How Many Helium Atoms Are Needed To Make A Superfluid ?

March 31, 1998

The basic understanding of superfluidity has challenged theoretical physicists ever since its discovery in helium 60 years ago. One fundamental question has been the minimum number of atoms needed for superfluidity. The answer to this question was recently provided by spectroscopic experiments performed by the physicist Andrej Vilesov and the Ph.D. student Slava Grebenev, both natives of Russia, working together with Peter Toennies, scientific member and director at the Max-Planck-Institute for Fluid Dynamics in Göttingen. They discovered as reported in the March 27 issue of Science (Vol. 279) that a cluster having just 60 atoms of a helium-four isotope is already a superfluid.

When first confronted with this number Yuri Kagan, the well known director of the Theory Division of the Kurchatov Institute in Moscow said "Impossible!". As a former student of Lev Landau, the famous nestor of Russian theoretical physics who received the Nobel Prize in Physics in 1962 for his pioneering theoretical work on the superfluidity of helium, Kagan argued that superfluidity is by definition a macroscopic phenomenon. The name superfluid derives from the fact that below 2.2K liquid helium can flow through narrow channels without resistance, a property which has close analogies to superconductivity. Another remarkable phenomenon is that superfluid helium is able to defy gravity and creep up and over the walls of a beaker and thereby escape from the container. These and many other manifestations discovered already in 1938 are indeed macroscopic in nature and explain Kagan´s initial reaction. Since experimental tests based on the above macroscopic phenomena with so few atoms are impossible the Göttingen physicists had to devise new ways to explore superfluidity on a microscopic scale.

In a long series of experiments which go back more than ten years they were able to develop methods to produce and characterize molecular beams of small liquid helium droplets consisting of few thousands of atoms inside a high vacuum apparatus. Already in 1990 they found that these droplets were able to capture single foreign molecules or larger well-defined numbers of molecules, depending on the experimental conditions.The molecules then migrate towards the center of the droplets. In 1995 as a result of a bold venturesome experiment they were able to measure sharp spectral lines of embedded SF6 molecules which indicated quite unexpectedly that the molecules rotate freely inside the helium droplets. These and other spectroscopic studies provided evidence that the helium-four droplets have temperatures of only 0.38K. In the recent Science article they report on a new experiment which strongly suggests that the ability of molecules to rotate freely is a result of the superfluidity of the droplets. To demonstrate this they compared the spectrum in a superfluid with that in a normal fluid. For the latter they used droplets consisting of the rare isotope helium-three, which being a Fermion system, only becomes a superfluid at much lower temperatures of 3 millidegrees K and therefore at the helium-three droplet temperatures of 0.10K behaves as an ordinary classical fluid. For these experiments they chose the simple linear molecule OCS (oxygen carbon sulfide). Inside helium-four droplets a very sharp rotational line spectrum was observed whereas in helium-three only a single broad peak was found indicating that, as expected for an ordinary fluid, the rotational motion is strongly impaired by collisions. This experiment provided the key evidence that indeed the phenomenon of free molecular rotations in liquid helium is a new microscopic manifestation of superfluidity which they call "molecular superfluidity".

To determine the critical number of helium-four atoms for molecular superfluidity they then added to the pure helium-three droplets well defined numbers of helium-four atoms. From other experiments and theory they could precisely determine the actual number of atoms picked up. Moreover they had evidence that the helium-four atoms aggregate around the OCS molecule. On the addition of about 60 helium-four atoms the sharp spectral lines reappeared, indicating the return to free rotational motion. 60 atoms are in fact just sufficient to build up a cage consisting of a double layer of helium-four atoms which surround the molecule. The Figure shows the results of a snap shot of a molecular dynamics simulation of such a microscopic cluster inside a helium-three droplet.
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Max-Planck-Gesellschaft

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