Localized Bose-Einstein condensation of ⁴He confined in nanoporous media

⁴He confined in nanoporous media is an excellent model boson system in a confinement potential. We have studied the superfluid and thermodynamic properties of ⁴He confined in a porous glass that has nanopores of 2.5 nm diameter. It is shown that the confinement of ⁴He in nanopores produces a new quantum state, the localized Bose-Einstein condensation (LBEC) state, and markedly alters the pressuretemperature (P-T) phase diagram. In the LBEC state the global phase coherence is destroyed by strong atomic correlation or by the random potential of a substrate. The formation of LBEC leads to an anomalous reduction of the superfluid transition temperature T _c, determined by the torsional oscillator technique, and the behavior of a quantum phase transition near 0 K. The contributions of roton and phonon excitations to the heat capacity provide definitive evidence of the LBEC state.