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Physical Review Letters

Variational Monte Carlo Studies of the Rate of Transmission of an Atomic Helium Beam through a Slab of Superfluid Helium by a Condensate Mediated Process

A. K. Setty, J. W. Halleý, C. E. Campbell

Published Nov 17, 1997• 18 citations
Publisher

Abstract

We report variational Monte Carlo calculations which give amplitudes and phases of the reflected and transmitted components of states representing scattering of helium atoms normally incident on a superfluid ${}^{4}\mathrm{He}$ slab. The wave function describes a previously postulated condensate mediated process [J. W. Halley et al., Phys. Rev. Lett. 71, 2429 (1993)] and the results are consistent with uncertainty principle arguments suggesting that the transmission time for thin (but macroscopic) samples will be independent of slab thickness.

DOI
10.1103/physrevlett.79.3930

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We report variational Monte Carlo calculations which give amplitudes and phases of the reflected and transmitted components of states representing scattering of helium atoms normally incident on a superfluid 4He{}^{4}\mathrm{He}4He slab. The wave function describes a previously postulated condensate mediated process [J. W. Halley et al., Phys. Rev. Lett. 71, 2429 (1993)] and the results are consistent with uncertainty principle arguments suggesting that the transmission time for thin (but macroscopic) samples will be independent of slab thickness.
In previous work on the interaction of single helium atoms with a slab of superfluid helium the authors found a large amplitude, dependent on the condensate fraction, for transmission with re-emission of a helium atom at the other side of the slab. Here they report a variational formulation of the problem which permits a time dependent calculation and which does not require any perturbation expansion. The variational principle involves a minimization of the expectation value of the square of the difference H-E. They will present preliminary results of a variational Monte Carlo calculation using a simple variational form for the wave function.
We describe a measurement of the transmission probability of 4He atoms through a freely suspended slab of superfluid 4He at low temperatures. In our experiment the slab is realized by using an array of parallel cylindrical holes of diameter 51 microm in a glass disc of thickness 190 microm. By controlling the chemical potential, the holes can be made to fill or empty with liquid, and the surface curvature varied. We have measured the transmission of atom beams, generated by a thin-film heater and detected with a sensitive bolometer, through this structure. The results show that the dominant transmission channel is atom-R+ roton-atom with a probability p approximately 0.12 and that R+ rotons can undergo total internal reflection at the free liquid surfaces.
Path Integral Monte Carlo was used to calculate the Bose-Einstein condensate fraction at the surface of a helium film at T = 0:77 K, as a function of density. Moving from the center of the slab to the surface, the condensate fraction was found to initially increase with decreasing density to a maximum value of 0.9, before decreasing. Long wavelength density correlations were observed in the static structure factor at the surface of the slab. A surface dispersion relation was calculated from imaginary-time density-density correlations. Similar calculations of the superfluid density throughout He-4 droplets doped with linear impurities (HCN)(sub n) are presented. After deriving a local estimator for the superfluid density distribution, we find a decreased superfluid response in the first solvation layer. This effective normal fluid exhibits temperature dependence similar to that of a two-dimensional helium system.
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.