Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
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DOI：
10.1038/nphys3171
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发表时间：
2015-02-01
期刊：
影响因子：
19.6
通讯作者：
Goldman, N.
中科院分区：
文献类型：
--
作者：
Aidelsburger, M.;Lohse, M.;Goldman, N.
60年前，Karplus和Luttinger指出，在晶格上运动的量子粒子可以响应于力而获得异常的横向速度，为铁磁金属中不寻常的霍尔效应提供了解释。这种横向输运的一个显著表现在量子霍尔效应（2）中被揭示出来，其中霍尔电导率所描述的平台归因于表征布洛赫带的拓扑不变量：陈数（3）。到目前为止，与非零陈数相关的拓扑输运仅在电子系统中观察到（2，4，5）。在这里，我们使用原子云响应于光学梯度的横向偏转来测量人工产生的Hofstadter带的陈数（6）。这些拓扑带非常平坦，因此构成了实现分数陈氏绝缘体的良好候选者（7）。结合这些偏转测量和能带布居的确定，我们得到最低能带的陈数的实验值v（exp）= 0.99（5）。这是第一次在非电子系统中进行陈数测量，这是通过全光学人工规范场方案来实现的，在光学超晶格中产生均匀的通量。
Sixty years ago, Karplus and Luttinger pointed out that quantum particles moving on a lattice could acquire an anomalous transverse velocity in response to a force, providing an explanation for the unusual Hall effect in ferromagnetic metals(1). A striking manifestation of this transverse transport was then revealed in the quantum Hall effect(2) where the plateaux depicted by the Hall conductivity were attributed to a topological invariant characterizing the Bloch bands: the Chern number(3). Until now, topological transport associated with non-zero Chern numbers has only been observed in electronic systems(2,4,5). Here we use the transverse deflection of an atomic cloud in response to an optical gradient to measure the Chern number of artificially generated Hofstadter bands(6). These topological bands are very flat and thus constitute good candidates for the realization of fractional Chern insulators(7). Combining these deflection measurements with the determination of the band populations, we obtain an experimental value for the Chern number of the lowest band v(exp) = 0.99(5). This first Chern-number measurement in a non-electronic system is facilitated by an all-optical artificial gauge field scheme, generating uniform flux in optical superlattices.