Ultracold atoms in optical lattices have emerged as powerful quantum simulators of translationally invariant systems with many applications in e.g. strongly-correlated and topological systems. However, the ability to locally tune all Hamiltonian parameters remains an outstanding goal that would enable the simulation of a wider range of quantum phenomena. Motivated by recent advances in quantum gas microscopes and optical tweezers, we here show theoretically how local control over individual tunnelling links in an optical lattice can be achieved by incorporating local time-periodic potentials. We propose to periodically modulate the on-site energy of individual lattice sites and employ Floquet theory to demonstrate how this provides full individual control over the tunnelling amplitudes in one dimension. We provide various example configurations realising interesting topological models such as extended Su–Schrieffer–Heeger models that would be challenging to realise by other means. Extending to two dimensions, we demonstrate that local periodic driving in a Lieb lattice engineers a two-dimensional (2D) network with fully controllable tunnelling magnitudes. In a three-site plaquette, we show full simultaneous control over the relative tunnelling amplitudes and the gauge-invariant flux piercing the plaquette, providing a clear stepping stone to building a fully programmable 2D tight-binding model. We also explicitly demonstrate how utilise our technique to generate a magnetic field gradient in 2D. This local modulation scheme is applicable to many different lattice geometries.

中文翻译：

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使用局部周期驱动在光学晶格中单独可调隧道系数


光学晶格中的超冷原子已成为平移不变系统的强大量子模拟器，在强相关和拓扑系统等领域具有许多应用。然而，局部调整所有哈密顿参数的能力仍然是一个突出的目标，它将能够模拟更广泛的量子现象。受量子气体显微镜和光镊最新进展的推动，我们在这里从理论上展示了如何通过结合局部时间周期势来实现对光学晶格中各个隧道链路的局部控制。我们建议定期调制各个晶格位置的现场能量，并采用 Floquet 理论来演示这如何提供对一维隧道振幅的完全单独控制。我们提供了各种示例配置来实现有趣的拓扑模型，例如扩展的 Su-Schrieffer-Heeger 模型，这些模型很难通过其他方式实现。扩展到二维，我们证明了利布晶格中的局部周期性驱动设计了具有完全可控隧道大小的二维（2D）网络。在三点小板中，我们展示了对相对隧道振幅和穿透小板的规范不变通量的完全同步控制，为构建完全可编程的二维紧束缚模型提供了明确的垫脚石。我们还明确演示了如何利用我们的技术生成二维磁场梯度。这种局部调制方案适用于许多不同的晶格几何形状。