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Physical review. B, Condensed matter

Bose condensation and relaxation explosion in magnetically trapped atomic hydrogen

Tom W. Hijmans, Yu. Kagan, Georgy V. Shlyapnikov, Jook T. M. Walraven

Published Nov 1, 1993• 36 citations
Publisher

Abstract

We predict and analyze nontrivial relaxational behavior of magnetically trapped gases near the Bose-condensation temperature ${\mathit{T}}_{\mathit{c}}$. Due to strong compression of the condensate by the inhomogeneous trapping field, particularly at low densities, the relaxation rate shows a strong, almost jumplike, increase below ${\mathit{T}}_{\mathit{c}}$. As a consequence the maximum fraction of condensate particles is limited to a few percent. This phenomenon can be called a ``relaxation explosion.'' We discuss its implication for the detectability of Bose-Einstein condensation in atomic hydrogen.

DOI
10.1103/physrevb.48.12886

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We predict and analyze non-trivial relaxational behavior of magnetically trapped gases near the Bose condensation temperature T c . Due to strong compression of the condensate by the inhomogeneous trapping field, particularly at low densities, the relaxation rate shows a strong, almost jump wise, increase below T c . As a consequence the maximum fraction of condensate particles is limited to a few percent. This phenomenon can be called a “relaxation explosion”. We discuss its implications for the detectability of BEC in atomic hydrogen. Magnetostatic traps offer the possibility to study gases of Bose particles in the truly dilute limit, and have proved particularly fruitful [1, 2, 3, 4, 5] in the study of atomic hydrogen (H). In these traps, proposed for H by Hess [6], the effective elimination of physical boundaries is accomplished by creating a magnetic field minimum in free space. This minimum forms a potential well for electron spin-up polarized atoms (H↑), called low-field seekers. The occurrence of Bose–Einstein condensation (BEC) in such systems introduces qualitatively different behavior from the case of a homogeneous Bose gas. This is related to the explosive increase of the dipolar relaxation rate associated with the strong compression of the condensate in an external potential.
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.
We study the evaporative cooling of magnetically trapped atomic hydrogen on the basis of the kinetic theory of a Bose gas. The dynamics of trapped atoms is described by the coupled differential equations, considering both the evaporation and dipolar spin relaxation processes. The numerical time-evolution calculations quantitatively agree with the recent experiment of Bose-Einstein condensation with atomic hydrogen. It is demonstrated that the balance between evaporative cooling and heating due to dipolar relaxation limits the number of condensates to $9\ifmmode\times\else\texttimes\fi{}{10}^{8}$ and the corresponding condensate fraction to a small value of 4% as observed experimentally.
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 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.
Quasiparticles in quantum many-body systems have essential roles in modern physical problems. Bose–Einstein condensation (BEC) of excitons in semiconductors is one of the unobserved quantum statistical phenomena predicted in the photoexcited quasiparticles in many-body electrons. In particular, para-excitons in cuprous oxide have been studied for decades because the decoupling from the radiation field makes the coherent ensemble a purely matter-like wave. However, BEC has turned out to be hard to realize at superfluid liquid helium-4 temperatures due to a two-body inelastic collision process. It is therefore essential to set a lower critical density by further lowering the exciton temperature. Here we cool excitons to sub-Kelvin temperature and spatially confine them to realize the critical number for BEC. We show that BEC manifests itself as a relaxation explosion as has been discussed in atomic hydrogen. The results indicate that dilute excitons are purely bosonic and BEC indeed occurs. Bose–Einstein condensation of excitons in thermal equilibrium is a predicted quantum statistical phenomenon that has been difficult to observe. Yoshiokaet al. cool trapped excitons to sub-Kelvin temperatures and show that condensation manifests itself as a relaxation explosion as has been observed for atomic hydrogen.