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Physical Review Letters

New approach to the observation of the condensate fraction in superfluid helium-4

J. W. Halleý, C. E. Campbell, Clayton F. Giese, K. Goetz

Published Oct 11, 1993• 37 citations
Publisher

Abstract

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 ${\mathit{A}}^{2}$ (first process) and ${\mathit{A}}^{4}$ (second process), respectively, for small A. Aspects of a fully many body calculation and the performance of such an experiment are briefly discussed.

DOI
10.1103/physrevlett.71.2429

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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.
We show that very low velocity droplets can be used to carry out an experiment to test whether condensate mediated transmission processes can occur in a superfluid droplet of 4He^{4}\mathrm{He}4He. By appropriately choosing the droplet radius and temperature, we can eliminate the competing roton, phonon, and ripplon mediated elastic transmission events. Then a calculation shows that if a few percent or more of the incident atoms experience anomalous condensate mediated transmission, the effects should be detectable in the droplet trajectories. We consider two forms of the experiment, involving a freely falling droplet in ambient vapor in the first instance and an oscillating droplet in a magnetic trap in the second.
The classical integral cross sections of large superfluid 4HeN{}^{4}{\mathrm{He}}_{N}4HeN​ droplets and the number of atoms in the droplets ${(N=10}^{3}\ensuremath{-}{10}^{4})$ have been measured in molecular beam scattering experiments. These measurements are in good agreement with the cross sections predicted from density functional calculations of the radial density distributions. By using a simple model for the density profile a 10--90 % surface thickness of about 6--8 \AA{} is extracted directly from the data.
Free superfluid helium droplets constitute a versatile medium for a diverse range of experiments in physics and chemistry that extend from studies of the fundamental laws of superfluid motion to the synthesis of novel nanomaterials. In particular, the emergence of quantum vortices in rotating helium droplets is one of the most dramatic hallmarks of superfluidity and gives detailed access to the wave function describing the quantum liquid. This review provides an introduction to quantum vorticity in helium droplets, followed by a historical account of experiments on vortex visualization in bulk superfluid helium and a more detailed discussion of recent advances in the study of the rotational motion of isolated, nano- to micrometer-scale superfluid helium droplets. Ultrafast X-ray and extreme ultraviolet scattering techniques enabled by X-ray free-electron lasers and high-order harmonic generation in particular have facilitated the in situ detection of droplet shapes and the imaging of vortex structures inside individual, isolated droplets. New applications of helium droplets ranging from studies of quantum phase separations to mechanisms of low-temperature aggregation are discussed.
Quantum fluids are able to flow past obstacles without creating drag and through channels without any resistance. This superfluidity is a consequence of Bose–Einstein condensation, a process in which all the particles gather in the same, lowest-energy quantum state. At low flow velocities, energy exchanges between the obstacle and the fluid are forbidden because of the twin requirements of energy and momentum conservation. As the flow speed is increased, however, the superfluidity breaks down at some critical velocity above which excitations in the fluid can occur. These excitations can be phonons (i.e. quantized vibrations), vortices or, in the case of superfluid liquid helium, rotons (see Rotons: a low-temperature puzzle by Russell Donnelly Physics World February 1997 p25)
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.
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.