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Extra resources for Atomic, Molecular, and Optical Physics
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 . 3 shows a summary of results obtained both for attractively and repulsively interacting Bose-Fermi mixtures at typical experimental parameters.