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Physical Review Letters

Critical Landau Velocity in Helium Nanodroplets

N. Bräuer, Szymon Smolarek, Evgeniy Loginov, David Mateo, Alberto Hernando, Martí Pi, M. Barranco, Wybren Jan Buma, Marcel Drabbels

Published Oct 8, 2013• 76 citations
Publisher

Abstract

The best-known property of superfluid helium is the vanishing viscosity that objects experience while moving through the liquid with speeds below the so-called critical Landau velocity. This critical velocity is generally considered a macroscopic property as it is related to the collective excitations of the helium atoms in the liquid. In the present work we determine to what extent this concept can still be applied to nanometer-scale, finite size helium systems. To this end, atoms and molecules embedded in helium nanodroplets of various sizes are accelerated out of the droplets by means of optical excitation, and the speed distributions of the ejected particles are determined. The measurements reveal the existence of a critical velocity in these systems, even for nanodroplets consisting of only a thousand helium atoms. Accompanying theoretical simulations based on a time-dependent density functional description of the helium confirm and further elucidate this experimental finding.

DOI
10.1103/physrevlett.111.153002

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The best-known property of superfluid helium is the vanishing viscosity that objects experience while moving through the liquid with speeds below the so-called critical Landau velocity. This critical velocity is generally considered a macroscopic property as it is related to the collective excitations of the helium atoms in the liquid. In the present work we determine to what extent this concept can still be applied to nanometer-scale, finite size helium systems. To this end, atoms and molecules embedded in helium nanodroplets of various sizes are accelerated out of the droplets by means of optical excitation, and the speed distributions of the ejected particles are determined. The measurements reveal the existence of a critical velocity in these systems, even for nanodroplets consisting of only a thousand helium atoms. Accompanying theoretical simulations based on a time-dependent density functional description of the helium confirm and further elucidate this experimental finding.
Critical velocity and dissipation mechanism in finite superfluid 4^44He nanodroplets
A hallmark of superfluidity is the frictionless motion of an object below the Landau critical velocity; Whether this concept applies to nanoscale droplets remains unclear. Using time-dependent density functional theory, we investigate the motion of a sodium atom on the surface and inside a superfluid helium nanodroplet. For surface motion, we identify a critical velocity above which energy dissipation through ripplon excitation and the formation of surface-bound quantized vortices leads to rapid deceleration. Inside the droplet, the atom is slowed down to a steady-state velocity that depends on the initial speed, contrasting experiments reporting a critical velocity for dopants ejected from droplets [Phys. Rev. Lett. 111, 153002 (2013)]. Remarkably, the velocity of the ejected atom is nearly independent of its initial velocity. We demonstrate that this behavior results from the bursting of the bubble surrounding the atom at the droplet surface, challenging the previous experimental interpretation.
Helium nanodroplets are considered ideal model systems to explore quantum hydrodynamics in self-contained, isolated superfluids. However, exploring the dynamic properties of individual droplets is experimentally challenging. In this work, we used single-shot femtosecond x-ray coherent diffractive imaging to investigate the rotation of single, isolated superfluid helium-4 droplets containing ~10(8) to 10(11) atoms. The formation of quantum vortex lattices inside the droplets is confirmed by observing characteristic Bragg patterns from xenon clusters trapped in the vortex cores. The vortex densities are up to five orders of magnitude larger than those observed in bulk liquid helium. The droplets exhibit large centrifugal deformations but retain axially symmetric shapes at angular velocities well beyond the stability range of viscous classical droplets.
Abstract In this introductory chapter, we begin by informing the reader about the fascinating history of superfluidity in bulk liquid helium. This is followed by relating attempts in using liquid helium as a low temperature matrix for spectroscopy. After a brief review of the thermodynamic properties of helium in Sect. 1.2, the different types of free jet expansions used in experiments to produce clusters and nanodroplets of different sizes are described in Sect. 1.3. First it is shown how they depend on the nature and location in the phase diagram of the isentropes which determine the course of the expansion. Depending on the four regimes of isentropes, different number sizes and distributions are expected. Next in Sect. 1.4, the results of theoretical and, where available, experimental results on the total energies, excited states, radial density distributions, and temperatures of clusters and droplets are discussed. Finally, in Sect. 1.5 the theoretical and experimental evidence for the superfluidity of nanodroplets is briefly reviewed. For more information on the production and characteristics of nanodroplets, the reader is referred to the chapters in this book and to the reviews in Appendix.
The capture dynamics of a Ne atom by a superfluid helium nanodroplet (((4)He)N=1000; T = 0.37 K), Ne + ((4)He)N→ Ne@((4)He)N', was investigated using a quantum approach (TDDFT (helium) + quantum wave packet (Ne)) at zero angular momentum and a rather wide range of Ne atom initial mean velocities (〈v0〉: 90-1300 m s(-1)). This is probably the first quantum dynamics study focusing on the pick up process and the evolution of the dopant inside the nanodroplet and the second more detailed investigation on this topic. For 〈v0〉 = 210 m s(-1) and above the atom is always captured, but for lower velocities the probability of capture is somewhat below the unity and decreases as 〈v0〉 diminishes. The main energy exchange begins with the collision of the atom with the nanodroplet surface, and the excess of energy placed in the doped nanodroplet is progressively released by the evaporation of a small amount of (4)He atoms. Once the atom has entered into the nanodroplet its mean position follows an oscillatory trajectory, due to multiple sequential collisions with the inner surface of the nanodroplet, and its mean velocity reaches values which are below Landau's critical velocity. This probably corresponds to the general behavior of nanodroplets with a bulk-like region when moderate collision energies (i.e., similar to the ones considered here) are involved. In the future we hope to investigate the influence of angular momentum on the mechanism of the pick up process, using the same quantum dynamics method.