PhD thesis in English

4. Mean-field description of an interacting BECto the wings of the measured velocity distribution of a thermal cloud. The condensatecomponent was identified as a characteristic narrow central peak, and thecondensate fraction was obtained by fitting either an additional Gaussian profile ora parabolic TF profile to that part of the distribution, in accordance with the previouslydescribed almost-ideal model. These early experimental studies were only ableto validate that the phase diagram of the system is quite accurately described bythe noninteracting result from Eq. (1.10). The inherent statistical and systematicerrors prevented real quantitative tests of the mean-field models.The first clear experimental demonstration, which measured values of condensatefractions different from the corresponding ideal values of Eq. (1.10), was reportedin Ref. [89]. The experimental procedure included TOF absorption imaging andan additional technique, a coherent Brag scattering. The advantage of the lattertechnique is its ability to provide a complete spatial separation of the condensateand thermal cloud during the TOF expansion. The condensate fraction was determinedwith a high certainty by counting the scattered atoms. However, once again aballistic expansion of the thermal cloud was assumed, and the temperature was determinedby fitting the semiclassical density profile of the expanded noninteractinggas (1.13) to the measured density profile of the thermal cloud. Despite this, the obtainedphase diagram clearly demonstrated a reduced condensate fraction comparedto the noninteracting result (1.10). A good agreement of experimental values withthe results obtained within the semi-ideal model was found, while the agreement waseven better with the predictions of the TFSC model. The main focus of Ref. [89]was a precise measurement of the interaction-induced shift of the condensation temperatureand its comparison with Eq. (4.34). One of the main conclusions was thatimproved models are necessary for a good quantitative description of the expansionof finite-temperature BECs and reliable analysis of experimental data.In order to avoid intricacies of the accurate modeling of the TOF expansion,Ref. [24] has exploited the in-situ phase-contrast imaging to investigate the BECphase diagram experimentally. The values of the chemical potential µ and thetemperature T were determined by fitting to functions that stem from the interactingfinite-temperature models to the in-situ measured data. Most reliable fits wereobtained in the case of the Popov model [78], which is very similar to the presentedTFSC model. We stress that authors of Ref. [24] have used the consistent procedure:the same mean-field model was used for the extraction of all relevant quantities (µ, T,N 0 , N) from the experimental results, as well as for the analysis of the phase diagram.101