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Bulletin of the American Physical Society

Variational calculations of coupling of an incident helium atom to a slab of superfluid helium four

C. E. Campbell, J. W. Halleý, Stephen Robert Hoon

Published Apr 1, 1995• 0 citations
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Abstract

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.

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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 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.
We present a phenomenological analysis of an experiment to observe the condensate fraction of helium-4 by firing low-energy pulses of helium atoms at suspended droplets of the superfluid and observing the resulting emission of helium atoms from the fluid. Emission occurs through a conventional process in which rotons are produced and propagate to the other side of the droplet, and through a second process depending on the existence of the condensate. If A is the area of the incoming beam, the cross section scales with A2{\mathit{A}}^{2}A2 (first process) and A4{\mathit{A}}^{4}A4 (second process), respectively, for small A. Aspects of a fully many body calculation and the performance of such an experiment are briefly discussed.
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.
The ground state of homogeneous, superfluid - 4 He–normal- 3 He mixtures is studied by Fixed-Node Diffusion Monte Carlo simulations. The condensate fraction of the 4 He component only depends on the 3 He concentration through its effect on the average density. Slight deviations of the structural properties from previous variational results, obtained within the Average Correlation Approximation (ACA), are discussed. The momentum distribution and effective mass of the Fermi ( 3 He) component are also calculated.