Title: Entanglement properties of bound and resonant few-body states Show Chinese title

Title: 束缚和共振少体态的纠缠性质

Abstract: Studying the physics of quantum correlations has gained new interest after it has become possible to measure entanglement entropies of few body systems in experiments with ultracold atomic gases. Apart from investigating trapped atom systems, research on correlation effects in other artificially fabricated few-body systems, such as quantum dots or electromagnetically trapped ions, is currently underway or in planning. Generally, the systems studied in these experiments may be considered as composed of a small number of interacting elements with controllable and highly tunable parameters, effectively described by Schr\"odinger equation. In this way, parallel theoretical and experimental studies of few-body models become possible, which may provide a deeper understanding of correlation effects and give hints for designing and controlling new experiments. Of particular interest is to explore the physics in the strongly correlated regime and in the neighborhood of critical points. Particle correlations in nanostructures may be characterized by their entanglement spectrum, i.e. the eigenvalues of the reduced density matrix of the system partitioned into two subsystems. We will discuss how to determine the entropy of entanglement spectrum of few-body systems in bound and resonant states within the same formalism. The linear entropy will be calculated for a model of quasi-one dimensional Gaussian quantum dot in the lowest energy states. We will study how the entanglement depends on the parameters of the system, paying particular attention to the behavior on the border between the regimes of bound and resonant states. Show Chinese abstract

Abstract: 研究量子关联的物理特性在能够通过超冷原子气体实验测量少体系统的纠缠熵后重新引起了关注。 除了研究被束缚的原子系统外，目前正在进行或正在计划研究其他人工制造的少体系统中的关联效应，例如量子点或电磁束缚离子。 一般来说，这些实验中研究的系统可以看作是由少量相互作用的元件组成，其参数可控制且高度可调，可以通过薛定谔方程有效描述。 这样，就可以进行少体模型的平行理论和实验研究，这可能有助于更深入地理解关联效应，并为设计和控制新实验提供线索。 特别感兴趣的是探索强关联区域以及临界点附近的物理现象。 纳米结构中的粒子关联可以通过其纠缠谱来表征，即系统分成两个子系统时约化密度矩阵的本征值。 我们将讨论如何在同一形式体系中确定束缚态和共振态下少体系统的纠缠谱熵。 将在最低能量态下计算准一维高斯量子点模型的线性熵。 我们将研究纠缠如何依赖于系统的参数，特别关注束缚态和共振态区域边界的行为。