## Stationary Bessel modes can be generated by the superposition of counter-propagating travelling Bessel beams stationary in the azimuthal variable

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Figures are generally photos, graphs and static images that would be represented in traditional pdf publications.

**Figure 1.** Stationary Bessel modes can be generated by the superposition of counter-propagating travelling Bessel beams stationary in the azimuthal variable. The structure of the 3D lobes is illustrated for |*l*| = 2. The separation of consecutive maxima in the main direction of propagation coincides approximately with half the wavelength λ for paraxial beams, *k*_{⊥}*k _{z}*. In the picture

*k*

_{⊥}= 0.1

*k*. The transverse

_{z}*XY*-plane pictures in figures (a) and (b) describe the same beam. Figure (b) explicitly shows the transverse scales and, in it, the direction of the gradient force for a red detuned optical lattice is also illustrated. In this work, the gravity force is on the

*z*-axis.

**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.