Abstract
The classical dynamics of a cold atom trapped inside a static helical optical potential is investigated based on the Lagrangian formalism, which takes into account both the optical light field and the gravitational field. The resulting equations of motion are solved numerically and analytically. The topology of the helical optical potential, which drives the trapped cold atom, is responsible for two different types of oscillations, namely: the local oscillations, whereby the atomic motion is confined in a region smaller than the light field wavelength ( z < λ ) and the global oscillations, when the atomic motion is extended to larger regions comparable to the beam Rayleigh range ( z < z R ) . Local oscillations guide the atom along the helical structure of the optical potential. The global oscillations, which constitute the main topic of our paper, define the atomic motion along the z-axis as an oscillation between two turning points. For typical values of the beam waist w o the turning points are symmetrical around the origin. For large values of the beam waist w o , the global oscillations become asymmetric because the optical dipole potential weakens and the gravitational potential contributes to the determination of the turning points. For sufficiently large values of the beam waist w o , there are no global oscillations and only one upper turning point defines the atom's global motion.