论文标题
二元玻璃混合物中量子液滴的扩展毛皮的显微衍生物的微观推导
Microscopic derivation of the extended Gross-Pitaevskii equation for quantum droplets in binary Bose mixtures
论文作者
论文摘要
超级量子液滴是最近在超低玻色子凝结物中观察到的自结界液体状状态。在所有以前的理论研究中，它都是通过现象学低能有效理论描述的，该理论被称为扩展的总\ textendendash pitaevskii方程。在这里，我们从显微镜中得出了凝结物的总\ Textendendash Pitaevskii方程，以及在不均匀的量子液滴中，由Bose-Bose混合物实现的不均匀量子液滴，具有吸引人的物种间相互作用。我们表明，配对字段的包含是必不可少的，以便对液滴状态具有一致的描述。我们澄清说，早期使用的扩展总\ TextEndendash Pitaevskii方程应理解为配对场的运动方程，而不是凝结。配对场的波动引起了液滴的低能集体激发。我们还为无间隙的声子模式和间隙模式介绍了Bogoliubov方程，这是在真实空间中配对的，这表征了液滴的单粒子样激发。这项工作中为冷凝物和配对场得出的运动方程是理想的起点，可以理解正在进行的冷原子实验中非均匀超级量子液滴的结构和集体激发。
An ultradilute quantum droplet is a self-bound liquid-like state recently observed in ultracold Bose-Einstein condensates. In all previous theoretical studies, it is described by a phenomenological low-energy effective theory, termed as the extended Gross\textendash Pitaevskii equation. Here, we microscopically derive the Gross\textendash Pitaevskii equation for the condensate and also for a pairing field in an inhomogeneous quantum droplet realized by Bose-Bose mixtures with attractive inter-species interaction. We show that the inclusion of the pairing field is essential, in order to have a consistent description of the droplet state. We clarify that, the extended Gross\textendash Pitaevskii equation used earlier should be understood as the equation of motion for the pairing field, rather than the condensate. The fluctuations of the pairing field give rise to low-energy collective excitations of the droplet. We also present the Bogoliubov equations for gapless phonon modes and gapped modes due to pairing in real space, which characterizes single-particle-like excitations of the droplet. The equations of motion derived in this work for the condensate and the pairing field serve an ideal starting point to understand the structure and collective excitations of non-uniform ultradilute quantum droplets in on-going cold-atom experiments.
