Three-body recombination in two-dimensional atomic hydrogen gas J. Järvinen, J. Ahokas, S. Jaakkola, and S. Vasilyev Wihuri Physical Laboratory, Department of Physics, University of Turku, 20014 Turku, Finland Received 13 June 2005; published 16 November 2005 We study three-body recombination in the gas of spin-polarized atomic hydrogen adsorbed on the surface of superfluid helium at temperatures from 45 to 130 mK. The two-dimensional gas is thermally compressed to densities up to 4  10 12 cm -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 4.6 T, L s = 2.07  10 -25 cm 4 / 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 He- 4 He film and found L s = 1.34  10 -24 cm 4 / s. This larger value is attributed to an increased delocalization of adsorbed hydrogen atoms in the direction normal to the surface. DOI: 10.1103/PhysRevA.72.052713 PACS numbers: 34.50.s, 67.65.z, 32.70.Jz, 76.60.Jx I. INTRODUCTION Three-body recombination is an efficient tool to probe statistical correlations in quantum gases. It has been demon- strated in experiments with 87 Rb 1,2 and two-dimensional 2D spin-polarized atomic hydrogen 3 that appearance of a condensate in a Bose gas is accompanied by the reduction of the three-body recombination loss. On the other hand, three- body recombination appeared to be the most serious obstacle in achievement of high densities in the gas of spin-polarized hydrogen H↓. Compression experiments of bulk H↓ have shown that this process may lead to a strong overheating of the sample cell surface or even to a thermal runaway 4–7. Thus it has thwarted the achievement of Bose-Einstein con- densate BEC in bulk H↓ gas confined by material walls. The values of the surface three-body recombination constant obtained in several measurements 4,5,8 are quite consistent with each other, but exceed the theoretical results of de Goey et al. 9 by an order of magnitude. Two methods of local compression have been utilized to reach quantum degeneracy in two-dimensional H↓ gas. The highest values of the quantum degeneracy parameter reached by magnetic compression 3 were  =  2  9. Here  is the surface density and  is the thermal de Broglie wave- length. However, due to large field gradients, the magneti- cally compressed surface gas could not be studied directly. Thermal compression, known as the “cold spot” method, uses the enhanced adsorption of the H↓ gas at a colder sur- face. It does not require field gradients and allows a direct detection of the surface atoms by means of magnetic reso- nance. In our first experiments on the thermal compression of 2D H↓ 10 we attained   1.5. We also estimated that the three-body recombination rate constant is at least an or- der of magnitude smaller than the values obtained in earlier indirect measurements 4,5,8. The total recombination rate due to three-body recombination was found to be so small that we could not study it in detail. Thus it was not possible to conclude whether it is at all a limitation to the achieve- ment of higher  by the thermal compression techniques. In the present work we eliminated most of the uncertain- ties to make accurate and reliable measurement of the surface three-body recombination rate constant. Electron- spin resonance 11 was used for direct detection of thermally compressed H↓ gas adsorbed on liquid helium. Three-body recombination was made the dominant density decay channel by increasing the size of the cold spot and reducing the rates of undesired one-body and two-body relaxation to a negligible level. We found the value L s = 2.07  10 -25 cm 4 / s for the recombination rate constant at temperatures around 100 mK and revealed a weak tem- perature dependence of L s . For H↓ adsorbed on 3 He- 4 He mixture films we observed three-body recombination to be much faster with L s = 1.34  10 -24 cm 4 /s. Our results are in fair agreement with the calculations of de Goey et al. 9 bringing down the discrepancy between the theory and ex- periment. Finally, we discuss the limitations set by three- body recombination to the achievement of high quantum de- generacy by the thermal compression method. II. BACKGROUND The loss rate Rt of atoms due to their recombination into molecules is related to the density n of the gas confined in a volume V by 12 1 V Rt 1 V dN dt =- Gn - Kn 2 - Ln 3 . 1 Here G, K, and L are the first-, second-, and third-order loss rate constants, respectively, according to the number of at- oms taking part in a single recombination or relaxation with subsequent recombination event. Recombination may occur in the bulk gas as well as on the sample cell walls, and the rate constants in Eq. 1 are in general sums of the surface and volume contributions. The loss rate due to the surface processes can be also expressed through the bulk density using the adsorption isotherm which in its classical limit reads PHYSICAL REVIEW A 72, 052713 2005 1050-2947/2005/725/0527137/$23.00 ©2005 The American Physical Society 052713-1