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Physics of many-body systems where particles are restricted to move in twospatial dimensions is challenging and even controversial: On one hand, neitherlong-range order nor Bose condensation may appear in infinite uniform 2Dsystems at finite temperature, on the other hand this does not prohibitsuperfluidity or superconductivity. Moreover, 2D superconductors, such ascuprates, are among the systems with highest critical temperatures. Ultracoldatoms are a platform for studying 2D physics. Uniquely to other physicalsystems, quantum statistics may be completely changed in an ultracold gas: anatomic Fermi gas may be smoothly crossed over into a gas of Bose molecules (ordimers) by tuning interatomic interactions. We review recent experiments wheresuch crossover has been demonstrated as well as critical phenomena in theFermi-to-Bose crossover. We also present simple theoretical models describingthe gas at different points of the crossover and compare the data to these andmore advanced models.

Fermi-to-Bose crossover in a trapped quasi-2D gas of fermionic atoms