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Journal of Experimental and Theoretical Physics Letters

Coherence and recombination in two-dimensional atomic hydrogen on the surface of superfluid 4He

A. I. Safonov, S. S. Demukh, I. I. Safonova, I. I. Lukashevich

Published Jan 1, 2007• 0 citations

Abstract

Experimental results on the achievement of high degrees of quantum degeneration in two-dimensional atomic hydrogen (2D H↓) by the magnetic-compression method are analyzed by taking into account current data on the binding energy E a = 1.14(1) K of hydrogen atoms with the 4He surface and the constant K ab of the two-particle exchange recombination of adsorbed H atoms. The behavior of pair and three-particle correlation functions, as well as the transverse delocalization of the wavefunction of adsorbed atoms due to their interaction with each other, is taken into account self-consistently. A new mechanism of cooling of the compression region by means of the flow of H atoms on the helium surface with the subsequent evaporation and emission from a magnetic trap is proposed. This mechanism prevails at high densities, whereas the heat transfer at low densities occurs owing mainly to the interaction of ripplons with the phonons of the helium film. Existing data corroborate the achievement of the phase density σλ2 ≳ 10, which is certainly higher than the density necessary for both the arrangement of local coherence in 2D H↓ and its transition to the superfluid state. The results agree with the representations on quasi-condensation; however, direct evidence of this phenomenon is not revealed. The probability of three-particle dipole recombination that is corrected for the quantum correlation and delocalization is equal to 7(2) × 10−26 cm4 s−1 (T = 0.15, …, 0.21 K, B = 6.6 T, and σλ2 = 1, …, 9). The results are compared with other theoretical and experimental data.

DOI: 10.1134/s0021364006210107

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Experimental results on the achievement of high degrees of quantum degeneration in two-dimensional atomic hydrogen (2D H↓) by the magnetic-compression method are analyzed by taking into account current data on the binding energy E a = 1.14(1) K of hydrogen atoms with the 4He surface and the constant K ab of the two-particle exchange recombination of adsorbed H atoms. The behavior of pair and three-particle correlation functions, as well as the transverse delocalization of the wavefunction of adsorbed atoms due to their interaction with each other, is taken into account self-consistently. A new mechanism of cooling of the compression region by means of the flow of H atoms on the helium surface with the subsequent evaporation and emission from a magnetic trap is proposed. This mechanism prevails at high densities, whereas the heat transfer at low densities occurs owing mainly to the interaction of ripplons with the phonons of the helium film. Existing data corroborate the achievement of the phase density σλ2 ≳ 10, which is certainly higher than the density necessary for both the arrangement of local coherence in 2D H↓ and its transition to the superfluid state. The results agree with the representations on quasi-condensation; however, direct evidence of this phenomenon is not revealed. The probability of three-particle dipole recombination that is corrected for the quantum correlation and delocalization is equal to 7(2) × 10−26 cm4 s−1 (T = 0.15, …, 0.21 K, B = 6.6 T, and σλ2 = 1, …, 9). The results are compared with other theoretical and experimental data.

We study three-body recombination in the gas of spin-polarized atomic hydrogen adsorbed on the surface of superfluid helium at temperatures from

45\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}130\phantom{\rule{0.3em}{0ex}}\mathrm{mK}

. 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

45\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}130\phantom{\rule{0.3em}{0ex}}\mathrm{mK}

, ${L}_{s}=2.0(7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}25}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{4}∕\mathrm{s}$, 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.

We describe experiments where two-dimensional (2D) atomic hydrogen gas is compressed thermally at a small ``cold spot'' on the surface of superfluid helium and detected directly with electron-spin resonance. We reach surface densities up to $5\ifmmode\times\else\texttimes\fi{}{10}^{12}{\mathrm{cm}}^{\ensuremath{-}2}$ at temperatures $\ensuremath{\approx}100\mathrm{mK}$ corresponding to the maximum 2D phase-space density $\ensuremath{\approx}1.5.$ By independent measurements of the surface density and its decay rate we make a direct determination of the three-body recombination rate constant and get the upper bound ${L}_{3b}\ensuremath{\lesssim}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}25}{\mathrm{cm}}^{4}/\mathrm{s}$ which is an order of magnitude smaller than previously reported experimental results.

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 have performed magnetic compression experiments with the two-dimensional gas of hydrogen atoms on liquid

{}^{4}\mathrm{He}

at

T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}120--200\mathrm{mK}

. For 2D phase-space densities higher than 3, the probability of three-body dipole recombination is observed to decrease gradually by an order of magnitude in comparison to its low-density value ${K}_{\mathrm{bbb}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}8.4(3.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}25}{\mathrm{cm}}^{4}{\mathrm{s}}^{\ensuremath{-}1}$. This is attributed to local coherence developing in a 2D quasicondensate. We have also determined the value $U/k\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}5.1(5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}\mathrm{K}{\mathrm{cm}}^{2}$ for the mean-field energy of the gas.

Possible acoustic modes in a superfluid 2D gas of hydrogen atoms adsorbed on the surface of liquid helium at T ≲ 0.1 K are considered depending on the oscillation frequency and times of energy and momentum transfers both between 2D subsystems of hydrogen atoms and ripplons and into the bulk liquid or substrate. Analogues of the usual and second sounds are realized in 2D hydrogen at high frequencies. In the case of weak coupling with the bulk liquid and substrate, ripplons provide an addition to the normal hydrogen component, which leads to a change in the speed of the second sound. In the most interesting range of low frequencies, an analogue of the fourth sound is realized, when ripplons and the normal hydrogen component are immobile and only the superfluid hydrogen component moves. In this case, when the rate of heat transfer into the bulk liquid is much lower than the sound frequency, oscillations of the temperature of hydrogen can be observed in phase with density oscillations. Methods for exciting acoustic modes are discussed.

The experimental realization of a thin layer of spin-polarized hydrogen H↓ adsorbed on top of the surface of superfluid (4)He provides one of the best examples of a stable, nearly two-dimensional (2D) quantum Bose gas. We report a theoretical study of this system using quantum Monte Carlo methods in the limit of zero temperature. Using the full Hamiltonian of the system, composed of a superfluid (4)He slab and the adsorbed H↓ layer, we calculate the main properties of its ground state using accurate models for the pair interatomic potentials. Comparing the results for the layer with the ones obtained for a strictly 2D setup, we analyze the departure from the 2D character when the density increases. Only when the coverage is rather small the use of a purely 2D model is justified. The condensate fraction of the layer is significantly larger than in 2D at the same surface density, being as large as 60% at the largest coverage studied.