Study Of Universal Behaviour Of Ultracold Quantum Critical Bose Gases

The study on phase transitions and critical phenomena has always been a challenging and hot area in physics. Until now, the most successful theory describing the critical phenomena is the renormalization group theory, which predicts that the phase transitions in the same uni-versality group show the same behaviour near the critical point, no matter of the microcosmic details of the systems. For years, the critical behaviour in different systems have gained a lot of interest and been studied widely in theory and experiment. Ultracold Bose gases, in which a phase transition to Bose-Einstein condensation (BEC) occurs at the transition temperature, provide an excellent platform to explore the critical phenomena. In the thesis, we have studied the critical behaviour of the ultracold Bose gases near the transition point; besides, together with a one-dimensional optical lattice, we have also studied a universal behaviour of ultracold Bose gases in the quantum critical (QC) region of the phase transition from Superfluid to Mott Insulator.The detailed results are given as follows.1. We developed and verified a new method to identify the critical point for the phase transition to Bose-Einstein condensation of a trapped Bose gas. By calculating the mo-mentum distribution of an interacting Bose gas near the critical temperature, we found that it shows a singular point at the critical point, where the standard deviation between the calculated momentum spectrum and the Gaussian profile at the same temperature is continuous but the first-order derivative of it is not. Using this feature, we have de-termined the transition temperature in our experiment, and the result basically agrees with the theoretical prediction. When compared with the usual method which involves seeking the temperature point under which a bimodal structure begins to emerge in the momentum distribution, our method is less likely to be affected by noise.2. We studied the first-order spatial correlation function of ultracold Bose gases in a mag-netic trap above the critical temperature of the phase transition to BEC, and determined the two critical exponents which concern the correlation function. We theoretically verified that the 1D momentum distribution along the axial direction of the Bose gas trapped in the QUIC trap is related to the correlation function through a Fourier transi-tion. By using this relation and the measured momentum distribution, we obtained the corresponding correlation function, and finally determined the critical exponents to be v= 0.68± 0.14 and 77= 0.030 ± 0.036 by fitting. It is the first time that the measurement of ? have been done in ultracold Bose gases.3. We reported the observation of a universal density probability distributions of ultracold quantum critical Bose gases trapped in a one-dimensional optical lattice. We extracted the density probability distributions from the measured atomic density of the rubidi-um Bose gases after a free expansion time. The density probability was found to fol-low a simple exponential law once the lattice system has entered the QC region above the Berezinskii-Kosterlitz-Thouless (BKT) transition. The theoretical analyses showed that, in addition to relative phase fluctuations between the subcondensates in different lattice wells, there also exist spatial phase fluctuations within single lattice wells in this QC region. The universal density-probability distribution could thus be well understood by a simple theoretical model taking into account these two kinds of phase fluctuations. This work is an effective attempt to explore the universal behaviour in QC region.