SHOCK-WAVES IN A CHAIN OF 2-LEVEL ATOMS WITH EXCHANGE AND DIPOLE-DIPOLE INTERACTIONS

We use a small-amplitude multiple scale expansion to investigate the e xistence of shock waves in a chain of two-level atoms with both exchan ge and dipole-dipole interactions. We show that the exchange interacti on allows the formation of the system of both bright and dark shock wa ves. Conversely, the dipole-dipole interaction results in the instabil ity of the background and, as a consequence, in the prevention of the formation of shock waves. The analytical results are found to be in go od qualitative agreement with a direct numerical integration of the sy stem.