原子分数量子霍尔液体中的任意子分子：分数电荷和任意子统计的定量探针
Anyonic molecules in atomic fractional quantum Hall liquids: a quantitative probe of fractional charge and anyonic statistics
摘要：
研究了强相互作用二维原子气体中的大质量杂质在合成磁场作用下进入分数量子霍尔区的量子动力学行为。对于合适的原子-杂质相互作用强度值，每个杂质可以捕获一个或多个准空穴激发的H2 O2液体，形成一个绑定的分子状态与新的物理性质。这样的任意子分子的有效哈密顿量内Born-Oppenheimer近似，它提供了重整化的值，其有效质量，电荷和统计相结合的杂质的有限质量与分数电荷和准空穴的统计。单个分子的重整化质量和电荷可以从回旋加速器轨道中提取出来，它被描述为磁场中的自由粒子。任意子统计在一对不可区分的碰撞分子的直接散射通道和交换散射通道之间引入了统计相位，并且可以从微分散射截面中的干涉条纹的角位置来测量。这种方案的实现超出了冷原子气体的重点，特别是在光子系统。
英文摘要：
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 quasi-hole 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 quasi-holes. 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.
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