有限温度下含三体相互作用的玻色-爱因斯坦凝聚体的集体激发特性
2023-07-28梁青青周小燕李好财
梁青青 周小燕 李好财
摘要:提出了一种描述有限温度下囚禁在谐振势肼中包含两体和三体相互作用的玻色-爱因斯坦凝聚体的自洽模型,利用该模型讨论了三体相互作用对凝聚体转变温度、凝聚体和非凝聚体密度分布和凝聚体集体激发频率的影响.利用求得的凝聚体基态波函数和集体激发的本征函数计算了集体激发模和准粒子的耦合矩阵元,得到了最低集体激发模的朗道阻尼,讨论了三体相互作用对最低激发模的朗道阻尼的影响.
关键词:三体相互作用;有限温度;集体激发;朗道阻尼
中图分类号:O 469 文献标志码:A 文章编号:1001-988Ⅹ(2023)04-0054-05
自观察到超冷玻色-爱因斯坦凝聚(Bose-Einstein condensate,BEC)的集體模以来,实验上对低能集体激发的测量[1]已发展到有限温度.在理论方面,描述凝聚体的格罗斯-皮塔耶夫斯基(Gross-Pitayefsky,G-P)方程已被推广到有限温度[2,3],并非常成功地解释了系统的热力学性质,如凝聚分数、内能、比热和临界温度[3,4].粒子间的相互作用会导致集体激发振幅的衰减(阻尼)和频率的改变(频移).在能级分离的系统中,集体激发的阻尼机制主要是朗道阻尼,文献[5-8]计算了BEC中低能模的朗道阻尼.然而,这些计算主要考虑两体相互作用[9-11];如果提高原子密度,三体相互作用将开始发挥重要作用[12-19].理论研究结果表明,即使较小强度的三体相互作用也会导致特殊的调制不稳定性[20],凝聚态的稳定区域和能谱也会有相当大的改变[21,22].文中将HFB-Popov近似推广到包含三体相互作用情形,研究了三体相互作用对凝聚体集体激发特性的影响.
图5为87Rb原子气体的l=0集体模的计算结果.当Δ在0.07~0.20时,γL的变化较弱.通过将γ(Δ)的数据拟合为一条近似的直线,并将其外推到Δ=0,可以得到给定温度下集体激发模的朗道阻尼率.可以看到,阻尼率随着三体相互作用的增加而增加.
3 结论
文中将含时HFB-Popov近似推广到包含三体相互作用的情形,得到了一组耦合方程,通过数值求解这些方程研究了三体相互作用对凝聚体转变温度、凝聚体和非凝聚体原子分布、集体激发频率的影响.另外,利用所求得的基态波函数和集体激发的本征函数数值研究了三体相互作用对l=0集体模朗道阻尼的影响.计算结果显示三体相互作用会导致凝聚体转变温度减小,引起集体激发频率的移动,并能增强凝聚体最低激发模的朗道阻尼.
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