[论文解读] Sorting Fermionization from Crystallization in Many-Boson Wavefunctions

Bera, S., Barnali Chakrabarti+6 more|arXiv (Cornell University)|Jan 1, 2018

Cold Atom Physics and Bose-Einstein Condensates参考文献 2被引用 1

一句话总结

该论文通过使用多配置时变玻色子哈特ree方法（MCTDHB）分析一维超冷玻色子的单体和双体密度矩阵，区分了费米子化与结晶化行为。结果表明，受限系统中费米子化体系由于局域化导致密度的N重分裂不完全，而结晶化体系由于相互作用能无界导致完全分裂，从而可通过测量密度展宽实现实验上的区分。

ABSTRACT

Fermionization is what happens to the state of strongly interacting repulsive bosons interacting with contact interactions in one spatial dimension. Crystallization is what happens for sufficiently strongly interacting repulsive bosons with dipolar interactions in one spatial dimension. Crystallization and fermionization resemble each other: in both cases -- due to their repulsion -- the bosons try to minimize their spatial overlap. We trace these two hallmark phases of strongly correlated one-dimensional bosonic systems by exploring their ground state properties using the one- and two-body density matrix. We solve the $N$-body Schr\"odinger equation accurately and from first principles using the multiconfigurational time-dependent Hartree for bosons (MCTDHB) and for fermions (MCTDHF) methods. Using the one- and two-body density, fermionization can be distinguished from crystallization in position space. For $N$ interacting bosons, a splitting into an $N$-fold pattern in the one-body and two-body density is a unique feature of both, fermionization and crystallization. We demonstrate that the splitting is incomplete for fermionized bosons and restricted by the confinement potential. This incomplete splitting is a consequence of the convergence of the energy in the limit of infinite repulsion and is in agreement with complementary results that we obtain for fermions using MCTDHF. For crystalline bosons, in contrast, the splitting is complete: the interaction energy is capable of overcoming the confinement potential. Our results suggest that the spreading of the density as a function of the dipolar interaction strength diverges as a power law. We describe how to distinguish fermionization from crystallization experimentally from measurements of the one- and two-body density.

研究动机与目标

• 区分强关联一维玻色子系统中的费米子化与结晶化行为。
• 分析相互作用类型（接触相互作用与偶极相互作用）对基态波函数结构的影响。
• 识别可通过约化密度矩阵获得的实验可观测量，以区分这两种物相。
• 阐明为何费米子化在能量上趋于饱和，而结晶化则不会，尽管两者均最小化空间重叠。

提出的方法

• 使用多配置时变玻色子哈特ree方法（MCTDHB）从第一性原理求解多体薛定谔方程。
• 为与费米子系统对比，应用多配置时变费米子哈特ree方法（MCTDHF）。
• 分析单体与双体约化密度矩阵，提取空间关联性与密度展宽特性。
• 比较接触相互作用（导致费米子化）与偶极相互作用（导致结晶化）下密度矩阵的行为。
• 量化单体与双体密度的展宽随相互作用强度的变化关系。
• 利用能量收敛性与密度矩阵本征值分析来区分两种物相。

实验结果

研究问题

• RQ1 如何利用实验可测物理量区分一维玻色子中的费米子化与结晶化行为？
• RQ2 为何费米子化体系在单体与双体密度中表现出不完全的N重分裂，而结晶化体系则呈现完全分裂？
• RQ3 约束势在限制费米子化玻色子展宽方面起什么作用，与结晶化体系中无界的相互作用能相比有何差异？
• RQ4 在强耦合 regime 下，接触相互作用与偶极相互作用的能量行为有何不同？
• RQ5 单体与双体密度的展宽能否作为实验诊断工具，用于识别多体玻色子系统的相态？

主要发现

• 即使在无限排斥极限下，费米子化玻色子由于局域化效应，其单体与双体密度仍表现出不完全的N重分裂。
• 费米子化玻色子的能量趋于非相互作用费米子的基态能量，与Tonks-Girardeau极限一致。
• 结晶化玻色子在单体与双体密度中表现出完全的N重分裂，表明完全的空间分离。
• 随着偶极相互作用强度增加，密度矩阵的展宽以幂律方式发散，表明能量无界增长。
• 单体与双体密度展宽特性的显著差异为实验区分费米子化与结晶化提供了清晰的可观测量。
• MCTDHB与MCTDHF计算结果证实，费米子化体系中不完全分裂源于能量收敛性，而非残余相互作用。