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Dashed lines show the profiles at vanishing interactions. Strikingly, the fermionic cloud is much larger than the bosonic cloud with the same atom number; the volume of the clouds differs by a factor of about twenty! This is a remarkable manifestation of the different quantum statistics. a At attractive interspecies interactions the atomic density accumulates in the center until the system undergoes a meanfield collapse, when the interspecies attraction is increased beyond aBF ≈ −450 a0 . Note that aBF = −185 a0 approximately corresponds to the background scattering length between 87 Rb and 40 K (see Sect.

Within the formalism of second quantization it is simple to write down manyparticle ground states. For N noninteracting, spinless bosons with the single-particle ground state ψ E 0 , the many-particle ground state can be directly constructed via | B 1 = |N , 0, 0, . . ≡ √ (aˆ 0† ) N |0, 0, 0, . . N! 9) In this state, all particles occupy the same single-particle state, which is the defining property of a Bose-Einstein condensate (see Fig. 1). In a fermionic N -particle system each single-particle state can only be occupied by a single fermion at most.

The iteration can yield different outcomes: Either the procedure converges and the resulting density distributions constitute the self-consistent solutions of the problem, or the procedure diverges corresponding to an increasing central density for each iteration. The latter case can happen for attractive interspecies interactions and corresponds to a collapse of the mixture [15]. 3 shows a summary of results obtained both for attractively and repulsively interacting Bose-Fermi mixtures at typical experimental parameters.