Interaction potential between dynamic dipoles: Polarized excitons in strong magnetic fields

The interaction potential of a two-dimensional system of excitons with spatially separated electron-hole layers is considered in the strong magnetic field limit. The excitons are assumed to have free dynamics in the $x\ensuremath{-}y$ plane, while being constrained or ``polarized'' in the z direction. The model simulates semiconductor double layer systems under strong magnetic field normal to the layers. The residual interaction between excitons exhibits interesting features, arising from the coupling of the center-of-mass and internal degrees of freedom of the exciton in the magnetic field. This coupling induces a dynamical dipole moment proportional to the center-of-mass magnetic moment of the exciton. We show the explicit dependence of the interexciton potential matrix elements, and discuss the underlying physics. The unusual features of the interaction potential would be reflected in the collective response and nonequilibrium properties of such system.