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arXiv:cond-mat/0303496 · Physical Review A

Thermal compression of two-dimensional atomic hydrogen gas

Sergey A. Vasilyev, Jarno Järvinen, A. I. Safonov, S. Jaakkola

Published Feb 18, 2004• 14 citations
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Abstract

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.

DOI
10.1103/physreva.69.023610

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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.

Journal of Experimental and Theoretical Physics Letters•Jan 1, 2007•0 citations
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×\else\texttimes\fi1012cm\ensuremath−25\ifmmode\times\else\texttimes\fi{}{10}^{12}{\mathrm{cm}}^{\ensuremath{-}2}5\ifmmode×\else\texttimes\fi1012cm\ensuremath−2 at temperatures \ensuremath≈100mK\ensuremath{\approx}100\mathrm{mK}\ensuremath≈100mK corresponding to the maximum 2D phase-space density \ensuremath≈1.5.\ensuremath{\approx}1.5.\ensuremath≈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 L3b\ensuremath≲2\ifmmode×\else\texttimes\fi10\ensuremath−25cm4/s{L}_{3b}\ensuremath{\lesssim}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}25}{\mathrm{cm}}^{4}/\mathrm{s}L3b​\ensuremath≲2\ifmmode×\else\texttimes\fi10\ensuremath−25cm4/s which is an order of magnitude smaller than previously reported experimental results.
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.
Doubly polarized hydrogen has been produced up to densities of 2\ifmmode\times\else\texttimes\fi{}1018{10}^{18}1018 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ with the use of a compression technique. Samples were compressed up to five orders of magnitude into small bubblelike volumes under a column of liquid helium. This technique enabled us to study the volume decay of a bubble at almost constant gas density for minutes. The analysis of the volume decay of such a bubble is discussed. A bulk three-body recombination process was observed with rate constant C3{C}_{3}C3​=[7(2)]\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}39}$ cm6{\mathrm{cm}}^{6}cm6 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$, as well as bulk electronic b\ensuremath{\rightarrow}c relaxation with rate constant Gbcv{G}_{\mathrm{bc}}^{v}Gbcv​\ensuremath{\downarrow}=[12(4)]\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}16}$ cm3{\mathrm{cm}}^{3}cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$. The nature of the three-body process is analyzed with a set of extended rate equations. The samples were very delicate and rapid compressions could result in explosions.
We have performed magnetic compression experiments with the two-dimensional gas of hydrogen atoms on liquid 4He{}^{4}\mathrm{He}4He at T=120−−200mKT\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}120--200\mathrm{mK}T=120−−200mK. 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.
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Spin-polarized atomic hydrogen (H↓) gas at low temperatures (<0.5 K) has been studied using Electron Spin Resonance (ESR) techniques which allow direct measurements of the densities of H atoms in each of the two lower hyperfine states (a and b). It has been demonstrated that ESR can be made to yield accurate and detailed information about the decay of H↓ densities in time. Crucial to the analysis of the data is the ability to confine the sample of H↓, gas inside the liquid ⁴He coated microwave cavity where the magnetic field and temperature are well known. Measurements of K[sub aa] and K[sub ab], the two surface recombination rate constants, and their ratio γ=K[sub aa]/K[sub ab] have been made and from these results the binding energy of H on liquid ⁴He has been extracted. Also reported are the results of the first detailed study of the one-body surface relaxation rate which we find is due to microscopic magnetic impurities in the cell walls. Theoretical calculations of the two-body dipole-dipole relaxation rate of H↓ in the gas and on the surface are also presented.
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.