PhD thesis in English

Figure 1.1: The hallmark of the Bose-Einstein condensation - a prominent densitypeak appears below the condensation temperature. Density profiles of the expandedcloud are shown at three different temperatures. From the left to the right we seebosonic cloud right above the condensation transition, just below the condensationtransition and in the regime with almost a pure condensate. The experimental resultis originally presented in Ref. [3] and this figure is taken from Ref. [5].the BEC, the relationn(0)λ 3 T ≈ ζ(3/2) ≈ 2.61238 (1.15)holds. Not surprisingly, this condition is very close to the intuitive argument givenat the beginning of the Chapter.The noticeable feature of the condensate phase in the harmonic trap, not presentin the gas phase, is a prominent density peak located at the trap center that reflectsmacroscopically occupied ground state which has the symmetry of the trap potential,superimposed onto the broad thermal distribution. This is illustrated in Fig. 1.1.A bimodality of the density distribution is an important signature of the onset ofBose-Einstein condensation.An important and convenient aspect of the harmonic trap is that the singleparticleground-state is localized both in the real and in the momentum space.Hence, beside static density profiles of the trapped atoms, another possibility forthe experimental differentiation of the phases is free expansion of the gas from thetrap. Initially, the gas is in the thermal equilibrium in the trap, and then suddenlythe trap is switched off and the gas is allowed to expend freely. To describe thethermal gas we use the semiclassical approximation. The density profile after the7