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Science

Superfluidity Within a Small Helium-4 Cluster: The Microscopic Andronikashvili Experiment

Slava Grebenev, Jan Peter Toennies, Andrei F. Vilesov

Published Mar 27, 1998• 620 citations
Publisher

Abstract

The infrared spectrum of single oxygen carbon sulfide (OCS) molecules was measured inside large superfluid pure helium-4 droplets and nonsuperfluid pure helium-3 droplets, both consisting of about 10(4) atoms. In the helium-4 droplets, sharp rotational lines were observed, whereas in helium-3 only a broad peak was found. This difference is interpreted as evidence that the narrow rotational lines, which imply free rotations, are a microscopic manifestation of superfluidity. Upon addition of 60 helium-4 atoms to the pure helium-3 droplets, the same sharp rotational lines were found; it appears that 60 is the minimum number needed for superfluidity.

DOI
10.1126/science.279.5359.2083

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The infrared spectrum of single oxygen carbon sulfide (OCS) molecules was measured inside large superfluid pure helium-4 droplets and nonsuperfluid pure helium-3 droplets, both consisting of about 10(4) atoms. In the helium-4 droplets, sharp rotational lines were observed, whereas in helium-3 only a broad peak was found. This difference is interpreted as evidence that the narrow rotational lines, which imply free rotations, are a microscopic manifestation of superfluidity. Upon addition of 60 helium-4 atoms to the pure helium-3 droplets, the same sharp rotational lines were found; it appears that 60 is the minimum number needed for superfluidity.
Many microscopic properties of the only natural superfluid element helium have become available within the last 18 years through a number of novel experiments. The diffraction of matter-waves of small helium clusters has established the unusually large bond distance (5.2 nm) and extremely weak binding energy (10−7 eV) of the dimer and other exotic properties of small helium clusters. The high-resolution spectroscopy of closed-shell chromophore molecules attached to small clusters or embedded inside large superfluid droplets have revealed that as a result of superfluidity, molecules rotate virtually without friction and that only a handful of He atoms are required for microscopic superfluidity. The frictionless translational motion of atoms and molecules inside the droplets has also been observed. These and a number of other experiments demonstrate that helium droplets are the most gentle and coldest of all cryomatrices with enormous potential for a wide range of future applications.
In this paper, quantum fluctuations of a carbonyl sulfide molecule in helium-4 clusters are studied as a function of cluster size N in a small-to-large size regime (2<or=N<or=64). The molecular rotation of the dopant shows nonmonotonic size dependence in the range of 10<or=N<or=20, reflecting the density distribution of the helium atoms around the molecule. The size dependence on the rotational constant shows a plateau for N>or=20, which is larger than the experimental nanodroplet value. Superfluid response of the doped cluster is found to show remarkable anisotropy especially for N<or=20. The superfluid fraction regarding the axis perpendicular to the molecular axis shows a steep increase at N=10, giving the significant enhancement of the rotational fluctuation of the molecule. On the other hand, the superfluid fraction regarding the axis parallel to the molecular axis reaches 0.9 at N=5, arising from the bosonic exchange cycles of the helium atoms around the molecular axis. The anisotropy in the superfluid response is found to be the direct consequence of the configurations of the bosonic exchange cycles.
The first minimum appearing in molecular rotational constants as a function of helium droplet size has been previously associated with the onset of superfluidity in these finite systems. We investigate this relationship by bosonic density functional theory calculations of classical molecular rotors (OCS, N2O, CO, and HCN) interacting with the surrounding helium. The calculated rotational constants are in fair agreement with the existing experimental data, demonstrating the applicability of the theoretical model. Inspection of the spatial evolution of the global phase and density shows the increase in the rotational constant after the first minimum correlates with continuous coverage of the molecule by helium and the appearance of angular phase coherence rather than completion of the first solvent shell. We assign the observed phenomenon to quantum phase transition between a localized state and one-dimensional superfluid, which represents the onset of rotational superfluidity in small helium droplets.
In this paper, quantum fluctuations of a carbonyl sulfide molecule in helium-4 clusters are studied as a function of cluster size N in a small-to-large size regime (2 ≤ N ≤ 64). The molecular rotation of the dopant shows nonmonotonic size dependence in the range of 10≤N≤20, reflecting the density distribution of the helium atoms around the molecule. The size dependence on the rotational constant shows a plateau for N≥20, which is larger than the experimental nanodroplet value. Superfluid response of the doped cluster is found to show remarkable anisotropy especially for N ≤20. The superfluid fraction regarding the axis perpendicular to the molecular axis shows a steep increase at N = 10, giving the significant enhancement of the rotational fluctuation of the molecule. On the other hand, the superfluid fraction regarding the axis parallel to the molecular axis reaches 0.9 at N=5, arising from the bosonic exchange cycles of the helium atoms around the molecular axis. The anisotropy in the superfluid response is found to be the direct consequence of the configurations of the bosonic exchange cycles. © 2007 American Institute of Physics.
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.
What is the minimum number of atoms needed for superfluidity? According to the results of a remarkable molecular spectroscopy experiment, there is definite proof that a system of only 60 atoms can be superfluid. Slava Grebencv and colleagues at the Max Planck Institute for Fluid Dynamics in Göttingen, Germany, found that small molecules dissolved in droplets of liquid helium can rotate freely, just like they do in a vacuum (S Grebencv, J P Tocnnies and A Vilesov 1998 Science 279 2083). The molecules rotate freely because the surrounding helium is a "superfluid" – a liquid without viscosity. In effect, the liquid helium acts as a vacuum.