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Physical review. B, Condensed matter

Degeneracy effects on the relaxation and recombination of adsorbed doubly polarized atomic hydrogen

Henk T. C. Stoof, M. Bijlsma

Published Jan 1, 1994• 6 citations
Publisher

Abstract

We determine the influence of the Kosterlitz-Thouless transition on the stability of doubly spin-polarized atomic hydrogen adsorbed on a superfluid helium film and find that the lifetime of the gas is enhanced dramatically in the superfluid phase. Moreover, the relevant rate constants have a discontinuous behavior at the critical point. The observation of these effects is an unambiguous way to establish the achievement of the phase transition experimentally.

DOI
10.1103/physrevb.49.422

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We determine the influence of the Kosterlitz-Thouless transition on the stability of doubly spin-polarized atomic hydrogen adsorbed on a superfluid helium film and find that the lifetime of the gas is enhanced dramatically in the superfluid phase. Moreover, the relevant rate constants have a discontinuous behavior at the critical point. The observation of these effects is an unambiguous way to establish the achievement of the phase transition experimentally.
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We study the decay of magnetically trapped doubly spin-polarized atomic hydrogen in the density and temperature regime of the Bose-Einstein phase transition and calculate the temperature and magnetic field dependence of all relevant relaxation rate constants ${G}_{\mathrm{dd}\ensuremath{\rightarrow}\ensuremath{\kappa}\ensuremath{\lambda}}$. At the transition temperature Tc{T}_{c}Tc​ the rate constants have a discontinuous second derivative with respect to T. Below Tc{T}_{c}Tc​ they show a pronounced decrease relative to the extrapolated above-Tc{T}_{c}Tc​ values, the observation of which is a clear signal for the experimental realization of Bose-Einstein condensation.
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.
We argue that helium film-mediated hydrogen-hydrogen interactions strongly reduce the magnitude of cold collision shifts in spin-polarized hydrogen adsorbed on a helium film. With plausible assumptions about experimental parameters this can explain (i) the 2 orders of magnitude discrepancy between previous theory and recent experiments and (ii) the anomalous dependence of the cold collision frequency shifts on the film's 3He covering. The mediated interaction is attractive, suggesting that in current experiments the gas will become unstable before reaching the Kosterlitz-Thouless transition.
The possibility of superfluidity in a film of spin-polarized atomic hydrogen adsorbed at the surface of the hydrogen-containing vessel is studied. It is shown that the transition to the superfluid phase occurs as a topological phase transition. A criterion for the transition of the hydrogen film into the superfluid (but not crystalline) phase is established. It is shown that the superfluid transition can occur only when the interaction constant γ, related to the interaction potential of hydrogen atoms by the relation V(ρ1 − ρ2) = γδ(p1 − p2), satisfies the inequality γ ≲ πħ2/m, where m is the mass of a hydrogen atom. The transition temperature is found.
We review the recent activity in the theoretical description of spin-polarized atomic hydrogen and its isotopes at very low temperatures. Spin-polarized hydrogen is the only system in nature that remains stable in the gas phase even in the zero temperature limit due to its small mass and weak interatomic interaction. Hydrogen and its heavier isotope tritium are bosons, the heavier mass of tritium producing a self-bound (liquid) system at zero temperature. The other isotope, deuterium, is a fermion with nuclear spin one making possible the study of three different quantum systems depending on the population of the three degenerate spin states. From the theoretical point of view, spin-polarized hydrogen is specially appealing because its interatomic potential is very accurately known making possible its precise quantum many-body study. The experimental study of atomic hydrogen has been very difficult due to its high recombination rate, but it finally led to its Bose-Einstein condensate state in 1998. Degeneracy has also been observed in thin films of hydrogen adsorbed on the 4He surface allowing for the possibility of observing the Berezinskii–Kosterlitz–Thouless superfluid transition.