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Physical Review B

Possible transmission experiments with low-velocity helium droplets

A. Wynveen, Keith A. Lidke, Y. Lutsyshyn, J. W. Halleý

Published Feb 9, 2007• 2 citations
Publisher

Abstract

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 $^{4}\mathrm{He}$. 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.

DOI
10.1103/physrevb.75.054506

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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.
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.
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)
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.
We address the collision of two superfluid 4He droplets at non-zero initial relative velocities and impact parameters within the framework of liquid 4He time-dependent density functional theory at zero temperature. Despite the small size of these droplets (1000 He atoms in the merged droplet) imposed by computational limitations, we have found that quantized vortices may be readily nucleated for reasonable collision parameters. At variance with head-on collisions, where only vortex rings are produced, collisions with a non-zero impact parameter produce linear vortices that are nucleated at indentations appearing on the surface of the deformed merged droplet. Whereas for equal-size droplets, vortices are produced in pairs, an odd number of vortices can appear when the colliding droplet sizes are different. In all cases, vortices coexist with surface capillary waves. The possibility for collisions to be at the origin of vortex nucleation in experiments involving very large droplets is discussed. An additional surprising result is the observation of the drops coalescence even for grazing and distal collisions at relative velocities as high as 80 and 40 m/s, respectively, induced by the long-range van der Waals attraction between the droplets.