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Physical Review Letters

Atomic Hydrogen in Contact with a Helium Surface: Bose Condensation, Adsorption Isotherms, and Stability

Isaac F. Silvera, Victor V. Goldman

Published Sep 15, 1980• 35 citations
Publisher

Abstract

The energy of interacting spin-polarized atomic hydrogen (${\mathrm{H}}_{\mathrm{\ensuremath{\downarrow}}}$) on a helium surface and the density dependence of the adsorption energy have been calculated, permitting a realistic determination of the adsorption isotherms. Surface interactions are shown to allow Bose-Einstein condensation in the gas. At the Bose-Einstein condensation the surface coverage attains a maximum which is essentially independent of the isotherm temperature. Also calculated is the stability condition for surfaces in magnetic fields. Easily met requirements are found.

DOI
10.1103/physrevlett.45.915

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Physical Review Letters•May 26, 1980•22 citations
The energy of interacting spin-polarized atomic hydrogen (H\ensuremath↓{\mathrm{H}}_{\mathrm{\ensuremath{\downarrow}}}H\ensuremath↓​) on a helium surface and the density dependence of the adsorption energy have been calculated, permitting a realistic determination of the adsorption isotherms. Surface interactions are shown to allow Bose-Einstein condensation in the gas. At the Bose-Einstein condensation the surface coverage attains a maximum which is essentially independent of the isotherm temperature. Also calculated is the stability condition for surfaces in magnetic fields. Easily met requirements are found.
The binding energy of a hydrogen atom to the surface of liquid 4He has been calculated to be at least 0.6K by Mantz and Edwards. This means that the properties of adsorbed spin-polarized hydrogen (H↑), a 2D Bose fluid, may soon be observed experimentally. Since 4He is used as a neutral coating for vessels to contain H↑ gas, adsorption onto the 4He surface may enhance the rate of recombination into H2 molecules. For given temperature and density in the gas, the amount of H↑ adsorbed depends strongly on the H↑-H↑ interaction on the 4He surface. We estimate the interaction in a simple approximation, and find that it limits the surface density to not more than 1014 cm-2. Nevertheless this density should be sufficient for a 2D superfluid transition to be observed, under conditions close to those achieved experimentally.
Current limitations on the density of stabilized spin-polarized deuterium (D\ensuremath{\downarrow}) to \ensuremath{\sim} 1014{10}^{14}1014 atoms/cm3{\mathrm{cm}}^{3}cm3 are shown to arise from condensation on the 4He^{4}\mathrm{He}4He surface and subsequent recombination. A new technique for measuring the adsorption energy is employed to provide the first such measurement for D\ensuremath{\downarrow} on helium, yielding $\frac{{\ensuremath{\epsilon}}_{a}}{{k}_{B}}=2.5\ifmmode\pm\else\textpm\fi{}0.4$ K.
We study three-body recombination in the gas of spin-polarized atomic hydrogen adsorbed on the surface of superfluid helium at temperatures from 45to130mK45\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}130\phantom{\rule{0.3em}{0ex}}\mathrm{mK}45to130mK. The two-dimensional gas is thermally compressed to densities up to $\ensuremath{\approx}4\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$ using the ``cold spot'' method which makes the three-body process the dominant decay channel in the system. We measure the loss rate and surface density of atoms directly and independently and observe the former to be proportional to the third power of the latter. The result for the surface three-body recombination rate constant at 4.6T4.6\phantom{\rule{0.3em}{0ex}}\mathrm{T}4.6T, ${L}_{s}=2.0(7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}25}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{4}∕\mathrm{s}$, significantly reduces the discrepancy between the theory and earlier measurements where the surface density was inferred from the adsorption isotherm. We also measured the three-body rate constant on a 0.1% $^{3}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}$ film and found ${L}_{s}=1.3(4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{4}∕\mathrm{s}$. This larger value is attributed to an increased delocalization of adsorbed hydrogen atoms in the direction normal to the surface.
Under normal circumstances a gas of atomic hydrogen (H) is highly unstable with respect to recombination to molecular hydrogen, H2. We have succeeded in stabilizing a gas of spin polarised hydrogen (H↓) at T = 300 mK in magnetic fields up to 10 Tesla in a superfluid helium coated cell. Densities of at least 1016atoms/cc have already been achieved. H is found to have a surprisingly long life even in zero magnetic field. Evidence points to H↓ remaining in the gaseous form and not liquifying or condensing out on the surfaces to any large extent. The crucial experimental techniques used to stabilize H↓ will be discussed as well as some of the observed properties and expectations of this new Bose gas.
Spin-polarized atomic hydrogen continues to be one of the most promising candidates for Bose condensation of an atomic system. In contrast to liquid helium, hydrogen is gaseous and therefore its density can be changed to vary its behavior from the weakly to the strongly interacting Bose gas. Until now, efforts to Bose condense hydrogen have been thwarted by recombination and relaxation phenomena. After a long introduction to the subject, two promising approaches to observe quantum degenerate behavior are discussed: the microwave trap and a two-dimensional gas of hydrogen. Introduction Since the stabilization of atomic hydrogen as a spin-polarized gas (H↓), reported in 1980 [1], there has been a continuous effort to observe Bose–Einstein condensation (BEC) or other effects of quantum degeneracy in this Bose gas. This challenge has not yet been realized due to the instability of H↓ towards recombination to H 2 or relaxation among hyperfine states as the conditions for BEC are approached. Although this difficulty is formidable, hydrogen presents a unique opportunity to study BEC and the related superfluidity, as it remains a gas to T = 0 [2]. By comparison, 4 He, the only experimentally observed boson fluid, is a strongly interacting superfluid Bose liquid, with little flexibility for varying its density. As a result of the gaseous nature of hydrogen, its density, n , can be varied over several orders of magnitude with the possibility of studying BEC and its relationship to superfluidity, ranging from the weakly to the strongly interacting boson gas.
A model of spin-polarized hydrogen (H\ensuremath{\uparrow}) is treated in which interactions between atoms are neglected while the single-atom Zeeman and hyperfine interactions are treated exactly. These magnetic terms in the Hamiltonian are found to affect substantially the Bose-Einstein condensation and the various thermodynamic variables. Computations are discussed of the condensation temperature, condensate density, and specific heat in order to indicate how changes in magnetic field strength might be expected to affect future measurements on this quantum system.