A Method for Determining the Phase Transition Point of the Bose--Einstein Condensation by Judging the Fitting Errors

In this paper, We demonstrate an approach to determine the phase transition point and critical temperature of Bose-Einstein condensation. During the fitting sequence of time-of-flight images, for just one picture we take four kinds of different calculations instead of only one. By calculating the quantitative least-square errors, which have always been neglected before, we find out that this value can act as a criterion to judge the status of atom clouds. Using this criterion, we can not only discriminate the status around the phase transition point, but can also find the critical point precisely. Also with this method, we can achieve the totally automatical running of calculating programs without human's judgments.