A Fermi gas described within the Bardeen—Cooper—Schrieffer theory (BCS) may be converted into a Bose—Einstein condensate (BEC) of composite molecules (dimers) by adiabatically tuning interaction. The sequence of the states that emerges in the process of such a conversion is referred to as the BCS—BEC crossover. We review here the theoretical and experimental results obtained for the BCS—BEC crossover in three- and quasi-two-dimensional quantum gases in the limiting geometry of traps and on optical lattices. We discuss nontrivial phenomena in the hydrodynamics of the superfluid quantum gases and fluids including the collective excitation spectrum in the BCS—BEC crossover, hydrodynamics of the rotating Bose condensates containing a large number of quantized vortices, and the involved and yet unresolved problem of the chiral anomaly in the hydrodynamics of superfluid Fermi systems with an anisotropic p-wave pairing. We also analyze spin-imbalanced quantum gases and the possibilities to realize the triplet p-wave pairing via the Kohn—Luttinger mechanism in those gases. Recent results on two-dimensional Fermi-gas preparation and observation of the fluctuational phenomena related to the Berezinskii—Kosterlitz—Thouless transition in those gases are also reviewed. We briefly discuss the recent experimental discovery of the BCS—BEC crossover and anomalous superconductivity in bilayer graphene and the role of graphene, other Dirac semimetals (such as, for example, bismuth), and 2D optical lattices as potential reference systems that exhibit all of the effects reviewed here.

Keywords: BCS-BEC crossover, hydrodynamics of superfluid quantum fluids and gases, Feshbach resonance, composite fermions and bosons, rotating Bose condensates, chiral anomaly, fermion Goldstone mode, collective excitation spectrum, imbalanced Fermi gas, anomalous pairing, Kohn-Luttinger mechanism, Berezinskii-Kosterlitz-Thouless transition, bilayer graphene PACS: 03.75.Hh, 67.10.−j, 74.20.−z, 74.25.Uv (all) DOI: 10.3367/UFNe.2018.10.038471 URL: https://ufn.ru/en/articles/2019/3/a/ 000469214700001 2-s2.0-85070731309 2019PhyU...62..215K Citation: Kagan M Yu, Turlapov A V "BCS—BEC crossover, collective excitations, and hydrodynamics of superfluid quantum fluids and gases" Phys. Usp. 62 215–248 (2019) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Received: 18th, January 2018, revised: 3rd, October 2018, accepted: 31st, October 2018 Оригинал: Каган М Ю, Турлапов А В «Кроссовер БКШ—БЭК, коллективные возбуждения и гидродинамика сверхтекучих квантовых жидкостей и газов» УФН 189 225–261 (2019); DOI: 10.3367/UFNr.2018.10.038471