We are preparing to make the first experimental study of the two-dimensional Bose gas in the regime of quantum degeneracy. The realization is <href="sph.html"atomic hydrogen adsorbed on liquid helium. The superfluid phase transition will be studied optically using Lyman-alpha radiation.
The two-dimensional Bose gas is an important fundamental system in physics and has been the subject of intense theoretical scrutiny . Of particular interest is the relationship between Bose-Einstein condensation and superfluidity. As is well-known, a condensate cannot exist in two dimensions: long-range order is destroyed by phase fluctuations. Paradoxically, superfluidity exists in films of liquid helium. The theoretical explanation is that at low temperature, despite the absence of a true condensate, the atoms of the fluid do comprise a macroscopic quantum entity, or quasi-condensate. A liquid is a strongly-interacting system, however, which precludes a microscopic understanding. Therefore it would be invaluable to do experiments on a weakly-interacting two-dimensional superfluid gas. Such a gaseous superfluid has yet to be realized and, hence, the theoretical picture of a quasi-condensate remains untested. We will make the first experimental study of the two-dimensional Bose gas in the regime of quantum degeneracy.
We will use atomic hydrogen (H) adsorbed on liquid helium, which will be a (new!) superfluid under attainable conditions. H on liquid helium is the ideal system for these experiments because of its solid foundations in existing research. The interaction between H atoms is the best-known in nature. The behaviour of H on helium is also rather well understood. In particular, there is no 2-d liquid phase: H remains gaseous to absolute zero . Apart from being a gas, there are other exciting differences from traditional superfluids. The gas can be studied optically, using light resonant with the Lyman-alpha transition (wavelength 121.6nm). This gives us a sensitive probe with good spatial resolution. Optical spectroscopy can also yield important information via Doppler, Zeeman and interaction effects. The magnetism of H gives us a convenient way to manipulate it. Furthermore, the chemical reactivity of H (H atoms recombine to diatomic hydrogen molecules) provides a probe of the microscopic "structure" of the gas, related to the quasi-condensate density.
The technology for creating samples of H at low temperature is well developed. Research directed towards attaining the Bose-Einstein phase transition in H has led to a thorough understanding of this gas . To suppress recombination, the H is electron-spin polarized by a strong magnetic field; inelastic collisional processes complete the transformation to a stable doubly-polarized state (electron and proton spins parallel). The gas may then be adsorbed on liquid helium to a high density limited only by recombination in three-atom collisions, induced by the weak spin-dipole interaction. Ordinarily this recombination results in heating which is sufficient to prevent the density from approaching the superfluid transition. However, significant improvement in the attainable density of H on helium has been made recently in Turku and Kyoto. Experiments in Kyoto show that quantum degeneracy of 2-d H is now within reach .
To avoid overheating due to recombination we must use an "open geometry", meaning that the superfluid must be confined to a small part of a larger substrate. This allows the newly formed (and highly excited) hydrogen molecules to fly from the recombination site and deposit the recombination energy (4.5 eV per molecule) elsewhere. This confinement will be done magnetically. We have designed a magnetic system which will function both as a source of doubly-polarized H and a magnetic confinement.
The 2-d gas will be studied optically, using light resonant with the hydrogen 1S-2P Lyman-alpha transition, which gives us a sensitive probe with good spatial resolution. The unique cryogenic/Lyman-alpha facility at the UvA is well-suited to this work.
Optical detection of the adsorbed gas is far from trivial. Firstly, there are the technical challenges associated with generating the narrowband Lyman-alpha radiation and bringing it to the sample, which is in a dilution refrigerator at a temperature of 0.1K. Fortunately, these have been surmounted . Secondly, the 2-d gas density will be approximately 1e13 atoms per square centimeter, or 1/100 monolayer, and in addition the optical resonance will be severely broadened due to interaction with the liquid helium. As a result, the optical thickness of the surface is expected to be very low, less than 1/1000. Background scattering of light from the 3-d H gas present in the apparatus will be a serious complication.
Svistunov et al.  first suggested using Lyman-alpha light to detect the Kosterlitz-Thouless (KT) transition to the superfluid phase. They analyzed the optical absorption by the 2-d gas at large detuning (to avoid resonant scattering by the 3-d gas) and showed that optical detection is feasible. The KT transition is manifested through its influence on inelastic processes (recombination) and on the adsorption isotherm. Measurement of the adsorption isotherm is particularly useful, as it gives directly the chemical potential of the 2-d gas - a rather strong test of existing ab initio calculations.
The work proposed here will incidentally yield the first measurement of the optical spectrum of H on liquid helium. A model calculation of the optical absorption by a hydrogen atom adsorbed on helium  indicates that the calculations of Ref. 6 were very conservative. In addition, it appears likely that there exist stable weakly physisorbed states for optically-excited H. These will lead to sharp features in the absorption spectrum which can perhaps be exploited to study the superfluid.
The first experiment will implement the idea of Svistunov et al.  and measure the recombination rate and adsorption isotherm as the density is increased through the KT transition. A brief description of the experiment follows. The entire apparatus is housed in a dilution refrigerator, with the H residing within the bore of a 10T superconducting solenoid. Using standard techniques a sample of doubly-polarized H will be prepared in a buffer volume. This H will be injected into a narrow vertical tube partially filled with liquid helium cooled by a dilution refrigerator to a temperature of 0.1K. At this temperature the H will strongly adsorb on the helium meniscus to form our 2-d gas, which will be confined to a characteristic size of 1mm by a strong magnetic field gradient (190 T/m). The inhomogeneous magnetic field determining the H injection and confinement will be generated by cobalt-iron components magnetized by the strong field of the solenoid.
A beam of Lyman-alpha light, propagating upwards along the axis of the tube, will pass through the surface of the helium at the position of peak gas density. A small fraction of the light will be scattered by the 2-d gas, and part of this will fall onto a phosphor on the front surface of a light pipe, be frequency converted to blue, piped to room temperature and detected by a photomultiplier tube. The scattered intensity is proportional to the 2-d gas density. Recombination will be measured calorimetrically. These data will be analyzed to yield the recombination rate constant as a function of density. In addition, optical spectroscopy will give the density and temperature of the 3-d gas above the surface. This will allow a determination of the adsorption isotherm and provide important information on heating due to recombination.
This research is made possible by a fellowship for Dr. Meritt Reynolds from the Royal Netherlands Academy of Arts and Sciences (KNAW).
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 Yu. Kagan, G.V. Shlyapnikov, I.A. Vartan'yants, and N.A. Glukov, JETP Lett. 35, 477 (1982).
 I.F. Silvera and J.T.M. Walraven, Prog. Low Temp. Phys. X, 139 (1986). D.F. Brewer, ed., Elsevier Sci. Pub.
 A. Matsubara, T. Arai, S. Hotta, J.S. Korhonen, T. Suzuki, A. Masaike, J.T.M. Walraven, T. Mizusaki, and A. Hirai, Physica B 194-196, 899 (1994).
 O.J. Luiten, Ph.D. thesis, University of Amsterdam, 1993.
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 M.W. Reynolds and J.T.M. Walraven, Physica B 194-196, 905 (1994).
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