近日，浙江师范大学的梁兆新及其研究团队取得一项新进展。经过不懈努力，他们提出从全三维空间到一维空间的相互作用诱导的维度交叉。相关研究成果已于2024年7月9日在国际知名学术期刊《物理评论A》上发表。

这项工作的核心在于引入一种创新的场景，旨在实现维度交叉，其独特之处在于动力学和相互作用能量自由度展现出低维度特性。为实现此目标，研究人员深入探索了二维光学捕获玻色气体的领域，尤其聚焦于其有限范围相互作用的特性。研究的重点在于，通过晶格诱导的方式，在动力学和相互作用层面探究从全三维向一维(1D)的维度转换过程。

利用函数路径积分法，研究人员推导了模型系统的状态方程，包括关键量，如基态能量和量子损耗。这些方程使研究人员能够分析有限范围相互作用和光学晶格对BEC系统量子涨落的综合影响。值得注意的是，这一分析结果调和了李黄杨(Lee-Huang-Yang, LHY)对三维基态能量的修正和一维极限里布利尼格(Lieb-Liniger, LL)对基态能量的修正，从而为LHY和LL修正之间有趣的差异提供了新的见解。

据悉，维度交叉的探索具有深刻的基础意义，是理解在物理系统的两个不同维度的过渡现象中观察到的显著差异的关键桥梁。操纵维度的普遍策略包括精心控制外部捕获几何形状，从而限制动能从三维(3D)到低维空间的自由度，同时保持相互作用能量自由度的3D性质。

附：英文原文

Title: Interaction-induced dimensional crossover from fully three-dimensional to one-dimensional spaces

Author: Tao Yu, Xiaoran Ye, Zhaoxin Liang

Issue&Volume: 2024/07/09

Abstract: The exploration of dimensional crossover carries profound fundamental significance, serving as a crucial bridge in comprehending the remarkable disparities observed in transitional phenomena across the two distinct dimensions of a physical system. The prevalent strategy for manipulating the dimensionality involves meticulously controlling the external trapping geometry, thereby restricting the degrees of freedom of the kinetic energy from three-dimensional (3D) to lower-dimensional spaces, while maintaining the 3D nature of the interaction energy degrees of freedom. The aim of this work is to introduce an innovative scenario to achieve dimensional crossover, characterized by lower-dimensional nature of both the kinetic and the interaction energy degrees of freedom. To accomplish this objective, we delve deeply into the realm of a two-dimensional optically trapped Bose gas, focusing specifically on its finite-range interaction. Our emphasis lies in exploring the lattice-induced dimensional crossover from full 3D to one-dimensional (1D) in both kinetic and interaction terms. Utilizing the functional path integral method, we derive the equation of states of the model system, encompassing crucial quantities, such as the ground-state energy and quantum depletion. These equations enable us to analyze the combined effects of finite-range interaction and an optical lattice on quantum fluctuations of the BEC system. Notably, our analytical findings reconcile the Lee-Huang-Yang (LHY) correction to the ground-state energy in the 3D and Lieb-Liniger (LL) ones in the 1D limit, thereby providing fresh insights into the intriguing disparities between LHY and LL corrections.

DOI: 10.1103/PhysRevA.110.013304

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.013304