论文标题
一维耦合的玻色 - 哈伯德模型中的两个粒子状态
Two-particle States in One-dimensional Coupled Bose-Hubbard Models
论文作者
论文摘要
我们研究了动态耦合的一维玻色纸模型，并求解了两粒子本征态的波函数和能量。即使波函数并未直接遵循Bethe Ansatz的形式，我们还是描述了一种直观的结构，以表达它们作为Choy-Haldane状态的组合，用于具有物种间和种间相互作用的模型。我们发现，具有通用相互作用的系统的两粒子频谱一般包括四个不同的连续图和三个doublon分散体。双龙的存在取决于两种玻色子之间的耦合强度$ω$，它们的能量随$ω$和相互作用强度而变化。我们提供了一个特定极限的详细信息，即具有无限相互作用，并得出所有类型的两粒子状态及其空间和纠缠特性的光谱。我们证明了不同耦合强度下的时间演变差异，并检查系统的长期行为与Doublon分散体之间的关系。这些动态原则上可以在冷原子中观察到，也可以通过数字量子计算机模拟。
We study dynamically coupled one-dimensional Bose-Hubbard models and solve for the wave functions and energies of two-particle eigenstates. Even though the wave functions do not directly follow the form of a Bethe Ansatz, we describe an intuitive construction to express them as combinations of Choy-Haldane states for models with intra- and inter-species interaction. We find that the two-particle spectrum of the system with generic interactions comprises in general four different continua and three doublon dispersions. The existence of doublons depends on the coupling strength $Ω$ between two species of bosons, and their energies vary with $Ω$ and interaction strengths. We give details on one specific limit, i.e., with infinite interaction, and derive the spectrum for all types of two-particle states and their spatial and entanglement properties. We demonstrate the difference in time evolution under different coupling strengths, and examine the relation between the long-time behavior of the system and the doublon dispersion. These dynamics can in principle be observed in cold atoms and might also be simulated by digital quantum computers.
