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Contributions to Plasma Physics

Matter in Strong Magnetic Field: Superfluidity of a Hydrogenlike Gas

M. A. Liberman

Published Jan 1, 1993• 0 citations
Publisher

Abstract

Abstract As is known, so far only helium has appeared to be unique quantum liquid which does not solidify and becomes superfluid at low temperature. The situation is dramatically changed in presence of a strong magnetic field such that the distance between the Landau levels exceeds the Coulomb unit of energy. Under the circumstances, the interaction between hydrogenlike atoms in the triplet ground state is strongly anisotropic and pretty weak. For such a Bose gas of hydrogenlike atoms, there is a possibility of forming a Bose condensate and a superfluid state. The importance of the problem is due to the fact that it arises in various areas of physics, especially in astrophysics and physics of semiconductors. In semiconductors, a high density exciton gas is the unique object for the laboratory studies of the extreme states of matter in a ultrastrong magnetic field, where the “atomic” scale of a magnetic field for the hydrogenlike excitons is of the order of a few Tesla, quite realizable in a laboratory.

DOI
10.1002/ctpp.2150330520

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Physical Review A•May 1, 1998•26 citations
Abstract As is known, so far only helium has appeared to be unique quantum liquid which does not solidify and becomes superfluid at low temperature. The situation is dramatically changed in presence of a strong magnetic field such that the distance between the Landau levels exceeds the Coulomb unit of energy. Under the circumstances, the interaction between hydrogenlike atoms in the triplet ground state is strongly anisotropic and pretty weak. For such a Bose gas of hydrogenlike atoms, there is a possibility of forming a Bose condensate and a superfluid state. The importance of the problem is due to the fact that it arises in various areas of physics, especially in astrophysics and physics of semiconductors. In semiconductors, a high density exciton gas is the unique object for the laboratory studies of the extreme states of matter in a ultrastrong magnetic field, where the “atomic” scale of a magnetic field for the hydrogenlike excitons is of the order of a few Tesla, quite realizable in a laboratory.
It is shown that a system of excitons in a high magnetic field is similar to a weakly nonideal Bose gas and is capable of forming the Bose-Einstein condensate as well as a superfluid state even at a relatively high temperature. The stability of the Bose condensate due to an essential decrease of the interaction between excitons and an increase of their binding energy in a high magnetic field is established. The possible observable effects of the Bose condensate and the interaction of light with the Bose-Einstein condensate of excitons is studied. The appearance of the Bose condensate in a broad range of the densities significantly changes the spectrum of the coupled excitons and photons. The dielectric theory of polaritons which accounts for the new excitation spectrum predicts a number of interesting phenomena.
Spin-polarized atomic hydrogen continues to be one of the most promising candidates for Bose condensation of an atomic system. In contrast to liquid helium, hydrogen is gaseous and therefore its density can be changed to vary its behavior from the weakly to the strongly interacting Bose gas. Until now, efforts to Bose condense hydrogen have been thwarted by recombination and relaxation phenomena. After a long introduction to the subject, two promising approaches to observe quantum degenerate behavior are discussed: the microwave trap and a two-dimensional gas of hydrogen. Introduction Since the stabilization of atomic hydrogen as a spin-polarized gas (H↓), reported in 1980 [1], there has been a continuous effort to observe Bose–Einstein condensation (BEC) or other effects of quantum degeneracy in this Bose gas. This challenge has not yet been realized due to the instability of H↓ towards recombination to H 2 or relaxation among hyperfine states as the conditions for BEC are approached. Although this difficulty is formidable, hydrogen presents a unique opportunity to study BEC and the related superfluidity, as it remains a gas to T = 0 [2]. By comparison, 4 He, the only experimentally observed boson fluid, is a strongly interacting superfluid Bose liquid, with little flexibility for varying its density. As a result of the gaseous nature of hydrogen, its density, n , can be varied over several orders of magnitude with the possibility of studying BEC and its relationship to superfluidity, ranging from the weakly to the strongly interacting boson gas.
Spin-polarized, atomic hydrogen at temperatures below 1K shows promise of becoming the first physically realizable example of a degenerate, weakly interacting Bose gas. Because of the hyperfine structure of the hydrogen atom the Bose condensed state is expected to exhibit novel magnetic properties such as spin wave excitations of the superfluid and possibly a coherent precessing, spontaneous magnetization. This paper discusses a variety of theoretical problems which arise in the study of atomic hydrogen gas. Theories are presented for spin relaxation of the hyperfine levels and for the recombination of H-atoms into H2 molecules. The problem of the binding of H atoms to a surface of superfluid 4He is reviewed together with the theory of surface superfluidity in the hydrogen film proposed by Edwards and Mantz. Finally we consider the problem of superfluidity in the bulk atomic hydrogen gas. We describe the theory of Siggia and Ruckenstein of double Bose condensation into the two lowest hyperfine states and speculate about the possible observable consequences of this phenomenon.
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.
We investigate the hydrogen molecule in a strong parallel magnetic field using a fully numerical Hartree-Fock approach. We find that for magnetic fields below $4.2\ifmmode\times\else\texttimes\fi{}{10}^{4}$ T the ground state of H2{\mathrm{H}}_{2}H2​ is the strongly bound singlet state ${}^{1}{\ensuremath{\Sigma}}_{g},$ for magnetic fields stronger than $3\ifmmode\times\else\texttimes\fi{}{10}^{6}$ T the ground state of the molecule is the strongly bound triplet ${}^{3}{\ensuremath{\Pi}}_{u},$ and for magnetic fields between $4.2\ifmmode\times\else\texttimes\fi{}{10}^{4}$ T and $3\ifmmode\times\else\texttimes\fi{}{10}^{6}$ T the symmetry of the ground state is the triplet state ${}^{3}{\ensuremath{\Sigma}}_{u},$ which is characterized by repulsion at intermediate internuclear distances and by a weak quadrupole-quadrupole interaction between atoms at large internuclear separation. In this region of magnetic field strength the hydrogen molecule is bound weakly, if at all; the hydrogen atoms behave like a weakly nonideal gas of Bose particles and can form a superfluid phase predicted in earlier works [Korolev and Liberman, Phys. Rev. Lett. 72, 270 (1994)]. For magnetic fields between $\ensuremath{\approx}3\ifmmode\times\else\texttimes\fi{}{10}^{5}$ T and $3\ifmmode\times\else\texttimes\fi{}{10}^{6}$ T the triplet state ${}^{3}{\ensuremath{\Pi}}_{u}$ is found to be metastable. This state may be responsible for an unknown excitonic line observed experimentally [Timofeev and Chernenko, JETP Lett. 61, 617 (1995)].