Studies On Quantum Phase Transition Of Ultra-cold Rubidium Atomic Gases

At the end of last century, the realization of Bose-Einstein condensates (BEC) in a dilute atomic vapor has attracted lots of scientists to study quan-tum degenerate gases. Moreover, the optical lattice is becoming an important tool to study the ultracold atom system, as its parameters are easy to control. Particularly, the novel platform of the combination of BEC and optical lattice would bring many more fascinating quantum phenomena. In this thesis, we have studied the phase fluctuation of the subcondensates and the density probability distributions of ultracold bosonic gases in quantum critical region in a one di-mensional (1D) optical lattice, and studied the first order coherence of ultracold bosonic gases above the BEC phase transition temperature in a quadrupole-Ioffe configuration (QUIC) trap. The main works are summarized as follows:1. We have developed and verified experimentally a new method to measure the phase fluctuation of the subcondensates confined in 1D optical lattice. In our method, the phase fluctuation can be obtained from the Fourier spectra of the released atomic clouds. Compared with the traditional one, in which the phase fluctuation can be obtained from the visibility of the interference pattern of atomic gases released from the optical lattice, our method does still work even for very deep lattice depth where interference peaks disappear in the atomic density distribution.2. The density probability distributions of ultracold quantum critical bosonic gases in 1D optical lattice was studied. It shows that the density probabili-ty distributions follows a simple exponential law once the lattice system has entered the quantum critical region above the Berezinskii-Kosterlitz-Thouless transition. Considering the relative phase fluctuation among the subcon-densates in different lattice wells and the spatial phase fluctuation within single lattice well, a simple theoretical model can well explain the universal density-probability distribution.3. The momentum distribution of ultracold bosonic gases in QUIC trap n-ear the phase transition temperature of BEC has been studied. According to the statistical results of the full width at half maximum of momentum distribution (FWHMMD) at different temperatures, we find that the FWH-MMD suddenly reduces, thus revealing a very notable singularity behavior when the temperature is very close to the phase transition temperature Tc. The research of the momentum distribution can give us a new insight to understand the critical behavior of the ultracold bosonic gases.4. The first order coherence of ultracold bosonic gases in QUIC trap above the BEC phase transition temperature was studied by the Kapitza-Dirac scattering. According to the statistical results of the visibility of the inter-ference pattern, it is found that the coherence of ultracold bosonic gases is better than the normal thermal gases above the phase transition tem-perature. With the temperature of bosonic gases increasing, the coherence of ultracold bosonic gases has become worse and completely same as the thermal gases finally.