Fractals and chaotic scattering of atoms in the field of a standing light wave

Abstract

The motion of a two-level atom with an internal degree of freedom that interacts with the field of a single-mode standing light wave in a high-Q cavity is treated as a scattering problem. At detunings between atomic and field resonances δ, atomic recoil frequencies α, initial atomic momenta ρ0, and numbers of excitations N at which the semiclassical equations have chaotic solutions (in the sense of their exponential sensitivity to small changes in the initial conditions), atomic scattering is fractal with strongly pronounced self-similarity of the dependence of time T at which the atom leaves the cavity at its initial momentum; the fractal dimension of this curve is 1.84. In the chaotic regime, there are two infinite sets of atomic initial momenta for which T=∞ (in the idealized case of the absence of any loss). They correspond to separatrix-like trajectories along which the atom asymptotically approaches certain configuration space points and to the trajectories of infinitely long chaotic wandering of atoms in the cavity. These trajectories make up countable and uncountable fractals, respectively. Correlations between Rabi atomic oscillations and atomic motion can lead to Doppler-Rabi resonances, that is, deep oscillations of the internal energy of the atom, for large detunings δ that satisfy the condition |αρ 0|≈|δ|.