Using quantum gas microscopy we study the late-time effective hydrodynamics of an isolated cold-atom Fermi-Hubbard system subject to an external linear potential (a ``tilt"). The tilt is along one of the principal directions of the two-dimensional (2D) square lattice and couples mass transport to local heating through energy conservation. Due to this coupling the system quickly heats up to near infinite temperature in the lowest band of the lattice. We study the high-temperature transport and thermalization in our system by observing the decay of prepared initial density waves as a function of wavelength $\lambda$ and tilt strength and find that the associated decay time $\tau$ crosses over as the tilt strength is increased from characteristically diffusive to subdiffusive with $\tau \propto {\lambda }^4$. In order to explain the underlying physics and emphasize its universal nature we develop a hydrodynamic model that exhibits this crossover. For strong tilts, the subdiffusive transport rate is set by a thermal diffusivity, which we are thus able to measure as a function of tilt in this regime. We further support our understanding by probing the local inverse temperature of the system at strong tilts, finding good agreement with our theoretical predictions. Finally, we discuss the relation of the strongly tilted limit of our system to recently studied 1D models which may exhibit nonergodic dynamics.

中文翻译：

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倾斜二维费米-哈伯德系统中的子扩散和热传递

我们使用量子气体显微镜研究了受外部线性电势（“倾斜”）影响的孤立冷原子费米-哈伯德系统的后期有效流体动力学，该倾斜沿二维的主要方向之一（2D）方格并通过能量守恒将传质耦合到局部加热，由于这种耦合，系统在格的最低带迅速加热到接近无限温度，我们通过以下方法研究了系统中的高温传热和热化：观察准备的初始密度波随波长的衰减 $\lambda$ 和倾斜强度，发现相关的衰减时间 $\tau$ 随着倾斜强度从特征扩散增加到亚扩散而交叉 $\tau \propto {\lambda }^4$。为了解释基础物理学并强调其普遍性，我们开发了一种表现出这种交叉的流体力学模型。对于强烈的倾斜，亚扩散传输速率由热扩散率设置，因此我们可以在这种情况下根据倾斜的函数对其进行测量。我们通过探测系统在强倾斜下的局部逆温度来进一步支持我们的理解，并与我们的理论预测很好地吻合。最后，我们讨论了系统的强烈倾斜极限与最近研究的一维模型之间的关系，该模型可能表现出非遍历动力学。