【作者】 熊祖周；

【导师】 谭磊；

【作者基本信息】 兰州大学 ， 理论物理， 2010， 硕士

【摘要】 激光制冷与蒸发制冷技术的结合促成了宏观量子现象——玻色-爱因斯坦凝聚体(BEC)—在稀薄原子气体中的实现。随着研究工作的进一步深入,人们的研究兴趣逐步深入到玻色-爱因斯坦凝聚与相关方向的交叉方面,如BCS-BEC结、BECs中的量子纠缠与量子信息、BECs的激发与宇宙膨胀的相似性研究等。本论文主要研究了约束势场下玻色-爱因斯坦凝聚体中的量子涨落及其效应,得出了一些相关的结果,并与宇宙学的有关方法结果作了简单的对比。全文共四章,第一章前言中简单介绍玻色-爱因斯坦凝聚的形成、描述及其研究进展,以及本论文的研究目的和具体内容。第二章,主要采用粒子数守恒平均场近似方法研究了BECs中的量子涨落及其反作用力,并与有效相互作用方法做一简单比较。最后,就一维情况详细讨论了涨落对凝聚体半径的影响。第三章中采用了同样的近似讨论了随时间变化谐约束势下二维BECs中的量子涨落。通过引入了一对自共轭算符将涨落项满足的方程线性化,进而得出密度和相涨落所满足的方程。并就静态凝聚态情形,得出本征模方程和激发模频率的依赖关系。最后,在Thomas-Fermi近似下讨论了外势或相互作用随时间变化对量子涨落的影响,发现,可以控制外势或相互作用变化来打破绝热环境,从而达到抑制甚至冻结量子涨落的目的。第四章,结论与展望。更多还原

【Abstract】 The combination of laser cooling and evaporative cooling led to the formation of a kind of macroscopic quantum phenomenon—Bose-Einstein condensation—in dilute atomic vapors in experiment. Along with research work’s thorough, people’s research interests have extended step-by-step to intersection of BEC with relevant fields, such as BCS-BEC Crossover, Quantum Entanglement and Quantum Information in BECs, similarity between elementary excitation in BECs and cosmic inflation and so on. This thesis studies the quantum fluctuations and related effects of BECsin trap potential, and gets some corresponding results. In addition, we make some simple comparison with effective-action method.This thesis comprises four parts. we first present the formation, discription and research progress of BEC.,then introduce the background of this thesis and the major content of this thesis in the first chapter. In the following, adopting particle-number-conserving mean-field ansatz, we put emphasis on the study of the Quantum Fluctuations and Quantum Back-reaction of quantum fluid in BECs in chapter 2, in addition, we make a simple comparison with the effective-action method. At last, we take into account the quasi—1D case.,and calculate carefully the influence on the condensates radius from quantum fluctuations.In chapter 3, we discuss the quantum fluctuations in time-dependent harmonic potential, adopting the same ansatz. By introducing a pair of self-conjugate operators, we may linearize the equation of fluctuation term., and get the equations of density and phase fluctuations. In addition, we get the eigenmode equation and frequency relation of excitation modes on initial static BECs. At last, in Thomas-Fermi approximation we discuss the influence on quantum fluctuation brought by the variation of external potential or interaction intensity. We find that one can regulate the external potential or interaction intensity to control adiabaticity so as to restrain or freeze quantum fluctuation. In the last chapter of the thesis, we give a simple summary of the above-mentioned works and the outlook.更多还原