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Journal of Physics C Solid State Physics

Inhomogeneous Bose condensation in spin-polarised hydrogen

H. Stenschke

Published Feb 29, 1988• 0 citations
Publisher

Abstract

The author assumes that Bose condensation of spin-aligned hydrogen is enhanced near the helium-coated containment walls, and represent this enhancement by adding a surface term to the Ginzburg-Landau free energy of the system. In this way he discusses inhomogeneous Bose condensation and calculate the order parameter profile and the surface free energy.

DOI
10.1088/0022-3719/21/6/001

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The author assumes that Bose condensation of spin-aligned hydrogen is enhanced near the helium-coated containment walls, and represent this enhancement by adding a surface term to the Ginzburg-Landau free energy of the system. In this way he discusses inhomogeneous Bose condensation and calculate the order parameter profile and the surface free energy.
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.
Experimental efforts to produce a Bose Einstein condensed (BEC) gas of spin-polarized atomic hydrogen have been intensely pursued since 1980. Initial efforts studied hydrogen in contact with superfluid helium surfaces. In order to avoid the limiting wall recombination a static magnetic trap was developed which utilizes magnetic barriers to isolate atoms from the van der Wals walls. In this approach traps can be filled to about 10{sup 14} atoms/cm{sup 3} for which the critical temperature is in the region of 20-30 {mu}K. However, approaching BEC conditions, a new instability dominates the behavior. The authors have developed a new type of electromagnetic trap, a microwave (mw) trap in which the trapped atoms are in the ground spin-state so that at low temperature relaxation to a barrier state is strongly suppressed and BEC should be attainable. The shallow mw trap has recently been demonstrated experimentally for the cesium atom. Because the mw trap is so shallow it is necessary to precool the atoms for loading. The authors are constructing a hybrid trap in which the atoms are cooled in a static trap and then transferred to a mw trap where they can be further evaporatively cooled in an effort to achieve BEC.more » This trap should have density limits in the region of 10{sup 16} to 10{sup 17}/cm{sup 3} due to three-body recombination. A second, promising approach is in a 2-D geometry for which in finite sized systems BEC is allowed. Hydrogen atoms are confined to a superfluid helium surface by the absorption potential to form a 2-D gas. Although recombination is an important process on helium surfaces, recently the authors have shown that only a very small fraction of the recombination energy is coupled into the surface. With an appropriate geometry the recombination energy can be removed from the sample region to suppress heating to a negligible level. Furthermore in 2-D a magnetic field can have a maximum so that atoms can be confined to a very small area.« less
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.
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.
The density profiles for an interacting gas of atomic hydrogen in an inhomogeneous axial magnetic field are determined by extending the Gross-Pitaevskii theory to finite temperature. The profiles can be used as an identifying feature of Bose-Einstein condensation for all TTT. Radial inhomogeneities in the field are also treated.
We present arguments that the low density surface region of self-bounded superfluid 4He{}^{4}\mathrm{He}4He systems is an inhomogeneous dilute Bose gas, with almost all of the atoms occupying the same single-particle state at T=0T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0T=0. Numerical evidence for this complete Bose-Einstein condensation was first given by the many-body variational calculations of 4He{}^{4}\mathrm{He}4He droplets by Lewart, Pandharipande, and Pieper in 1988 [Phys. Rev. B 37, 4950 (1988)]. We show that the low density surface region can be treated rigorously using a generalized Gross-Pitaevskii equation for the Bose order parameter.