BCS-BEC crossover-like phenomena driven by quantum-size effects in quasi-one-dimensional fermionic condensates

Abstract: Quantum confinement is known to influence fermionic condensates, resulting in quantum-size oscillations of superfluid/superconducting properties. Here we show that the impact of quantum-size effects is even more dramatic. Under realistic conditions, a significant phase-space reconfiguration induced by quantum-size effects opens a quasi-molecule channel in the fermionic pairing so that the condensed pairs exhibit features typical of a molecular state. As an illustration we consider a quasi-one-dimensional fermionic condensate, as realized, e.g., in cigar-shaped atomic Fermi gases or superconducting quantum wires. In this case the transverse quantization of the particle motion favors pairing through a coherent superposition of quantum channels that are formed due to the grouping of single-particle levels into a series of well distinguished subbands. Whenever the bottom of a subband approaches the Fermi level, the longitudinal spatial distribution of fermions in a condensed pair becomes strongly localized within the corresponding quantum channel. The fermionic pairs in this channel resemble molecules with bosonic character.