PhD thesis in English

4. Mean-field description of an interacting BECn 0 (r)n th (r)n(r)4⋅10 19 0 10 20 30 40 503⋅10 192⋅10 191⋅10 190r[µm]Figure 4.2: Density profiles of different components (m −3 ) versus the radial coordinater within the almost-ideal model for the parameters N = 10 6 , T = 60 nK,ω = 100 Hz.Obviously, in order to have a well-behaved value of n th (0), we have to use theapproximation µ = 0 for the thermal gas in the condensate phase. A typical densityprofiles are shown in Fig. 4.2. Within this framework, the two components do notinteract mutually and their density profiles are monotonously decreasing functions ofthe radial coordinate. Although the model is oversimplified and the thermodynamicproperties of a BEC it provides correspond to the noninteracting gas, it has beenwidely used since the first observation of a BEC until the present state-of-the-artexperiments.4.2.2 Semi-ideal modelA basic premise of this model is to treat thermal atoms as an ideal gas within theeffective potential, which is a combination of the external trap potential and themean-field repulsive interaction of the condensate: V eff (r) = V (r)+2gn 0 (r) [88, 89].Additionally, we neglect the influence of the thermal component on the condensate,and describe the BEC ground-state within the TF approximation. With this setof simplifications, from Eqs. (1.13) and (4.14), we obtain the following system of92