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A short review is given of recent progress in understanding the demixing transition in a mesoscopic gaseous cloud of bosonic and fermionic alkali atoms under the effect of their mutual repulsions at zero temperature. The mixture is confined inside a magnetic trap exerting external harmonic potentials on the atoms and the bosonic component is taken in a Bose-Einstein condensed state while the fermions are in a spin-polarized state. Main emphasis is placed on the role of the confinement: in a mesoscopic system (i) the phase transition becomes smooth as a function of the driving parameter, which is the boson-fermion  s -wave scattering length; and (ii) various configurations of the phase-separated gaseous cloud are allowed, including some very exotic ones in an anisotropic trap. The transition inside a spherical trap leads to an egg-type structure, with the bosonic condensate being surrounded by a shell of fermions, and is best identified from a sharp upturn of the frequency of low-lying monopolar and dipolar oscillations of fermionic character. This dynamical signature of the transition appears when the overlap between the two components has already started to decrease, but is still quite appreciable. A system of specific experimental interest is the mixture of  6 Li and  7 Li isotopes, whose parameters could be driven towards the phase transition.

Phase Separation in Ultracold Boson–Fermion Mixtures under Confinement