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Physical Review A

Dipolar decay in two recent Bose-Einstein condensation experiments

H. M. J. M. Boesten, A. J. Moerdijk, BOUDEWIJN J. VERHAAR

Published Jul 1, 1996• 36 citations
Publisher

Abstract

In view of two recent Bose-Einstein condensation experiments, we have calculated the magnetic-dipolar decay-rate constants of the atomic density for the doubly polarized state in $^{87}\mathrm{Rb}$ and $^{85}\mathrm{Rb}$, and for the highest state of the lower hyperfine manifold in $^{23}\mathrm{Na}$.

DOI
10.1103/physreva.54.r29

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In view of two recent Bose-Einstein condensation experiments, we have calculated the magnetic-dipolar decay-rate constants of the atomic density for the doubly polarized state in 87Rb^{87}\mathrm{Rb}87Rb and 85Rb^{85}\mathrm{Rb}85Rb, and for the highest state of the lower hyperfine manifold in 23Na^{23}\mathrm{Na}23Na.
We study conditions necessary for the observation of Bose-Einstein condensation in a magnetically trapped sample of atomic Cs gas. These conditions are associated with the value of the elastic scattering length, the rate of elastic scattering events, and the lifetime for decay of the density due to both magnetic dipole relaxation in two-body collisions, as well as recombination to Cs2{\mathrm{Cs}}_{2}Cs2​ in three-body collisions. We find that, on the basis of these conditions, the prospects for observing Bose-Einstein condensation are favorable for a gas of ground-state Cs atoms in the highest state of the lowest hyperfine manifold. In all calculated elastic and inelastic two-body rates we find a pronounced resonance structure, which can be understood in terms of the interplay between the singlet-triplet interaction and the hyperfine, Zeeman, and magnetic dipole interactions. The experimental observation of these resonances may help to eliminate present uncertainties about interaction potentials.
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 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 .