We present a path integral Monte Carlo study of the global superfluid fraction and local superfluid density in cylindrically symmetric reservoirs of liquid
4He separated by nanoaperture arrays. The superfluid response to both translations along the axis of symmetry (longitudinal response) and rotations about the cylinder axis (transverse response) are computed, together with radial and axial density distributions that reveal the microscopic inhomogeneity arising from the combined effects of the confining external potential and the $^{4}\mathrm{He}{\ensuremath{-}}^{4}\text{He}$ interatomic potentials. We make a microscopic determination of the length scale of decay of superfluidity at the radial boundaries of the system by analyzing the local superfluid density distribution to extract a displacement length that quantifies the superfluid mass displacement away from the boundary. We find that the longitudinal superfluid response is reduced in reservoirs separated by a septum containing sufficiently small apertures compared to a cylinder with no intervening aperture array, for all temperatures below ${T}_{\ensuremath{\lambda}}$. For a single aperture in the septum, a significant drop in the longitudinal superfluid response is seen when the aperture diameter is made smaller than twice the empirical temperature-dependent
4He healing length, consistent with the formation of a weak link between the reservoirs. Increasing the diameter of a single aperture or the number of apertures in the array results in an increase of the superfluid density toward the expected bulk value.
Motivated by the search for an experimentally realizable high density and strongly interacting one-dimensional quantum liquid, we have performed quantum Monte Carlo simulations of bosonic helium-4 confined inside a nanopore with cylindrical symmetry. By implementing two numerical estimators of superfluidity corresponding to capillary flow and the rotating bucket experiment, we have simultaneously measured the finite size and temperature superfluid response of
4He to the longitudinal and rotational motion of the walls of a nanopore. Within the two-fluid model, the portion of the normal liquid dragged along with the boundaries is dependent on the type of motion, and the resulting anisotropic superfluid density plateaus far below unity at
T=0.5K. The origin of the saturation is uncovered by computing the spatial distribution of superfluidity, with only the core of the nanopore exhibiting any evidence of phase coherence. The superfluid core displays a scaling behavior consistent with Luttinger liquid theory, thereby providing an experimental test for the emergence of a one-dimensional quantum liquid.
We present path integral Monte Carlo (PIMC) calculations of the superfluid fraction, ${\ensuremath{\rho}}_{S}/\ensuremath{\rho}$, and the one-body density matrix (OBDM) [Bose-Einstein condensation (BEC)] of liquid
4He confined in nanopores. Liquid
4He in nanopores represents a dense Bose liquid at reduced dimension and in disorder. The goal is to determine the effective dimensions of the liquid in the pores. It is to test whether observed properties, such as a very low onset temperature for superflow,
Tc, can be predicted by a standard, static PIMC ${\ensuremath{\rho}}_{S}/\ensuremath{\rho}$. We simulate a cylinder of liquid of diameter
dL surrounded by 5 \AA{} of inert solid
4He in a nanopore of diameter
d;
d=dL+10A˚. We find a PIMC ${\ensuremath{\rho}}_{S}(T)/\ensuremath{\rho}$ and OBDM that scales as a 1D fluid Luttinger liquid at extremely small liquid pore diameters only,
dL=6A˚. At this
dL, the liquid fills the pore in a 1D line at the center of the pore and there is no PIMC superflow. In the range $8\ensuremath{\le}{d}_{L}\ensuremath{\le}22\phantom{\rule{0.28em}{0ex}}\AA{}$ the PIMC ${\ensuremath{\rho}}_{S}(T)/\ensuremath{\rho}$ scales as a 2D liquid. In this
dL range the liquid fills the pores in 2D-like cylindrical layers. The crossover from no superflow at
d=16A˚ to superflow at $d\ensuremath{\ge}18\phantom{\rule{0.28em}{0ex}}\AA{}$ agrees with experiment. There is a crossover to 3D scaling at larger ${d}_{L}\ensuremath{\simeq}22\phantom{\rule{0.28em}{0ex}}\AA{}$. In the range $8\ensuremath{\le}{d}_{L}\ensuremath{\le}22\phantom{\rule{0.28em}{0ex}}\AA{}$, the
Tc predicted using the Kosterlitz-Thouless 2D scaling criterion of the OBDM agrees well with that obtained from ${\ensuremath{\rho}}_{S}(T)/\ensuremath{\rho}$. These results suggest that the superflow observed in small pore media is standard static superflow with the low
Tc arising from its 2D character. An operational onset temperature,
TBEC, for BEC can be defined as the temperature at which there is a crossover from exponential to algebraic decay in the OBDM. This definition leads to a ${T}_{\mathrm{BEC}}\ensuremath{\ge}{T}_{c}$ as observed in larger pore media.
Arrays of nanoscale apertures have been found to exhibit fascinating quantum phenomena such as the Josephson effect and collective quantized phase-slippage. To be in the Josephson regime, the aperture size must be comparable to the healing length of the 4He order parameter. For 50nm apertures this regime is attained ∼mK below T λ . Collective phase slippage occurs at considerably lower temperatures. Fabricating aperture arrays with appropriate properties (strength, temporal stability and reproducibility) at these length scales has been a long-standing goal for our group. Here, we present the techniques used thus far, based on recent work performed at the Cornell Nanoscale Facility. We discuss some issues that arise and their possible solutions.
Below Tλ = 2.17 K, bulk 4He is a superfluid and has a non-zero Bose-Einstein condensate fraction. This work will focus primarily on how phenomena such as superfluidity, Bose condensation and superfluid vortices are manifested in microscopic, inhomogeneous helium systems. Path Integral Monte Carlo is a powerful method for calculating the equilibrium properties of quantum systems at finite temperature. We have achieved linear scaling of computer time with number of particles through the use of neighbor lists, allowing us to simulate systems of several thousand atoms. We have derived a local superfluid estimator and used it to examine the microscopic superfluid response around a molecule rotating in a helium nanodroplet. We found that the first solvation layer is well-described by a two dimensional superfluid, with thermal excitations occuring at a lower temperature than in bulk helium. The effective moment of inertia of a linear impurity in a helium droplet is calculated, and compared with experimental scattering results. In addition, we calculated the vortex formation energy for both pure droplets and droplets doped with linear impurities, and found that the linear impurities had a negligible impact on the formation energy. A possible spectroscopic signature of vortices in doped helium droplets was suggested. After deriving a local estimator, we calculated the condensate fraction throughout the free helium surface of a semi-infinite slab. These results, along with densitydensity correlation functions, were used to characterize the surface excitations and calculate the extent to which ripplons are present. In addition, the ripplon dispersion relation was calculated using imaginary-time correlation functions, and found to be lll in good agreement with experimental results. Finally, we have calculated the Dey be-Waller factor in solid helium for a range of temperatures and densities, and compared the scaling behavior with the predictions of harmonic theory. The first non-Gaussian contribution to the density distribution was calculated.
We consider 4He particles confined in a nanoscale quasi-one-dimensional channel in the liquid density range and numerically calculate the total energy per particle and the superfluid fraction by an imaginary time path integral Monte Carlo method. TBEC at which the total energy drops owing to particle exchange, shifts to a lower value with decreasing channel diameter, and disappears below a diameter of 0.48 nm. It was found that TBEC is close to the superfluid onset temperature observed in the torsional oscillator experiment. In addition, the superfluid fraction along the channel grows slowly below TBEC. Its magnitude decreases with increasing channel length, and the superfluid coherence in terms of thermodynamics disappears in infinitely long channels.