The nature of superfuidity and Bose-Einstein condensation: from liquid ⁴He to dilute ultracold atomic gases (Review Article)

We present a brief overview of crucial historical stages in creation of superfluidity theory and of the current state of the microscopic theory of superfluid ⁴He. We pay special attention to the role of Bose-Einstein condensates (BECs) in understanding of physical mechanisms of superfluidity and identification of quantum mechanical structure of ⁴He superfluid component below -point, in particular — the possibility that at least two types of condensates may appear and coexist simultaneously in superfluid ⁴He. In this context we discuss the properties of the binary mixtures of BECs and types of excitations, which may appear due to intercomponent interaction in such binary mixtures of condensates. We also discuss current status of investigations of persistent currents in toroidal optical traps and present an outlook of our recent findings on this subject