BECBCS

The BEC-BCS crossover, sometimes referred to as the BECBCS crossover, is a phenomenon in quantum many-body physics observed in ultracold fermionic gases. It describes a smooth evolution between a Bose-Einstein condensate of tightly bound fermion pairs and a Bardeen-Cooper-Schrieffer superfluid of loosely bound Cooper pairs, driven by tuning the strength and sign of the interparticle interaction.

Experimentally, the crossover is realized by exploiting a Feshbach resonance to tune the s-wave scattering length a between opposite-spin fermions. A dimensionless control parameter 1/(kF a), with kF the Fermi wave number, tracks the crossover from positive a (BEC side) to negative a (BCS side).

On the BEC side (a>0), fermions bind into diatomic molecules that behave as bosons and can undergo Bose-Einstein condensation. Molecule-molecule interactions and finite density lead to a molecular superfluid described at low energy by bosonic theories. On the BCS side (a<0), pairing is weak and the system is described by BCS-like superfluidity of overlapping Cooper pairs; the pair size exceeds the interparticle spacing.

Between these limits lies the unitary regime, where |a| is large and the scattering length diverges. In this regime the system exhibits universal thermodynamic behavior largely independent of microscopic details. The crossover has been studied theoretically with mean-field approaches and fluctuation corrections, as well as with quantum Monte Carlo methods, and is probed experimentally through spectroscopy, collective modes, equation of state measurements, and observation of vortices in ultracold gases.