Condensation of Fermionic Pairs
In this chapter, we discuss the many-body theory for fermions with an attractive interaction. We focus in particular on the phase transition to the superfluid state. To this end, we use the functional formalism to elegantly incorporate the Bardeen-Cooper-Schrieffer order parameter into our theory by means of the Hubbard-Stratonovich transformation. The traditional approach used by Bardeen, Cooper, and Schrieffer, which is based on a variational wavefunction to minimize the second-quantized Hamiltonian for interacting fermions, has been left as Exercise 6.6. We determine the critical temperature, the gapped quasiparticle dispersion and the ther-modynamic potential of the superfluid state with the use of mean-field theory. Since the interatomic interaction between fermionic atoms is precisely tunable with the use of a Feshbach resonance, which is discussed in more detail in Chap. 17, it turns out to be possible to study both experimentally and theoretically a crossover between a Bardeen-Cooper-Schrieffer (BCS) superfluid and a Bose-Einstein condensate (BEC) of diatomic molecules. This is the last topic of the chapter.
KeywordsCritical Temperature Josephson Junction Cooper Pair Feshbach Resonance Thouless Criterion
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