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Dense cold atomic clouds have been shown to be similar to plasmas. Previous studies showed that such clouds exhibit instabilities induced by long-range interactions. However they did not describe the spatial properties of the dynamics. In this Letter, we study experimentally the spatial nature of stochastic instabilities and find out that the dynamics is localized. Data are analyzed both in the spectral domain and in the spatial domain (principal component analysis). Both methods fail to describe the dynamics in terms of eigenmodes, showing that space and time are not separable.

Magneto-Optical Traps have been used for several decades. Among fundamental mechanisms occuring in such traps, the magnitude of the multiple scattering is still unclear. Indeed, many experimental situations cannot be modeled easily, different models predict different values of the re-absortion cross section, and no simple experimental measurement of this cross section are available. We propose in this paper a simple measurement of this cross section through the size and the shape of the cloud of cold atoms. We apply this method to traps with a configuration where theoretical values are available, and show that the measured values are compatible with some models. We also apply the method to configurations where models are not relevant, and show that the re-absorption is sometimes much larger than the usually assumed value.

The cloud of cold atoms produced by a Magneto-Optical Trap is known to exhibit instabilities. We examine in this paper in which limits it could be possible to realize an experimental trap similar to the configurations studied theoretically, i.e. mainly traps where one direction is privileged. We study the static behavior of an anisotropic trap, where anisotropy results essentially from the use of two different laser frequencies for the arms of the trap. Such a trap has very surprising behaviors, in particular the cloud disappears for some laser frequencies, while it exists for smaller and larger frequencies. A model is build to explain these behaviors. We show in particular that, to reproduce the experimental observations, the model has to take into account the cross saturation effects. Moreover, the couplings between the different directions cannot be neglected.

An exhaustive kinetic model for the atoms in a 1D Magneto-Optical Trap is derived, without any approximations. It is shown that the atomic density is described by a Vlasov-Fokker-Planck equation, coupled with two simple differential equations describing the trap beam propagation. The analogy of such a system with plasmas is discussed. This set of equations is then simplified through some approximations, and it is shown that corrective terms have to be added to the models usually used in this context.

The dynamics of cold atoms in conservative optical lattices obviously depends on the geometry of the lattice. But very similar lattices may lead to deeply different dynamics. For example, in a 2D optical lattice with a square mesh, the sign of the detuning plays a crucial role: in the blue detuned case, trajectories of an atom inside a well are chaotic for high enough energies. On the contrary, in the red detuned case, chaos is completely inhibited inside the wells. Here, we study in details the dynamical regimes of atoms inside a well of a red detuned lattice, with the aim to understand the dynamical mechanisms leading to the disappearance of chaos. We show that the motions in the two directions of space are frequency locked in most of the phase space, for most of the parameters of the lattice and atoms. This synchronization, not as strict as that of a dissipative system, is nevertheless a mechanism powerful enough to explain that chaos cannot appear in red detuned lattices.

We examine here the classical dynamics of cold atoms in square optical lattices, i.e. lattices obtained with two orthogonal stationary plane waves. Contrary to much of the past studies in this domain, the potential is here time independent and non dissipative. We show that, as a function of the experimental parameters, very different behaviors are obtained, both for the dynamics of atoms trapped inside individual sites, and for atoms travelling between sites: inside the sites, chaos may be a main regime or, on the contrary, may be negligible; outside the sites, chaos sometimes coexists with other regimes. We discuss what are the consequences of these differences on the macroscopic behavior of the atoms in the lattice, and we propose experimental measurements able to characterize these dynamics and to distinguish between the different cases.

We propose a new geometry of optical lattice for cold atoms, namely a lattice made of a 1D stack of dark ring traps. It is obtained through the interference pattern of a standard Gaussian beam with a counter-propagating hollow beam obtained using a setup with two conical lenses. The traps of the resulting lattice are characterized by a high confinement and a filling rate much larger than unity, even if loaded with cold atoms from a MOT. We have implemented this system experimentally, and obtained a lattice of ring traps populated with typically 40 atoms per site with a life time of 30 ms. Applications in statistical physics, quantum computing and Bose-Einstein condensate dynamics are conceivable., Comment: 4 pages, submitted to PRA

A new geometry of optical lattice is proposed, namely a lattice made of a 1D stack of ring traps. It is obtained though the interference pattern of two counterpropagating beams: one of the beam is a standard gaussian beam, while the other one is a hollow beam obtained through a setup with two conical lenses. The resulting lattice is shown to have a high filling rate and a good confinement, so that it could be loaded directly from a MOT with applications in the domain of quantum computing, or with a Bose-Einstein condensate, which would have in this case a 1D ring geometry.

The cloud of cold atoms obtained from a magneto-optical trap is known to exhibit two types of instabilities in the regime of high atomic densities: stochastic instabilities and deterministic instabilities. In the present paper, the experimentally observed deterministic dynamics is described extensively. Three different behaviors are distinguished. All are cyclic, but not necessarily periodic. Indeed, some instabilities exhibit a cyclic behavior with an erratic return time. A one-dimensional stochastic model taking into account the shadow effect is shown to be able to reproduce the experimental behavior, linking the instabilities to a several bifurcations. Erraticity of some of the regimes is shown to be induced by noise.

The cloud of cold atoms obtained from a magneto-optical trap is known to exhibit two types of instabilities in the regime of high atomic densities: stochastic instabilities and deterministic instabilities. In the present paper, the experimentally observed stochastic dynamics is described extensively. It is shown that it exists a variety of dynamical behaviors, which differ by the frequency components appearing in the dynamics. Indeed, some instabilities exhibit only low frequency components, while in other cases, a second time scale, corresponding to a higher frequency, appears in the motion of the center of mass of the cloud. A one-dimensional stochastic model taking into account the shadow effect is shown to be able to reproduce the experimental behavior, linking the existence of instabilities to folded stationary solutions where noise response is enhanced. The different types of regimes are explained by the existence of a relaxation frequency, which in some conditions is excited by noise., Comment: 13 pages, 16 figures, submitted to EPJD

The properties of the hollow beam produced by a conical lens are studied in detail. In particular, the impact of a rounded vertex is examined. It is shown that it could lead to drastic changes in the transverse distribution of the hollow beam, determined by the ratio between the transverse size of the incident beam and the size of the blunt area. An adequate choice for this ratio allows us to either minimize the losses or optimize the distribution symmetry., Comment: 13 pages, 10 figures, submitted to Optics Communications

The paper reports on the observation of a new type of instabilities in the atomic cloud of a magneto-optical trap (MOT). They appear as large amplitude self-oscillations, either periodic or erratic, depending on the parameters. An original model taking into account the shadow effect and an homogeneous distribution of the atoms in the cloud is developped. It allows us to show that these instabilities originate on the one hand from an anomalous Hopf bifurcation, and on the other hand from the extreme sensitivity of the system to noise., Comment: 4 pages, 5 figures, submitted to PRL