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.     

Phonons, rotons, and layer modes of liquid 4He in aerogel

We report the first observation of two-dimensional layer modes in both fully filled and partially filled aerogel. Using complementary high-energy resolution and high statistical precision neutron scattering instruments, and two different 87% porous aerogel samples, we show that the three-dimensional (3D) phonon-roton excitation energies and lifetimes of liquid 4He in aerogel are the same as in bulk 4He within current precision. The layer modes are the excitations that distinguish aerogel from the bulk rather than a difference in the 3D roton energy.     

Excitations of metastable superfluid 4He at pressures up to 40 bars

Neutron scattering measurements of the fundamental excitations of liquid 4He confined in 44 A pore diameter gelsil glass at pressures up to 40 bars in the wave vector range 0.41.6 A(-1), especially the rotons, are observed up to complete solidification of all the liquid at a pressure of approximately 40 bars where the roton vanishes. At and above a pressure of 35.1 bars, Bragg peaks are observed, indicating coexistence of liquid and solid in the pores at pressures 35 less than or approximately equal P less than or approximately equal 40 bars.     

Crystallization of the charged Bose gas at 0 K

From variational upper bounds of the ground state energies of the fluid and solid phases, we estimate that charged bosons melt at r_s ≈ 135, while charged fermions melt around r_s ≈ 70.