We present precision neutron scattering measurements of the Bose-Einstein condensate (BEC) fraction
n0(T) and the atomic momentum distribution ${n}^{\ensuremath{\star}}(\mathbf{k})$ of liquid
4He as a function of temperature at pressure
p=24 bars. Both the temperature dependence of
n0(T) and of the width of ${n}^{\ensuremath{\star}}(\mathbf{k})$ are determined. The
n0(T) can be represented by ${n}_{0}(T)={n}_{0}(0)[1\ensuremath{-}{(T/{T}_{\ensuremath{\lambda}})}^{\ensuremath{\gamma}}]$ with a small ${n}_{0}(0)=2.80\ifmmode\pm\else\textpm\fi{}0.20$
and large $\ensuremath{\gamma}=13\ifmmode\pm\else\textpm\fi{}2$ for $T<{T}_{\ensuremath{\lambda}}$, indicating a strong interaction. The onset of BEC is accompanied by a significant narrowing of the ${n}^{\ensuremath{\star}}(\mathbf{k})$. The narrowing accounts for 65
of the drop in kinetic energy below ${T}_{\ensuremath{\lambda}}$ and reveals an important coupling between BEC and
k>0 states. The experimental results are well reproduced by path integral Monte Carlo calculations.
A search was made for Bose-Einstein condensation in superfluid
4He using neutron inelastic scattering. A two-component scattering distribution has been resolved for
4He at 1.2 \ifmmode^\circ\else\textdegree\fi{}K giving direct evidence for the existence of the zero-momentum state. Analysis of the measured data leads to a condensate fraction of (2.4 \ifmmode\pm\else\textpm\fi{} 1)%, a value much smaller than previously estimated.
We present neutron-scattering measurements of the momentum distribution of liquid $^{3}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}$ mixtures. The experiments were performed at wave vectors
Q, $26\ensuremath{\leqslant}Q\ensuremath{\leqslant}29\phantom{\rule{0.3em}{0ex}}{\mathrm{\AA{}}}^{\ensuremath{-}1}$, on the MARI time-of-flight spectrometer at the ISIS Facility, Rutherford Appleton Laboratory, a spallation neutron source. Mixtures with
3He concentrations
x between 0 and 20% were investigated both in the superfluid and normal phases. From the data, we extract the Bose-Einstein condensate fraction
n0 and the momentum distributions of
3He and
4He atoms. We find that
n0 increases somewhat above the pure
4He value when
3He is added; e.g., from ${n}_{0}=(7.25\ifmmode\pm\else\textpm\fi{}0.75)%$ at
x=0 to $(11\ifmmode\pm\else\textpm\fi{}3)%$ at
x=15−−20. This agrees with predictions but is less than the only previous measurement. We find a
4He kinetic energy
K4 for pure
4He that agrees with previous determinations.
K4 decreases somewhat with increasing
3He concentration, less than observed previously and found in early calculations but in agreement with a more recent Monte Carlo calculation. The
3He response is not well reproduced by a Fermi-gas momentum distribution,
n(k). Rather an
n(k) having a small step height at the Fermi surface and a substantial high-momentum tail characteristic of a strongly interacting Fermi liquid provides a good fit. This
n(k) is consistent with calculated
n(k). Thus agreement between theory and experiment is obtained comparing
n(k) in contrast to earlier findings based on comparing calculated and observed
3He kinetic energies.
Several microscopic theories point out that Bose-Einstein condensation (BEC), i.e., a macroscopic occupation of the lowest energy single particle state in many-boson systems, may appear also in quantum fluids and solids and that it is at the origin of the phenomenon of superfluidity. Nevertheless, the connection between BEC and superfluidity is still matter of debate, since the experimental evidences indicating a non zero condensate fraction in superfluid helium are only indirect. In the theoretical study of BEC in quantum fluids and solids, perturbative approaches are useless because of the strong correlations between the atoms, arising both from the interatomic potential and from the quantum nature of the system. Microscopic Quantum Monte Carlo simulations provide a reliable description of these systems. In particular, the Path Integral Monte Carlo (PIMC) method is very suitable for this purpose. This method is able to provide exact results for the properties of the quantum system, both at zero and finite temperature, only with the definition of the Hamiltonian and of the symmetry properties of the system, giving an easy picture for superfluidity and BEC in many-boson systems. In this thesis, we apply PIMC methods to the study of several quantum fluids and solids. We describe in detail all the features of PIMC, from the sampling methods to the estimators of the physical properties. We present also the most recent techniques, such as the high-order approximations for the thermal density matrix and the worm algorithm, used in PIMC to provide reliable simulations. We study the liquid phase of condensed 4He, providing unbiased estimations of the one-body density matrix g1(r). We analyze the model for g1(r) used to fit the experimental data, highlighting its merits and its faults. In particular we see that, even if it presents some difficulties in the description of the overall behavior of g1(r), it can provide an accurate estimation of the kinetic energy K and of the condensate fraction n0 of the system. Furthermore, we show that our results for n0 as a function of the pressure are in a good agreement with the most recent experimental results. The study of the solid phase of 4He is the most significant part of this thesis. The recent observation of non classical rotational inertia (NCRI) effects in solid helium has generated big interest in the study of an eventual supersolid phase, characterized at the same time by crystalline order and superfluidity. Nevertheless, until now it has been impossible to give a theoretical model able to describe all the experimental evidences. In this work, we perform PIMC simulations of 4He at high densities, according to different microscopic configurations of the atoms. In commensurate crystals we see that BEC does not appear, our model being able to reproduce the momentum distribution obtained form neutron scattering experiments. In a crystal with vacancies, we have been able to see a transition to a superfluid phase at temperatures in agreement with experimental results if the vacancy concentration is low enough. In amorphous solids, superfluid effects are enhanced but appear at temperatures higher than the experimental estimation for the transition temperature. Finally, we study also metastable disordered configurations in molecular para-hydrogen at low temperature. The aim of this study is to investigate if a Bose liquid other than helium can display superfluidity. Choosing accurately a ¿quantum liquid¿ initial configuration and the dimensions of the simulation box, we have been able to frustrate the formation of the crystal and to calculate the temperature dependence of the superfluid density, showing a transition to a superfluid phase at temperatures close to 1 K.
Since the early days of Bose–Einstein condensates (BECs) in atomic gases, comparisons have been drawn to the other familiar bosonic systems: liquid helium-4 and the Cooper pairs of superconductors. Two of the early questions asked of BECs were whether they had similar coherence properties and whether they were superfluids. In He4, it is rather difficult to study properties of the condensate, such as the condensate fraction, whereas the measurement of superfluidity is fairly straightforward. The opposite has proved true for atomic condensates: The condensate fraction as a function of temperature was found early on, but only recently has their superfluidity been placed on firm footing (see PHYSICS TODAY, November 1999, page 17).