自由膨胀准二维玻色-爱因斯坦凝聚中的密度-密度关联

摘要

The effective Lagrangian density function and the quantum fluctuation of the wave function in the form of quantized operators are presented for a quasi two-dimensional Bose-Einstein condensate by means of Madelung transformation. This paper calculates the two-point density-density correlation function of the condensate during its free expansion after its confinement potential is removed. Results show that the two-point density-density correlation function in the long-wave limit is proportional to the wave number k and it tends to be a constant in the short-wave limit.%利用Madelung变换,考虑密度和相位涨落,给出了准二维玻色-爱因斯坦凝聚体的有效拉格朗日密度函数和波函数量子涨落的算符化表示,计算了凝聚体在去除约束势场自由膨胀时两点之间的密度-密度关联函数,结果表明在长波极限下,两点之间的密度关联函数正比于波数k,而在短波极限下,密度关联函数趋近于一个常数。