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The Journal of Physical Chemistry Letters

Probing the Superfluid Response of para-Hydrogen with a Sulfur Dioxide Dopant

Tao Zeng, Grégoire Guillon, Joshua T. Cantin, Pierre–Nicholas Roy

Published Jul 7, 2013• 21 citations
Publisher

Abstract

We recently presented the first attempt at using an asymmetric top molecule (para-water) to probe the superfluidity of nanoclusters (of para-hydrogen) [ Zeng , T. ; Li , H. ; Roy , P.-N. J. Phys. Chem. Lett. 2013 , 4 , 18 - 22 ]. Unfortunately, para-water could not be used to probe the para-hydrogen superfluid response. We now report a theoretical simulation of sulfur dioxide rotating in para-hydrogen clusters and show that this asymmetric top can serve as a genuine probe of superfluidity. With this probe, we predict that as few as four para-hydrogen molecules are enough to form a superfluid cluster, the smallest superfluid system to date. We also propose the concept of "exchange superfluid fraction" as a more precise measurement. New superfluid scenarios brought about by an asymmetric top dopant and potential experimental measurements are discussed.

DOI
10.1021/jz401188j

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We recently presented the first attempt at using an asymmetric top molecule (para-water) to probe the superfluidity of nanoclusters (of para-hydrogen) [ Zeng , T. ; Li , H. ; Roy , P.-N. J. Phys. Chem. Lett. 2013 , 4 , 18 - 22 ]. Unfortunately, para-water could not be used to probe the para-hydrogen superfluid response. We now report a theoretical simulation of sulfur dioxide rotating in para-hydrogen clusters and show that this asymmetric top can serve as a genuine probe of superfluidity. With this probe, we predict that as few as four para-hydrogen molecules are enough to form a superfluid cluster, the smallest superfluid system to date. We also propose the concept of "exchange superfluid fraction" as a more precise measurement. New superfluid scenarios brought about by an asymmetric top dopant and potential experimental measurements are discussed.
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 interplay between magic number stabilities and superfluidity of small para-hydrogen clusters with sizes N=5N = 5N=5 to 40 and temperatures $0.5 K \leq T \leq 4.5 $K is explored with classical and quantum Path Integral Monte Carlo calculations. Clusters with N<26N < 26N<26 and T ≤1.5K\leq 1.5 K≤1.5K have large superfluid fractions even at the stable magic numbers 13, 19, and 23. In larger clusters, superfluidity is quenched especially at the magic numbers 23, 26, 29, 32, and 37 while below 1 K, superfluidity is recovered for the pairs (27,28)(27,28)(27,28), (30,31)(30,31)(30,31), and (35,36)(35,36)(35,36). For all clusters superfluidity is localized at the surface and correlates with long exchange cycles involving loosely bound surface molecules.
We study by quantum Monte Carlo simulations the local superfluid response of small (up to 27 molecules) parahydrogen clusters, down to temperatures as low as 0.05 K. We show that at low temperature superfluidity is not confined at the surface of the clusters, as recently claimed by Khairallah et al. [Phys. Rev. Lett. 98, 183401 (2007)10.1103/PhysRevLett.98.183401]. Rather, even clusters with a pronounced shell structure are essentially uniformly superfluid. Superfluidity occurs as a result of long exchange cycles involving all molecules.
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.
We perform detailed analytical and numerical studies of a recently proposed method for a spectroscopic measurement of the superfluid fraction of an ultracold atomic gas [N. R. Cooper and Z. Hadzibabic, Phys. Rev. Lett. 104, 030401 (2010)]. Previous theoretical work is extended by explicitly including the effects of nonzero temperature and interactions, and assessing the quantitative accuracy of the proposed measurement for a one-component Bose gas. We show that for suitably chosen experimental parameters the method yields an experimentally detectable signal and a sufficiently accurate measurement. This is illustrated by explicitly considering two key examples: First, for a weakly interacting three-dimensional Bose gas it reproduces the expected result that below the critical temperature the superfluid fraction closely follows the condensate fraction. Second, it allows a clear quantitative differentiation of the superfluid and the condensate density in a strongly interacting Bose gas.