PhD thesis in English

4. Mean-field description of an interacting BEC-0.015-0.02-0.025-0.03-0.035-0.04Numerical resultsFirst-order correction-0.04510 5 10 6 10 7Figure 4.9: A relative shift in the condensation temperature δT c as a function of thenumber of particles in the trap N for ω = 100 Hz.Nwe approach the BEC phase transition from the gas phase. We stress that the sameresult can be obtained by considering condensate phase in the vicinity of the phasetransition within the TFSC model. It is important to note that we only obtainthe interaction-induced shift in the condensation temperature. Finite-size effects[91, 92] are beyond our consideration, because we rely on the TF and semiclassicalapproximation. A comparison of the analytical expression (4.34), which gives a firstordercorrection to T c in the interaction strength, and numerical results based onEqs. (4.26) and (4.27), is shown in Fig. 4.9. In this graph, δT c is given as a functionof the number of particles in the trap. We observe a reasonable agreement of theTFSC result (4.34) with the numerical data.4.3 Experimental assessment of different modelsDensity profile of a BEC cloud is experimentally measurable quantity, using eitherthe absorption TOF imaging or in-situ techniques described in Chapter 1. Thevalues of other physical quantities are then extracted from the experimental data ina roundabout way.Early experimental efforts [93, 94] to measure the occupation of the ground stateas a function of the temperature have usually employed the absorption TOF imaging.Thermometry was then performed by fitting the semiclassical result (1.17)100