Excitation spectrum of bosons in a finite one-dimensional circular waveguide via the Bethe ansatz
Excitation spectrum of bosons in a finite one-dimensional circular waveguide via the Bethe ansatz
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通过 Bethe ansatz 有限一维圆形波导中玻色子的激发谱
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
Matthew J. Davis
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文献类型：
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作者：
A. Sykes;P. Drummond;Matthew J. Davis
随着超冷原子实验开始探索这一机制，一维相互作用玻色子的精确可解的Lieb-Liniger模型又引起了人们的兴趣。在这里，我们数值求解所产生的方程从贝特anomaly解决方案的精确多体波函数在一个有限大小的系统，最多20个粒子的吸引力的相互作用。我们讨论的解决方案的特点，以及他们如何偏离著名的弦解决方案[Thacker，修订版。物理53，253（1981）]在有限密度。我们提出了激发态弦的解决方案，在强相互作用的极限，并讨论其物理解释，以及量子相变的特性，发生在平均场极限的相互作用强度的函数。最后，我们比较了我们的结果与截断基上的多体哈密顿量的精确对角化。我们也给出了环上排斥性一维玻色气体的激发态解和激发谱。
The exactly solvable Lieb-Liniger model of interacting bosons in one dimension has attracted renewed interest as current experiments with ultracold atoms begin to probe this regime. Here we numerically solve the equations arising from the Bethe ansatz solution for the exact many-body wave function in a finite-size system of up to 20 particles for attractive interactions. We discuss the features of the solutions, and how they deviate from the well-known string solutions [Thacker, Rev. Mod. Phys. 53, 253 (1981)] at finite densities. We present excited state string solutions in the limit of strong interactions and discuss their physical interpretation, as well as the characteristics of the quantum phase transition that occurs as a function of interaction strength in the mean-field limit. Finally we compare our results to those of exact diagonalization of the many-body Hamiltonian in a truncated basis. We also present excited state solutions and the excitation spectrum for the repulsive one-dimensional Bose gas on a ring.