Abstract
Our goal is to understand the phenomena arising in optical lattice fermions at low temperature in an external magnetic field. Varying the field, the attraction between any two fermions can be made arbitrarily strong, where composite bosons form via so-called Feshbach resonances. By setting up strong-coupling equations for fermions, we find that in spatial dimension d>2 they couple to bosons which dress up fermions and lead to new massive composite fermions. At low enough temperature, we obtain the critical temperature at which composite bosons undergo the Bose–Einstein condensate (BEC), leading to BEC-dressing massive fermions. These form tightly bound pair states which are new bosonic quasi-particles producing a BEC-type condensate. A quantum critical point is found and the formation of condensates of complex quasi-particles is speculated over.
Highlights
The attraction between any two fermions can be tuned, as a function of an external magnetic field, and be made so strong that the coupling constant reaches the unitarity limit of infinite s-wave scattering length “a” via a Feshbach resonance
A smooth BCS-Bose-Einstein condensate (BEC) crossover takes place, the Cooper pairs which form in the weak-coupling limit at low temperature and make the system a BCS superconductor, become so strongly bound that they behave like bosonic quasi-particles with a pseudogap at high temperature T ∗
In order to discuss the critical behaviors of the second-order phase transition, we focus our attention on the neighborhood of the critical line (9), where the characteristic correlation length ξ ∼ MB−1 is much larger than the lattice spacing, microscopic details of lattice are physically irrelevant
Summary
The attraction between any two fermions can be tuned, as a function of an external magnetic field, and be made so strong that the coupling constant reaches the unitarity limit of infinite s-wave scattering length “a” via a Feshbach resonance. In order to address strongcoupling fermions at finite temperature T , we incorporate the relevant s-wave scattering physics via a “ 0-range” contact potential in the Hamiltonian for spinor wave function ψ↑,↓(i), which represents a fermionic neutral atom of fermion number “e” that we call “charge”, and ψ↑†,↓(i) represents its “hole” state “−e”, βH = β ( d)ψσ† (i) − ∇2/(2m 2) − μ ψσ(i) i,σ=↑,↓. I β = 1/T , each fermion field ψσ(i) of length dimension [ −d/2], mass m and chemical potential μ is defined at a lattice site “i”.
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