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 .
The study of spin-polarized atomic hydrogen in the three-dimensional gas phase has been extended into a new regime of magnetic field strength. Analysis of decay data for B=10--20 T reveal for the first time the characteristic peak in the three-body dipolar-decay rate constant as predicted by Kagan, Vartanyants, and Shlyapnikov (Zh. Eksp. Teor. Fiz. 81, 1113 (1981) [Sov. Phys.---JETP 54, 590 (1981)]). Beyond 17 T we observe a rapid falloff of the three-body-decay rate constant. We also determine a value for the three-body-exchange rate constant which is in accord with the calculation of Kagan et al. In contrast to the picture which was emerging from previous studies at more moderate fields, the data presented here suggest that existing theories are capable of describing the decay of the system in the very-high-field limit. The new picture which is emerging suggests that Bose-Einstein condensation may be achievable at somewhat higher fields which are currently available at high-magnetic-field facilities.
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 and
85Rb, and for the highest state of the lower hyperfine manifold in
23Na.
Using magnetically trapped atomic hydrogen as an example, we investigate the prospects of achieving Bose–Einstein condensation in a dilute Bose gas. We show that, if the gas is quenched sufficiently far into the critical region of the phase transition, the typical time scale for the nucleation of the condensate density is short and of O(ħ/k B T c ). As a result we find that thermalizing elastic collisions act as a bottleneck for the formation of the condensate. In the case of doubly polarized atomic hydrogen these occur much more frequently than the inelastic collisions leading to decay and we are led to the conclusion that Bose–Einstein condensation can indeed be achieved within the lifetime of the gas. Introduction In the last few years it has been clearly demonstrated that not only charged ions but also neutral atoms can be conveniently trapped and cooled by means of electro-magnetic fields. Although the physics of the various ingenious scenarios developed to accomplish this is already interesting in itself [1], the opportunities offered by an atomic gas sample at very low temperatures are exciting in their own right. Examples in this respect are the performance of high-precision spectroscopy, the search for a violation of CP invariance by measuring the electric dipole moment of atomic cesium [2], the construction of an improved time standard based on an atomic fountain [3] and the achievement of Bose–Einstein condensation in a weakly interacting gas.
We have studied relaxation and recombination processes in compressed, doubly polarized atomic hydrogen at temperatures from 0.13 to 0.60 K and magnetic fields from 3 to 9 T. The gas and surface dipole three-body recombination rate constants at a field of 7.6 T are measured to be, respectively,
Lg=8.9(8)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}39}$
cm6 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ and
Ls=1.2(4)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}24}$
cm4 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$. They decrease slowly with field and
Ls exhibits no significant angular dependence. The three-body recombination rate due to hyperfine mixing has also been measured. Electronic and nuclear relaxation rates have been measured; the b-c electronic relaxation rate constant in the gas is
Gbc=1.03(7)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$
cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$exp(-
Ebc/
kBT). The temperature and field dependence of the nuclear relaxation rate in the gas are observed to be in excellent agreement with recent theoretical calculations. Three-body surface recombination-rate measurements using $^{3}\mathrm{\ensuremath{-}}^{4}$He surfaces indicate that as little as one monolayer of
3He on the liquid
4He surface appreciably decreases the adsorption energy of atomic hydrogen. Densities achieved include 4.5\ifmmode\times\else\texttimes\fi{}
1018 atoms${\mathrm{?}}^{\mathrm{\ensuremath{-}}3}$ at 0.55 K (pure
4He walls), and 1.4\ifmmode\times\else\texttimes\fi{}
1018 atoms${\mathrm{?}}^{\mathrm{\ensuremath{-}}3}$ at 0.19 K (8 at. ? sup 3---He).