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arXiv:physics/0312041 · Physical Review Letters

Evaporative Cooling of Helium Nanodroplets with Angular Momentum Conservation

Kevin K. Lehmann, Adriaan M. Dokter

Published Apr 27, 2004• 35 citations
arXivHTMLPDF

Abstract

Evaporative cooling of helium nanodroplets is studied with a statistical rate model that includes, for the first time, angular momentum conservation. While the final temperature of the droplets is almost identical to that previously predicted and later observed, the distribution of total droplet energy and angular momentum states is vastly more excited than a canonical distribution at the same temperature. It is found that the final angular momentum of the droplets is highly correlated with the initial direction, and that a significant fraction of the alignment of the total angular momentum should be transferred to the rotational angular momentum of an embedded molecule.

DOI
10.1103/physrevlett.92.173401

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Evaporative cooling of helium nanodroplets is studied with a statistical rate model that includes, for the first time, angular momentum conservation. While the final temperature of the droplets is almost identical to that previously predicted and later observed, the distribution of total droplet energy and angular momentum states is vastly more excited than a canonical distribution at the same temperature. It is found that the final angular momentum of the droplets is highly correlated with the initial direction, and that a significant fraction of the alignment of the total angular momentum should be transferred to the rotational angular momentum of an embedded molecule.
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.
Helium nanodroplets are considered ideal model systems to explore quantum hydrodynamics in self-contained, isolated superfluids. Rotation of a superfluid droplet is manifested as a collection of quantum vortices. Here, the authors use single-shot femtosecond X-ray coherent diffractive imaging to investigate the shapes and vorticity of rotating superfluid 4{}^{4}4He droplets. They find that most of the diffraction contours exhibit noticeable ellipticity. A smaller but still significant number of distorted diffraction contours are marked by regions of high intensity concentrated along the direction of the long axis in the diffraction image, indicating the presence of extremely deformed 4{}^{4}4He droplets. Forward modeling of the diffraction images shows that the shapes of superfluid 4{}^{4}4He droplets are very similar to their classical counterparts. In particular, the existence of both axially symmetric (oblate) and, for higher angular momenta, two-lobed (triaxial prolate) droplets is revealed. The latter shapes are strongly deformed compared to the spheroidal bodies that are expected for smaller rotational speeds. The observed shapes provide direct access to the droplet angular momenta, angular velocities, and estimated number of quantum vortices inside the 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.
A significant fraction of superfluid helium nanodroplets produced in a free-jet expansion has been observed to gain high angular momentum resulting in large centrifugal deformation. We measured single-shot diffraction patterns of individual rotating helium nanodroplets up to large scattering angles using intense extreme ultraviolet light pulses from the FERMI free-electron laser. Distinct asymmetric features in the wide-angle diffraction patterns enable the unique and systematic identification of the three-dimensional droplet shapes. The analysis of a large data set allows us to follow the evolution from axisymmetric oblate to triaxial prolate and two-lobed droplets. We find that the shapes of spinning superfluid helium droplets exhibit the same stages as classical rotating droplets while the previously reported metastable, oblate shapes of quantum droplets are not observed. Our three-dimensional analysis represents a valuable landmark for clarifying the interrelation between morphology and superfluidity on the nanometer scale.
We experimentally demonstrate that the rotation of molecules embedded in helium nanodroplets can be controlled with an optical centrifuge, allowing for the study of molecular dynamics inside the strongly interacting many-body environment of superfluid helium at variable levels of rotational excitation. By doping the droplets with dimers of nitric oxide, (NO)_{2}, and measuring the degree of their centrifuge-induced alignment as a function of time, we show both the forced in-field rotation of molecules in a continuous range of frequencies, as well as the field-free resonant rotation with a long nanosecond-scale decay. The ability to control and monitor the rotational dynamics of molecular rotors inside the superfluid medium may shed new light on superfluidity and the interaction of superfluids with defects at the atomic level.