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Physical Review Letters

Elementary Excitations of Bose-Condensed, Spin-Aligned Atomic Hydrogen

A. J. Berlinsky

Published Aug 8, 1977• 24 citations
Publisher

Abstract

Ground-state properties and elementary excitations of superfluid spin-aligned atomic H are studied using methods adapted from the theory of liquid $^{4}\mathrm{He}$. The ground state is a $k=0$ condensate of the $|\ensuremath{\downarrow} (\mathrm{electron}), \ensuremath{\uparrow} (\mathrm{proton})〉$ hyperfine state with a small admixture of $|\ensuremath{\uparrow}\ensuremath{\downarrow}〉$ due to the hyperfine interaction. Excitations can also be labeled approximately by their hyperfine states. ${\ensuremath{\phi}}_{\ensuremath{\downarrow}\ensuremath{\uparrow}}(k)$ excitations are phononlike. ${\ensuremath{\phi}}_{\ensuremath{\downarrow}\ensuremath{\uparrow}}(k)$ and ${\ensuremath{\phi}}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}(k)$ are free-particle-like with energy gaps, and ${\ensuremath{\phi}}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}(k)$ excitations resemble spin waves.

DOI
10.1103/physrevlett.39.359

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Ground-state properties and elementary excitations of superfluid spin-aligned atomic H are studied using methods adapted from the theory of liquid 4He^{4}\mathrm{He}4He. The ground state is a k=0k=0k=0 condensate of the ∣\ensuremath↓(electron),\ensuremath↑(proton)〉|\ensuremath{\downarrow} (\mathrm{electron}), \ensuremath{\uparrow} (\mathrm{proton})〉∣\ensuremath↓(electron),\ensuremath↑(proton)〉 hyperfine state with a small admixture of ∣\ensuremath↑\ensuremath↓〉|\ensuremath{\uparrow}\ensuremath{\downarrow}〉∣\ensuremath↑\ensuremath↓〉 due to the hyperfine interaction. Excitations can also be labeled approximately by their hyperfine states. \ensuremathϕ\ensuremath↓\ensuremath↑(k){\ensuremath{\phi}}_{\ensuremath{\downarrow}\ensuremath{\uparrow}}(k)\ensuremathϕ\ensuremath↓\ensuremath↑​(k) excitations are phononlike. \ensuremathϕ\ensuremath↓\ensuremath↑(k){\ensuremath{\phi}}_{\ensuremath{\downarrow}\ensuremath{\uparrow}}(k)\ensuremathϕ\ensuremath↓\ensuremath↑​(k) and \ensuremathϕ\ensuremath↑\ensuremath↓(k){\ensuremath{\phi}}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}(k)\ensuremathϕ\ensuremath↑\ensuremath↓​(k) are free-particle-like with energy gaps, and \ensuremathϕ\ensuremath↑\ensuremath↓(k){\ensuremath{\phi}}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}(k)\ensuremathϕ\ensuremath↑\ensuremath↓​(k) excitations resemble spin waves.
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.
We conclude our study of superfluidity in Bose liquids with a brief summary of the strengths, and of the inadequacies, of the theory. The cornerstone of our fundamental understanding of superfluidity has been the recognition of the central importance of the condensate, a single quantum state which is macroscopically occupied. For the Bose liquid one has a particle condensate, characterized by a non-vanishing expectation value of ψ (r). The existence of the condensate explains all major aspects of superfluid behavior; in particular, we now possess: A clear understanding of the static and the long wavelength dynamic properties of an equilibrium Bose liquid, including a microscopic basis for the two-fluid model. A precise microscopic theory at T = 0 for a specific model, the dilute Bose gas. Variational calculations of the excitation spectrum of liquid He II (and of the ground state properties as well), which are in good quantitative agreement with experiment. A satisfactory phenomenological treatment of the interactions between elementary excitations which give rise to various irreversible phenomena. A qualitative understanding of the role which is played by quantized vortices in both equilibrium and non-equilibrium 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.
We study the condensate dynamics of the so-called entangled Bose-Einstein condensation (EBEC), which is the ground state of a mixture of two species of pseudospin-12\frac{1}{2}21​ atoms with interspecies spin-exchange scattering in certain parameter regimes. EBEC leads to four interdependent superfluid components, each corresponding to the orbital wave function associated with a spin component of a species. The four superflows have various counter-relations, and altogether lead to a conserved total supercurrent and a conserved total spin supercurrent. In the homogeneous case, we also obtain the elementary excitations due to variations of the single-particle orbital wave functions, by exactly solving the generalized time-dependent Bogoliubov equations. There are three gapless Bogoliubov modes and one Klein-Gordon-like gapped mode. The origin of these excitations are also discussed from the perspective of spontaneous breaking of the symmetries possessed by the system.