We study the quantum dynamics of massive impurities embedded in a strongly interacting, two-dimensional atomic gas driven into the fractional quantum Hall (FQH) regime under the effect of a synthetic magnetic field. For suitable values of the atom-impurity interaction strength, each impurity can capture one or more quasihole excitations of the FQH liquid, forming a bound molecular state with novel physical properties. An effective Hamiltonian for such anyonic molecules is derived within the Born-Oppenheimer approximation, which provides renormalized values for their effective mass, charge, and statistics by combining the finite mass of the impurity with the fractional charge and statistics of the quasiholes. The renormalized mass and charge of a single molecule can be extracted from the cyclotron orbit that it describes as a free particle in a magnetic field. The anyonic statistics introduces a statistical phase between the direct and exchange scattering channels of a pair of indistinguishable colliding molecules and can be measured from the angular position of the interference fringes in the differential scattering cross section. Implementations of such schemes beyond cold atomic gases are highlighted—in particular, in photonic systems.

中文翻译：

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原子分数分数霍尔效应液体中的非质子分子：分数电荷和非质子统计的定量探针

我们研究了在合成磁场的作用下，嵌入到相互作用的二维原子气体中的大量杂质的量子动力学，这些原子气体被驱动进入分数量子霍尔（FQH）机制。对于适当的原子-杂质相互作用强度值，每种杂质都可以捕获FQH液体的一个或多个准孔激发，从而形成具有新颖物理性质的键合分子态。在Born-Oppenheimer近似中，得出了此类非离子分子的有效哈密顿量，它通过将杂质的有限质量与分数电荷和准孔的统计量结合起来，为其有效质量，电荷和统计量提供了重新归一化的值。可以从回旋加速器轨道提取单个分子的重新归一化的质量和电荷，该回旋加速器轨道描述为磁场中的自由粒子。非调子统计量在一对不可区分的碰撞分子的直接和交换散射通道之间引入统计相位，并且可以从微分散射截面中干涉条纹的角位置进行测量。重点介绍了这种方案的实现，而不是冷原子气体，尤其是在光子系统中。