Bose-Einstein Condensation In Optical Lattices

Bose-Einstein condensate (BEC), as a new form of matter, is one of the research hotspots in the physics area in recent years. The most basic characteristics of Bose-Einstein condensate are: when the temperature of Bose gas is below the critical temperature, macroscopic bosons will gather on the macroscopically quantum coherent state (the ground state) where the energy is the lowest. In the Bose-Einstein condensate, all the particles which gather on the lowest energy state and have same physical characteristics can be described by only one wave function. The achievement of optical lattice opened up a new direction for people to study the BEC of cold atoms. At present, cold atomic optical lattice has become an important topic in the controlling cold atoms. The research of BEC in the optical lattices has achieved breakthroughs, and has wide application prospects in quantum computing, quantum information and quantum transport. At first, this thesis investigates the thermodynamic properties of the system during the process of the ultracold atomic gases loaded into the optical lattices by the method of statistical mechanics. The thermodynamic parameters of Bose systems, such as the total number of particles, the critical temperature, the condensate fraction, the internal energy, the specific heat and the entropy of systems, are calculated in this thesis. In addition, we analyze the changes of the thermodynamic parameters and the stability of the system nearby the critical temperature during the loading process. The results show that: If the T Tc is equal, the occupation rate of particles on the ground state in the harmonic oscillating trap is higher than that of in the optical lattice, and the condensate is more stable in the harmonic oscillating trap. The internal energy of the condensate is in proportion to Tα+1, and the specific heat is in proportion to Tα. The entropy of systems keeps balance during the loading process of the ultracold atomic gases slowly and adiabatically loaded into optical lattices from the harmonic oscillating trap. If T Tcis less than 0.30, the occupation rate of particles on the ground state becomes higher with the increasing loading intensity of the optical lattices, and the Bose system becomes more stable. However, if T Tcis greater than 0.70, the Bose system becomes be unstable with the increasing loading intensity of the optical lattices. Bose-Einstein condensate is in line with the Gross-Pitaevskii equation. Finally, this thesis investigates the ground state properties of Bose-Einstein condensate in the optical lattices by solving the Gross-Pitaevskii equation. We solve the wave function of the ground state and the energy of the condensate in the optical lattice potentials with different potential depths. The results show that the wave crests of the ground wave function correspond to wave troughs of potential field of the optical lattices. The energy of the Bose system is low in the wave troughs of potential field, the particle number and density of particle number are large, and the system is more stable. With increasing optical lattices potential, the wave crests of the ground wave function become higher, and the wave troughs become lower. When the optical lattice potential is increased to a certain degree, the number of particles in each lattice point tends to balance. With increasing optical lattice potential field, the ground-state energy and the first excited-state energy of the condensate decrease. Energy gap appears in the energy band structure of BEC. The smaller the energy band number is, the narrower the width of energy band is, and the energy state density also becomes greater. The energy of condensate increases with increasing particle numbers, which is consistent to the front thermodynamic analyses.