[论文解读] Supersymmetrically bounding of asymmetric states and quantum phase transitions by anti-crossing of symmetric states

Muhammad Imran Afzal, Yong Tak Lee|arXiv (Cornell University)|Feb 18, 2016

Topological Materials and Phenomena参考文献 42被引用 3

一句话总结

该论文表明，在非均匀应变晶格中，对称光子态的反交叉可诱导高阶超对称性，导致非对称本征态的束缚，并触发量子相变。通过在一维三角形孤子晶格中的共振，实验实现了哈密顿和非哈密顿的异常点，产生包括量子Zeno相和安德森局域化在内的拓扑与几何相变。

ABSTRACT

Von Neumann and Wigner theorized the bounding and anti-crossing of eigenstates. Experiments have demonstrated that owing to anti-crossing and similar radiation rates, the graphene-like resonance of inhomogeneously strained photonic eigenstates can generate a pseudomagnetic field, bandgaps and Landau levels, whereas exponential or dissimilar rates induce non-Hermicity. Here, we experimentally demonstrate higher-order supersymmetry and quantum phase transitions by resonance between similar one-dimensional lattices. The lattices consisted of inhomogeneous strain-like phases of triangular solitons. The resonance created two-dimensional, inhomogeneously deformed photonic graphene. All parent eigenstates were annihilated. Eigenstates of mildly strained solitons were annihilated at similar rates through one tail and generated Hermitian bounded eigenstates. The strongly strained solitons with positive phase defects were annihilated at exponential rates through one tail, which bounded eigenstates through non-Hermitianally generated exceptional points. However, strongly strained solitons with negative defects were effectively amplified. Supersymmetry was evident, with preservation of the shapes and relative phase differences of the parent solitons. Localizations of energies generated from annihilations of mildly and strongly strained soliton eigenstates were responsible for geometrical (Berry) and topological phase transitions, respectively. Both contributed to generating a quantum Zeno phase, whereas only strong twists generated topological (Anderson) localization. Anti-bunching-like condensation was also observed.

研究动机与目标

• 探讨对称光子态的反交叉如何诱导非对称本征态的超对称束缚。
• 研究非均匀应变光子晶格中量子相变的出现机制。
• 展示相似的一维晶格之间共振在生成高阶超对称性中的作用。
• 考察在指数衰减与相似衰减率下，哈密顿与非哈密顿本征态行为的差异。
• 将本征态湮灭与局域化联系至几何（Berry）相变和拓扑（Anderson）相变。

提出的方法

• 利用三角形孤子的非均匀应变相位，构建二维变形光子石墨烯晶格。
• 通过相同一维晶格之间的共振，诱导对称态的反交叉。
• 应用高阶超对称性，以在本征态湮灭过程中保持母孤子的形状与相对相位差。
• 区分在相似衰减率（哈密顿束缚态）与指数衰减（非哈密顿异常点）下的本征态行为。
• 追踪本征态湮灭过程中的能量局域化，以识别相变机制。
• 将反聚束类凝聚识别为量子Zeno相出现的特征。

实验结果

研究问题

• RQ1 对称光子态的反交叉如何导致非对称本征态的超对称束缚？
• RQ2 相似衰减率与指数衰减率在生成哈密顿或非哈密顿异常点中分别起什么作用？
• RQ3 在弱应变与强应变孤子中，本征态湮灭过程如何促成几何与拓扑相变？
• RQ4 该系统通过能量局域化在何种方式下实现量子Zeno相？
• RQ5 这种超对称光子晶格中反聚束类凝聚的机制是什么？

主要发现

• 在共振的一维晶格中，对称态的反交叉导致高阶超对称性的生成，成功保持了母孤子的形状与相位。
• 具有相似衰减率的弱应变孤子通过一端尾部湮灭，产生哈密顿束缚本征态。
• 具有正相位缺陷的强应变孤子以指数速率湮灭，形成非哈密顿异常点并束缚本征态。
• 具有负相位缺陷的强应变孤子表现出有效放大，表明存在非哈密顿增益动力学。
• 本征态湮灭导致的能量局域化驱动了几何（Berry）与拓扑（Anderson）相变。
• 系统表现出反聚束类凝聚并实现了量子Zeno相，其中仅在强扭曲条件下发生拓扑局域化。