Evidence for a common physical origin of the Landau and BEC theories of superfluidity.

There are two renowned theories of superfluidity in liquid (4)He, quite different and each with specific domains of application. In the first, the Landau theory, superflow follows from the existence of a well-defined collective mode supported by dense liquid (4)He, the phonon-roton mode. In the second, superflow is a manifestation of Bose-Einstein condensation (BEC) and phase coherence in the liquid. We present combined measurements of superfluidity, BEC and phonon-roton (P-R) modes in liquid (4)He confined in the porous medium MCM-41. The results integrate the two theories by showing that well-defined P-R modes exist where there is BEC. The two are common properties of a Bose condensed liquid and either can be used as a basis of a theory of superfluidity. In addition, the confinement and disorder suppresses the critical temperature for superfluidity, Tc, below that for BEC creating a localized BEC "phase" consisting of islands of BEC and P-R modes. This phase is much like the pseudogap phase in the cuprate superconductors.