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.

Bose-Einstein condensation in solid 4He.

We present neutron scattering measurements of the atomic momentum distribution n(k) in solid helium under a pressure p=41 bar (molar volume Vm=20.01+/-0.02 cm3/mol) and at temperatures between 80 and 500 mK. The aim is to determine whether there is Bose-Einstein condensation (BEC) below the critical temperature, Tc=200 mK, where a superfluid density has been observed. Assuming BEC appears as a macroscopic occupation of the k=0 state below Tc, we find a condensate fraction of n0=(-0.10+/-1.20)% at T=80 mK and n0=(0.08+/-0.78)% at T=120 mK, consistent with zero. The shape of n(k) also does not change on crossing Tc within measurement precision.

Quantum momentum distribution and kinetic energy in solid 4He.

We present measurements of neutron scattering from solid 4He at high momentum transfer. The solid is held close to the melting line at molar volume 20.87 cm3/mol and temperature T=1.6 K. From the data, we determine the shape of the momentum distribution, n(k), of atoms in the solid and the leading final state contribution to the scattering. We show that n(k) in this highly anharmonic, quantum solid differs significantly from a Gaussian. The n(k) is more sharply peaked with larger occupation of low momentum states than in a Maxwell-Boltzmann distribution, as found in liquid 4He and predicted qualitatively by path integral Monte Carlo calculations. The atomic kinetic energy is =(24.25+/-0.30) K. If n(k) is assumed to be Gaussian, as is usually the practice, a 10% smaller is obtained.

Dynamics of quantum liquids in confinement, theory and experiment.

Liquid (4)He immersed in porous media such as aerogel, Vycor, and Geltech silica are excellent examples of bosons in disorder and confinement. Of special interest is the impact of disorder on Bose-Einstein condensation (BEC), on the elementary excitations of the superfluid and on their connection to the superfluid properties. Indeed, the modifications induced by disorder can be used to reveal the interdependence of BEC, the excitations and superfluidity. To date, the superfluid properties in porous media are much more completely documented than BEC or the excitations. In this paper, we review measurements of the excitations by neutron scattering, focusing particularly on their temperature dependence and the existence of phonon-roton excitations at higher temperatures. The weight of single excitation response at higher temperatures suggests the existence of localized BEC above the superfluid-normal transition temperature in porous media. We sketch several recent predictions made for BEC, the excitations, and the superfluid properties in disorder. Connections with other "Dirty Bose systems" are made.