Realization of two-dimensional Aubry-André localization of light waves via electromagnetically induced transparency

Abstract

We propose a scheme to construct a two-dimensional Aubry-Andr\'e (AA) model and realize two-dimensional AA localization of light waves via electromagnetically induced transparency (EIT). The system we suggest is a cold, resonant atomic gas with an $N$-type level configuration and interacting with probe, control, assisted, and far-detuned laser fields. We show that under EIT conditions the probe-field envelope obeys a modified nonlinear Schr\"odinger equation with a quasiperiodic potential, which becomes a two-dimensional nonlinear AA model when the system parameters are suitably chosen. The quasiperiodic potential is obtained by the cross-phase modulation of the assisted field and the Stark shift of the far-detuned laser field. In addition, the cubic nonlinearity term appearing in the model is contributed by the self-phase modulation of the probe field. We demonstrate that the system can be used to not only realize various two-dimensional AA localizations of light waves, but also to display nonlinearity and dimensionality effects on the AA localizations.