Chaotic laser-matter interaction

Hamiltonian Silnikov orbits are shown to be produced when a system of two-level atoms interacting via a self-consistent electric field in a single-model lossless cavity is perturbed by a small-amplitude probe laser (a weak, externally imposed, monochromatic electromagnetic field). This result is obtained by utilizing the two constants of motion which exist in the perturbed problem and by calculating a Melnikov function whose nondegenerate zeros imply transverse intersections of the stable and unstable manifolds of a hyperbolic fixed point set. The dynamics of the system on the Silnikov orbits contains a Smale horsehoe construction, leading to intermittent switching of the sign of the electric field which has extreme sensitivity to initial conditions.