We quantum simulated the 2D Harper-Hofstadter (HH) lattice model in a highly elongated tube geometry—three sites in circumference—using an atomic Bose-Einstein condensate. In addition to the usual transverse (out-of-plane) magnetic flux, piercing the surface of the tube, we threaded a longitudinal flux ${\mathrm{\Phi }}_{\mathrm{L}}$ down the axis of the tube. This geometry evokes an Aharonov-Bohm interferometer, where noise in ${\mathrm{\Phi }}_{\mathrm{L}}$ would readily decohere the interference present in trajectories encircling the tube. We observe this behavior only when transverse flux is a rational fraction of the flux quantum and remarkably find that for irrational fractions the decoherence is absent. Furthermore, at rational values of transverse flux, we show that the time evolution averaged over the noisy longitudinal flux matches the time evolution at nearby irrational fluxes. Thus, the appealing intuitive picture of an Aharonov-Bohm interferometer is insufficient. Instead, we quantitatively explain our observations by transforming the HH model into a collection of momentum-space Aubry-André models.

中文翻译：

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Harper-Hofstadter模型中的相干和去相干

我们使用原子Bose-Einstein冷凝物在高度伸长的管几何形状（圆周上的三个位置）上对2D Harper-Hofstadter（HH）晶格模型进行了量子模拟。除了通常的横向（平面外）磁通量，它刺穿管子的表面，我们还穿了一个纵向磁通量。${\mathrm{\Phi }}_{\mathrm{大号}}$沿着管子的轴线。这种几何形状让人想起Aharonov-Bohm干涉仪，${\mathrm{\Phi }}_{\mathrm{大号}}$会轻易地消除围绕管子的轨迹中存在的干扰。我们仅在横向通量是通量量子的合理分数时才观察到这种行为，并且显着地发现，对于不合理的分数，不存在退相干。此外，在横向通量的合理值下，我们表明，在嘈杂的纵向通量上平均的时间演化与附近无理通量的时间演化相匹配。因此，Aharonov-Bohm干涉仪的吸引人的直观图像是不够的。相反，我们通过将HH模型转换为动量空间Aubry-André模型的集合来定量地解释我们的观察结果。