ABSTRACT
Fermions and Formation of Trimers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381 10.4 Crystalline Molecular Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387
10.4.1 Born-Oppenheimer Potential in a Many-Body System of Molecules of Heavy and Light Fermions . . . . . . . . . . . . . . . . . . . . . . . . . . 387
10.4.2 Gas-Crystal Quantum Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390 10.4.3 Molecular Superlattice in an Optical Lattice . . . . . . . . . . . . . . . . . . . . . . 391
10.5 Concluding Remarks and Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393
The field of quantum gases is rapidly expanding in the direction of ultracold clouds of fermionic atoms, with the goal of revealing novel macroscopic quantum states
and achieving various regimes of superfluidity. The initial idea was to achieve the Bardeen-Cooper-Schrieffer (BCS) superfluid phase transition in a two-component Fermi gas, which requires attractive interactions between the atoms of different components. Then, in the simplest version of this transition, at sufficiently low temperatures, fermions belonging to different components and with opposite momenta on the Fermi surface form correlated (Cooper) pairs in the momentum space. This leads to the appearance of a gap in the single-particle excitation spectrum and to the phenomenon of superfluidity (e.g., Ref. [1]). In a dilute ultracold two-component Fermi gas, the most efficient formation is that of Cooper pairs due to the attractive intercomponent interaction in the s-wave channel (negative s-wave scattering length a). However, for typical values of a, the superfluid transition temperature is extremely low. For this reason, the efforts of many experimental groups have been focused on modifying the intercomponent interaction using Feshbach resonances. The scattering length a near a Feshbach resonance can be tuned from −∞ to +∞. This has led to exciting developments (see Ref. [2] for review), such as the direct observation of superfluid behavior in the strongly interacting regime (n|a|3 1, where n is the gas density) through vortex formation [3], and the study of the influence of imbalance between the two components of the Fermi gas on superfluidity [4-8].
