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Physical Review Letters

Density, Magnetization, Compression, and Thermal Leakage of Low-Temperature Atomic Hydrogen

Jook T. M. Walraven, Isaac F. Silvera

Published Jan 21, 1980• 42 citations
Publisher

Abstract

The density distribution of low-temperature spin-polarized atomic hydrogen in a realistic magnetic field profile is calculated for densities below and above the critical value for Bose-Einstein condensation. The distribution is an identifying characteristic. Magnetic compression and instability due to thermal leakage of the atoms is treated.

DOI
10.1103/physrevlett.44.168

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Physical Review Letters•May 26, 1980•22 citations
The density distribution of low-temperature spin-polarized atomic hydrogen in a realistic magnetic field profile is calculated for densities below and above the critical value for Bose-Einstein condensation. The distribution is an identifying characteristic. Magnetic compression and instability due to thermal leakage of the atoms is treated.
The density profiles for an interacting gas of atomic hydrogen in an inhomogeneous axial magnetic field are determined by extending the Gross-Pitaevskii theory to finite temperature. The profiles can be used as an identifying feature of Bose-Einstein condensation for all TTT. Radial inhomogeneities in the field are also treated.
Atomic hydrogen (H) has recently been created in a long-lived state referred to as spin-polarized atomic hydrogen (H↓). A moderate density gas (n≃1017 atoms/ cc) has been produced at temperatures T≃400 mK. H↓ is predicted to be the only atomic substance that remains gaseous to T = 0 K; current experiments are consistent with this picture. Since the H↓ atoms behave as composite bosons the gas is expected to have a Bose-Einstein condensation (BEC) and related superfluidity at a sufficiently high density or low temperature. H↓ is expected to display spectacular static and dynamic properties. Since the gas is polarized, the dominant electronic magnetization, M⃗e, is proportional to the atomic density. In an inhomogeneous magnetic field M⃗e will also be highly inhomogeneous. BEC will be spatially localized and the static M⃗e should be an identifying feature of this state. The low-lying excitation spectrum should not only feature electronic and nuclear spin-transitions, but should also have magnetic translational modes of the gas. The experimental technique for stabilization of H↓ as well as many of the predicted magnetic properties are discussed.
A gas of spin-polarized atomic hydrogen can be prepared in the upper hyperfine states and loaded into a static magnetic trap. Evaporative cooling and magnetic compression of such a gas can produce temperatures of 30 \ensuremath{\mu}K and densities of 1014{10}^{14}1014 ${\mathrm{cm}}^{\ensuremath{-}3}$. Under these conditions a Bose-Einstein condensate may form.
We study the decay of magnetically trapped doubly spin-polarized atomic hydrogen in the density and temperature regime of the Bose-Einstein phase transition and calculate the temperature and magnetic field dependence of all relevant relaxation rate constants ${G}_{\mathrm{dd}\ensuremath{\rightarrow}\ensuremath{\kappa}\ensuremath{\lambda}}$. At the transition temperature Tc{T}_{c}Tc​ the rate constants have a discontinuous second derivative with respect to T. Below Tc{T}_{c}Tc​ they show a pronounced decrease relative to the extrapolated above-Tc{T}_{c}Tc​ values, the observation of which is a clear signal for the experimental realization of Bose-Einstein condensation.
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.