BCS-to-BEC crossover from the exact BCS solution

TL;DR

This paper provides an exact analysis of the BCS-to-BEC crossover in fermionic superfluids, revealing a continuous evolution of the ground state and deriving key analytic expressions, with implications for ultracold atomic gases.

Contribution

It introduces an exact ground state solution for the BCS Hamiltonian, unifying the crossover description and deriving analytic formulas for physical quantities.

Findings

Ground state evolves continuously from BCS to BEC regimes.

Derived exact expressions for binding energy and condensate fraction.

Results align with recent ultracold Fermi gas experiments.

Abstract

The BCS-to-BEC crossover, as well as the nature of Cooper pairs, in a superconducting and Fermi superfluid medium is studied from the exact ground state wavefunction of the reduced BCS Hamiltonian. As the strength of the interaction increases, the ground state continuously evolves from a mixed-system of quasifree fermions and pair resonances (BCS), to pair resonances and quasibound molecules (pseudogap), and finally to a system of quasibound molecules (BEC). A single unified scenario arises where the Cooper-pair wavefunction has a unique functional form. Several exact analytic expressions, such as the binding energy and condensate fraction, are derived. We compare our results with recent experiments in ultracold atomic Fermi gases.