually considered as the near-field enhanced configuration in atom optics, we indicate
that the displacement of the transmitted evanescent beam can be greatly enhanced to several tens of wavelengths
at transmission resonance under total internal reflection. Numerical simulations have been performed and it is
shown that the transmitted evanescent beam maintains well the shape of the incident beam when the thickness
of the thin film is required to be of the order of wavelength. Further, it is demonstrated that the stationary-phase
approach is also applicable to transmitted evanescent beam and the GH displacement of the transmitted beam is just half the GH displacement of the reflected beam. The discussions presented here may arouse interest in atom optics and near-field microscope.