Magnetic confinement of a neutral atom in a double-wire waveguide: A nonlinear dynamics approach

Abstract In this paper we focus on the classical dynamics of a neutral atom trapped in a double-wire waveguide in the presence of two uniform bias fields. Because the trapping region takes place in a plane perpendicular to the (parallel) wires, the dynamics is governed by a two-degrees of freedom Hamiltonian where, besides the energy, the two bias fields are the relevant system’s parameters. An exhaustive study of the critical points of the potential energy surface, their stability and bifurcations is carried out, so that, two different trapping regions are characterized. The dynamics in each of these regions is studied by applying classical perturbation theory, which provides an integrable approximation of the original Hamiltonian. The dynamics arising from this normalized Hamiltonian (stability of the equilibrium points, their bifurcations and the phase flow evolution) is then analyzed in a convenient set of phase variables. Poincare surfaces of section to describe the structure and evolution of the phase space governed by the full Hamiltonian are also used. A complete agreement between the descriptions of the dynamics provided by the perturbation theory and the numerical studies is obtained.