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Physical Review Letters

Bose Condensation in Spin-Polarized Atomic Hydrogen

Eric D. Siggia, Andrei E. Ruckenstein

Published May 26, 1980• 65 citations
Publisher

Abstract

A phenomenological description of spin-polarized hydrogen is proposed in terms of two Bose fields which correspond in the low-density limit to the two lowest atomic hyperfine states. Experiments should initially populate both states and the equilibration time of the relative population will be long. When Bose condensation occurs in both states, a spontaneous coherent magnetization perpendicular to the stabilizing field will appear that may be observable in a magnetic resonance experiment.

DOI
10.1103/physrevlett.44.1423

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Physical review. B, Condensed matter•Apr 1, 1981•23 citations
A phenomenological description of spin-polarized hydrogen is proposed in terms of two Bose fields which correspond in the low-density limit to the two lowest atomic hyperfine states. Experiments should initially populate both states and the equilibration time of the relative population will be long. When Bose condensation occurs in both states, a spontaneous coherent magnetization perpendicular to the stabilizing field will appear that may be observable in a magnetic resonance experiment.
A phenomenological description of spin-polarized hydrogen, suggested by the microscopic Hamiltonian, is proposed that includes two Bose particles which correspond in the low density limit to the two lowest hyperfine states. Experiments are expected to initially populate both states, and equilibration times will be long. When Bose condensation occurs in both states a spontaneous coherent magnetization perpendicular to the stabilizing field will appear ; that should be readily observable in a simple magnetic resonance experiment, Field inhomogeneities should not broaden the resonance signal in such an experiment, contrary to one's experience with uncondensed systems.
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.
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.
A calculation is presented of the relaxation rate T 1 -1 between the lower two branches of the atomic hyperfine states in spin-polarized atomic hydrogen H↓ below the Bose-Einstein condensation temperature T 0 . We find that T 1 -1 has a maximum between T =0 and T 0 , which is due to appearance of additional relaxation processes mediated by atoms in the condensed state. Theoretical estimation of T 1 is of the order of a minute with a magnetic field ∼100 kG and with density of H ↓∼10 18 atoms/cm 3 .
A model of spin-polarized hydrogen (H\ensuremath{\uparrow}) is treated in which interactions between atoms are neglected while the single-atom Zeeman and hyperfine interactions are treated exactly. These magnetic terms in the Hamiltonian are found to affect substantially the Bose-Einstein condensation and the various thermodynamic variables. Computations are discussed of the condensation temperature, condensate density, and specific heat in order to indicate how changes in magnetic field strength might be expected to affect future measurements on this quantum system.