A COMPARATIVE STUDY OF THE EXPERIMENTAL FEATURES OF THE BOSE–EINSTEIN CONDENSATES OF 7Li, 23Na, 41K, 85Rb, 87Rb AND 133Cs VIA A LINEARLY PERTURBED HARMONIC OSCILLATOR POTENTIAL

Abstract

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: [Formula: see text] where T denotes the temperature, m the mass of an atom of the trapped gas, ω 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 Tcs calculated via earlier treatments based solely on an r2-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 N } exc(T) and appealing to the experimental data at T = Tc. The values of b thus found are: 1.3426 (7 Li ), 1.8420 (23 Na ), 0.4998 (41 K ), 0.3486 (85 Rb ), 1.5332 (87 Rb ) and 1.2430 (133 Cs ). While these are used to calculate N exc (T) for each of the condensates at T = Tc/2 and Tc/10, we also report on: (a) the variation of b for each condensate for some selected values of the pair (N } exc, Tc) and (b) the possibility of realizing the state (N exc , pTc; p (a number) ≫1) for all of these condensates with a unique value of b, even though the parameter-sets {m, ω, N exc , Tc} characterizing them differ widely. Attention is drawn to diverse fields where T-dependent Hamiltonians have found useful application.