In the previous chapter, we have discussed the effects of the long-range interaction in cold atomic traps and have demonstrated some of its implications on the equilibrium features of the system. In the present chapter, we discuss some of the dynamical effects associated with such Coulomb-like interactions. We will discuss the case of two kind of oscillations: small and large scale oscillations. The first are related with the elementary excitations that can take place in a homogenous system, while the second refer to collective modes of a trapped system, occurring at wavelengths comparable with the size of the system. Centre-of-mass oscillations, Tonks-Dattner modes, breathing modes and surface modes are introduced. We then discuss the nonlinear coupling between different modes in the atom cloud, with emphasis on the coupling between the centre-of-mass oscillation and an hybrid acoustic wave. We also show that the linear mode analysis can be extended to a large spectrum of waves, leading to quasi-linear diffusion in the atom velocity space. Finally, the interesting concept of a phonon laser, and its possible realization in a MOT is briefly discussed.
Dispersion Relation Wigner Function Density Perturbation Magnetic Field Gradient Atomic Cloud
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