PhD thesis in English

3. Rotating ideal BECβ c (J)0.054840.054820.054800.054780.054760.054740.054720.054700.054680.05466κ BEC , η=1.04, N=3·10 50.0546450 100 150 200 250 300JFigure 3.7: Dependence of β c on the cumulant cutoff J for an over-critically (η =1.04) rotating condensate of N = 3·10 5 atoms of 87 Rb with the quartic anharmonicityof the trap κ = κ BEC . The discretization parameters are given in Table 3.3. Thedashed line corresponds to a value of β c obtained by fitting the numerical results tothe function (3.21), while the full line gives the fitted function f(J).the fitting functionf(J) = β c −c 1 e −c 2(J+1)1 + c 3 (J + 1) e −c 4(J+1) , (3.21)which reproduces the numerical data quite accurately and gives high-precision resultsfor the condensation temperature T c . The virtue of the derived estimates liesin the fact that they can be used to extract the information on the condensationtemperature even for moderate values of J, when a saturation is not yet achieved.This substantially speeds up the numerical calculation of condensation temperatures,especially when it has to be done for different values of potential parameters,such as the frequency ratio η = Ω/ω.Fig. 3.8 summarizes the numerical results for the condensation temperature T cfor the anharmonicity κ = κ BEC as well as the particle numbers N = 3 · 10 5 andN = 1 · 10 4 . If we compare the obtained numerical results with the semiclassicalapproximation from Ref. [65], we see that the agreement turns out to be relativelygood for the undercritical regime, but it becomes worse for an overcritical rotation ofthe condensate. After presenting results for the ground-state occupancy, which were73