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Physical Chemistry Chemical Physics

Quantum dynamics of the pick up process of atoms by superfluid helium nanodroplets: the Ne + ( 4 He) 1000 system

Arnau Vilà, Miguel González, R. Mayol

Published Dec 1, 2015• 17 citations

Abstract

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.

DOI: 10.1039/c5cp04176g

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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.

Critical velocity and dissipation mechanism in finite superfluid

^4

He 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.

Though vortices are an unavoidable presence in bulk superfluid helium, they have not been observed to date in helium nanodroplets. The energy and angular momentum of both straight and curved vortex states of a helium nanodroplet are examined as a function of droplet size. For droplets in the size range of many experiments, it is found that during the pickup of heavy solutes, a significant fraction of events deposit sufficient energy and angular momentum to form a straight vortex line. Curved vortex lines exist down to nearly zero angular momentum and energy, and thus could in principle form in almost any collision. Further, the coalescence of smaller droplets during the cooling by expansion could also deposit sufficient angular momentum to form vortex lines. Despite their high energy, most vortices are predicted to be stable at the final temperature (0.38 K) of helium nanodroplets due to lack of decay channels that conserve both energy and angular momentum.

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.

The desorption of excited rubidium atoms off the surface of helium nanodroplets is studied in detail using femtosecond time-resolved photoion and photoelectron imaging spectroscopy in combination with quantum wave-packet simulations. The good agreement of the measured time-dependent velocity distributions with the simulation when exciting the Rb dopant atoms into the

6p

state supports the pseudodiatomic model for the Rb-He droplet interaction, even on the level of quantum wave-packet dynamics. Time-resolved photoelectron spectra reveal the partitioning of excitation energy into the dopant and the droplet degrees of freedom.

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.