哈伯德模型在光晶格中的成功仿真激发了世界范围内的努力，以扩展其范围，以捕捉更复杂、不完全理解的多体物理场景。不幸的是，对于玻色子，费恩曼的基本“无节点”定理在非常一般的情况下预测了一个正定的基态波函数，与感兴趣的多体系统的相关性有限。围绕费恩曼陈述的一个有希望的方法是考虑具有多于一维的光晶格中的更高能带，其中由于多个轨道取向而具有其固有各向异性的轨道自由度引起结构多样性，例如，在强相关电子物质领域中高度相关。在均匀的二维光晶格中，激发带的寿命可能在100毫秒的量级，但隧穿动力学似乎不支持跨维相干性。在这里，我们报告的第一个观察到的超流体的$P$ -带的二分光学正方形晶格的$S$ -轨道和$P$ -轨道排列在棋盘图案。这使我们能够在几十毫秒的寿命内建立完整的跨维度相干性。根据晶格的小的可调各向异性，我们可以实现具有不同取向的$P_x \pm P_y$或复值$P_x \pm i P_y$序参量的实值条纹超流序参量，这打破了时间反演对称性，类似于高温超导体中提出的$π$ -通量模型。我们的实验开辟了轨道超流体的领域，以光学晶格模型的调查。
英文摘要：
The successful emulation of the Hubbard model in optical lattices has stimulated world wide efforts to extend their scope to also capture more complex, incompletely understood scenarios of many-body physics. Unfortunately, for bosons, Feynmans fundamental "no-node" theorem under very general circumstances predicts a positive definite ground state wave function with limited relevance for many-body systems of interest. A promising way around Feynmans statement is to consider higher bands in optical lattices with more than one dimension, where the orbital degree of freedom with its intrinsic anisotropy due to multiple orbital orientations gives rise to a structural diversity, highly relevant, for example, in the area of strongly correlated electronic matter. In homogeneous two-dimensional optical lattices, lifetimes of excited bands on the order of a hundred milliseconds are possible but the tunneling dynamics appears not to support cross-dimensional coherence. Here we report the first observation of a superfluid in the $P$-band of a bipartite optical square lattice with $S$-orbits and $P$-orbits arranged in a chequerboard pattern. This permits us to establish full cross-dimensional coherence with a life-time of several ten milliseconds. Depending on a small adjustable anisotropy of the lattice, we can realize real-valued striped superfluid order parameters with different orientations $P_x \pm P_y$ or a complex-valued $P_x \pm i P_y$ order parameter, which breaks time reversal symmetry and resembles the $π$-flux model proposed in the context of high temperature superconductors. Our experiment opens up the realms of orbital superfluids to investigations with optical lattice models.
Competition between pair and single-particle superfluidity in bosonic quasi-flat bands: A Gaussian state approach
Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles（布鲁塞尔自由大学非线性现象与复杂系统中心）；International Solvay Institutes（国际索尔维研究所）；Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université（巴黎文理研究大学卡斯勒布罗塞尔实验室）
