科研之友
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摘要
We show that the observed features of the above-named Bose-Einstein condensates can be understood via an effective confining potential of the form of: V (r, T) = 1/2 mw(2) [r(2) + 2(sic) (kT/mw(2)br) , ( r = | r|) where T denotes the temperature, m the mass of an atom of the trapped gas, ! the geometric mean of the three frequencies used for confinement, k the Boltzmann constant and b a dimensionless perturbation parameter. Such an exercise is undertaken because T(c)s calculated via earlier treatments based solely on an r(2)-potential lead to a mismatch with the experimental values. We fix b by substituting the density of states corresponding to V ( r, T) into the equation for the number of excited atoms Nexc( T) and appealing to the experimental data at T = T c. The values of b thus found are: 1.3426 (Li-7), 1.8420 (Na-23), 0.4998 (41 K), 0.3486 (85 Rb), 1.5332 (87 Rb) and 1.2430 (133 Cs). While these are used to calculate Nexc( T) for each of the condensates at T = T c/2 and T c/10, we also report on: ( a) the variation of b for each condensate for some selected values of the pair ( Nexc, T c) and ( b) the possibility of realizing the state ( Nexc, pT(c); p ( a number) %26gt;%26gt; 1) for all of these condensates with a unique value of b, even though the parameter-sets {m, w, Nexc, T-c} characterizing them differ widely. Attention is drawn to diverse fields where T-dependent Hamiltonians have found useful application.
- 出版日期2013-5-10
