Bose-Einstein Condensation Of Bose Gas In A Two-dimensional, Harmonic Trap

Einstein had predicated that the ideal bose gas would occur phase change when the thermal deBroglie wave-length becomes larger than the average spacing between particles, then a macroscopic population gathers in the lowest energy quantum state and quantum degeneracy happens, which is the famous Bose-Einstein condensation (BEC). During the following several decades, scientists did not find the BEC in experiments and could not give a definite answer for the phenomena, but the endeavors for realizing the BEC in experiments have never been stopped. Until 1980', scientists got substantial developments in BEC after the techniques of laser cooling and atom-captured method related to realizing BEC in experiments became mature. Finally, three groups realized BEC in experiments successfully in 1995, which motivated greatly scientists to do researches in BEC.The current researches are focused on three-dimensional system while the unique characteristics in two-dimensional system make 2D system have some particularities which 3D system has not The particularities of low-dimensional systems have been widely applied in manufacture of new materials and new devices, which agitates people's strong interests in 2D system. The theoreticalinresearches in 2D system will promote the realization of BEC in experiments.In this article, we begin with 1he original Ihree experiments on realization of BEC and several critical techniques for these experiments: magnetic-optics in gas cell, atomic Zeeman cooling technique and adsorbing imagination technique for BEC detection. Then we go on theoretical calculations on the characteristics of two-dimensional ideal bose system, followed by the discussions of two-dimensional ideal bose gas in a simple harmonic trap. We focus on getting characteristics of two dimensional ideal bose in potential through numerical calculations, such as the effect of the number of particles in bose system on the characteristics of BEC; the effect of fugacity on zero energy; the relations between heat capacity and temperature, the relations between temperature and the number of particles in the first excited state. Comparing the results obtained through numerical calculations and that obtained through other approximate analytic calculations, we can get further understanding on the 2D bose gas trapped in a simple harmonic trap. In the following chapters, we mainly concentrate on investigating and studying the latest progresses in bose gas with interaction between particles. The researches of 2D BEC in some degree guide the BEC in experiments. At last, we look into the future of BEC applied into our society.