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Lecture notes in physics

Superfluid Fermions: Partial Bosonization in the Particle–Particle Channel

Peter Kopietz, Lorenz Bartosch, Florian Schütz

Published Dec 25, 2009• 0 citations
Publisher
DOI
10.1007/978-3-642-05094-7_12

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We use the functional renormalization group approach with partial bosonization in the particle-particle channel to study the effect of order parameter fluctuations on the BCS-Bose-Einstein condensate (BEC) crossover of superfluid fermions in three dimensions. Our approach is based on a new truncation of the vertex expansion where the renormalization group flow of bosonic two-point functions is closed by means of Dyson-Schwinger equations and the superfluid order parameter is related to the single-particle gap via a Ward identity. We explicitly calculate the chemical potential, the single-particle gap, and the superfluid order parameter at the unitary point and compare our results with experiments and previous calculations.
We study the quantum dynamics of superfluids of bosons hybridized with Cooper pairs near Feshbach resonances and the influence of fermion–boson conversion on Mott states. We derive a set of equations of motion which describe novel low energy dynamics in superfluids and obtain a new distinct branch of gapped collective modes in superfluids which involve anti-symmetric phase oscillations in fermionic and bosonic channels. We also find that Mott states in general are unstable with respect to fermion–boson conversion; particles become delocalized and the off-diagonal long-range order of superfluids can be developed when a finite conversion is present. We further point out a possible hidden order in Mott states. It is shown that the quantum dynamics of Fermi–Bose states can be characterized by either an effective coupled U (1) ⊗ U (1) quantum rotor Hamiltonian in a large- N limit or a coupled XXZ ⊗ XXZ spin Hamiltonian in a single-orbit limit.
In this work we study the particle conductance of a strongly interacting Fermi gas through a quantum point contact. With an atom-molecule two-channel model, we compute the contribution to particle conductance by both the fermionic atoms and the bosonic molecules using the Keldysh formalism. Focusing on the regime above the Fermi superfluid transition temperature, we find that the fermionic contribution to the conductance is reduced by interaction compared with the quantized value for the noninteracting case; while the bosonic contribution to the conductance exhibits a plateau with nonuniversal values that is larger than the quantized conductance. This feature is particularly profound at temperature close to the superfluid transition. We emphasize that the enhanced conductance arises because of the bosonic nature of closed channel molecules and the low dimensionality of the quantum point contact.