# Trajectory of a trapped atom involving many lobes of the circular optical lattice in (a) the transverse plane and several potential wells in (d) the axial direction

**Figure 4.** Trajectory of a trapped atom involving many lobes of the circular optical lattice in (a) the transverse plane and several potential wells in (d) the axial direction. Notice the irregular character in the trajectory in the three spatial directions. The spectra illustrated in (b) and (e) are broad and noisy involving similar frequencies in all space directions. The quasi-Poincaré maps (c) and (f) give the (*y*, *v _{y}*) and (

*z*,

*v*) values when the atom's trajectory intersects the

_{z}*v*= 0 hyperplane. This kind of trajectory appears mainly if initially the distribution is centred at a node of the light beam, see table 1.

_{x}**Abstract**

We characterize the semiclassical dynamics of dilute thermal atom clouds located in three-dimensional optical lattices generated by stationary optical Bessel beams. The dynamics of the cold atoms is explored in the quasi-Hamiltonian regime that arises using laser beams with far-off resonance detuning. Although the transverse structure of Bessel beams exhibits a complex topological structure, it is found that the longitudinal motion along the main propagation axis of the beam is the detonator of a high sensitivity of the atoms' motion to the initial conditions. This effect would not be properly described by bidimensional models. We show that an experimental implementation can be highly simplified by an analysis of the behaviour of the dynamical system under scale transformations. Experimentally feasible signatures of the chaotic dynamics of the atom clouds are also identified.