Effective many-body parameters for atoms in nonseparable Gaussian optical potentials
Effective many-body parameters for atoms in nonseparable Gaussian optical potentials
复制标题
不可分离高斯光势中原子的有效多体参数
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
A. Rey
中科院分区：
文献类型：
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作者：
M. Wall;K. Hazzard;A. Rey
我们分析了由叠加高斯光束形成的三维势阱中粒子的性质，充分考虑了势阱非谐性和不可分离性的影响。虽然这些效应在更传统的光学晶格实验中可以忽略不计，但它们对新兴的超冷原子发展至关重要。我们特别关注在当前的超冷原子实验中使用的两个潜在的：紧密聚焦的光镊阵列和横向高斯限制和高度激发的横向模式的一维光学晶格。我们的主要数值工具是离散变量表示（DVR），它结合了联合收割机许多有利的功能，频谱和网格为基础的方法，如指数收敛的计算优势和方便的哈密尔顿矩阵元素的分析表示。最优化，如对称适应和变分方法建立在DVR方法的顶部，并讨论其收敛性。我们还提出了一个定量分析的本征态的不可分离的程度，借用矩阵乘积态（MPS）的理论的想法，导致概念和计算收益。除了开发数值方法，我们提出的结果，最佳本地化的Wannier函数和隧道和相互作用矩阵元素的光学晶格和镊子相关的多体物理学构建有效的模型的建设。
We analyze the properties of particles trapped in three-dimensional potentials formed from superimposed Gaussian beams, fully taking into account effects of potential anharmonicity and non-separability. Although these effects are negligible in more conventional optical lattice experiments, they are essential for emerging ultracold atom developments. We focus in particular on two potentials utilized in current ultracold atom experiments: arrays of tightly focused optical tweezers and a one-dimensional optical lattice with transverse Gaussian confinement and highly excited transverse modes. Our main numerical tools are discrete variable representations (DVRs), which combine many favorable features of spectral and grid-based methods, such as the computational advantage of exponential convergence and the convenience of an analytical representation of Hamiltonian matrix elements. Optimizations, such as symmetry adaptations and variational methods built on top of DVR methods, are presented and their convergence properties discussed. We also present a quantitative analysis of the degree of non-separability of eigenstates, borrowing ideas from the theory of matrix product states (MPSs), leading to both conceptual and computational gains. Beyond developing numerical methodologies, we present results for construction of optimally localized Wannier functions and tunneling and interaction matrix elements in optical lattices and tweezers relevant for constructing effective models for many-body physics.