Abstract
We describe the properties of a mixture of fermionic and bosonic atoms, as they are tuned across a Feshbach resonance associated with a fermionic molecular state. Provided the number of fermionic atoms exceeds the number of bosonic atoms, we argue that there is a critical detuning at which the Bose-Einstein condensate (BEC) is completely depleted. The phases on either side of this quantum phase transition can also be distinguished by the distinct Luttinger constraints on their Fermi surfaces. In both phases, the total volume enclosed by all Fermi surfaces is constrained by the total number of fermions. However, in the phase without the BEC, which has two Fermi surfaces, there is a second Luttinger constraint: the volume enclosed by one of the Fermi surfaces is constrained by the total number of bosons, so that the volumes enclosed by the two Fermi surfaces are separately conserved. The phase with the BEC may have one or two Fermi surfaces, but only their total volume is conserved. We obtain the phase diagram as a function of atomic parameters and temperature, and describe critical fluctuations in the vicinity of all transitions. We make quantitative predictions valid for the case of a narrow Feshbach resonance, but we expect the qualitative features we describe to be more generally applicable. As an aside, we point out intriguing connections between the BEC depletion transition and the transition to the fractionalized Fermi liquid in Kondo lattice models.
Highlights
The Feshbach resonance has emerged as a powerful tool in studying ultracold atoms in regimes of strong interactions
For a Feshbach resonance between two identical fermionic atoms, the many body ground state changes from a Bose-Einstein condensate (BEC) of molecules (ν ≪ 0) to a Bardeen-Cooper-Schrieffer (BCS) superfluid descended from a Fermi gas of atoms (ν ≫ 0)
We find an additional T = 0 quantum phase transition involving the disappearance of the molecular Fermi surface
Summary
The Feshbach resonance has emerged as a powerful tool in studying ultracold atoms in regimes of strong interactions. For a Feshbach resonance between two identical bosonic atoms, it has been argued recently[6,7] that there is a sharp singularity, i.e. a quantum phase transition, in the many body system as a function of ν. Our primary result is that such a mixture of fermionic and bosonic atoms has a quantum phase transition. This transition is a many body effect, and does not occur precisely at ν = 0. It is shown that the system is stable for a broad range of parameters
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