Quantum Tunneling Of Bose-Einstein Condensates In One-dimensional Optical Lattices

In quantum tunneling a particle with energy E can pass through a high potential barrier V (>E) due to the wave character of the particle. Bose-Einstein condensates also could pass through the optical lattices formed by laser standing waves. This paper introduces the basic principles and application of Bose-Einstein condensates, and the formation, properties and applications of optical lattices, including a method of barrier segmentation to calculate the quantum tunneling rate. We mainly research the quantum tunneling of Bose-Einstein condensates in one-dimensional optical lattices in Bose-Hubbard model. In the paper, we use a series of rectangular potential barriers substitute for the optical lattices potential traps, and the tunneling rate of 87Rb is calculated, also investigate the relations among tunneling rate, temperature of condensates and the depth of trap, the results show that, the method is more suitable for the higher temperature and lower trap. We especially consider the effect of repulsion of atoms to tunneling rate, and compare with the rate without the interaction, the results show the tunneling rate of atom increases. The repulsion depends on the atomic number, depth of trap and the width of condensates. Weak interaction has small effect on the tunneling rate and usually is ignored, when the interaction is strong, the effect is obviously. This work provides a certain basis for the campaign laws of boson in the optical lattices.