  Quantum-size oscillations of the basic physical characteristics of a confined
fermionic condensate are a well-known phenomenon. Its conventional
understanding is based on the single-particle physics, whereby the oscillations
follow the size-dependent changes in the single-particle density of states.
Here we present a study of a cigar-shaped ultracold superfluid Fermi gas, which
demonstrates an important many-body aspect of the quantum-size effects,
overlooked previously. The many-body physics is revealed in the atypical
crossover from the Bardeen-Cooper-Schrieffer (BCS) superfluid to the
Bose-Einstein condensate (BEC) induced by the size quantization of the particle
motion. Quantized perpendicular spectrum results in the formation of
single-particle subbands (shells) so that the aggregate fermionic condensate
becomes a coherent mixture of subband condensates. Each time when the lower
edge of a subband crosses the chemical potential, the BCS-BEC crossover is
approached in this subband, and the aggregate condensate contains both the BCS
and BEC-like components.
