A density wave (DW) is a fundamental type of long-range order in quantum matter tied to self-organization into a crystalline structure. The interplay of DW order with superfluidity can lead to complex scenarios that pose a great challenge to theoretical analysis. In the past decades, tunable quantum Fermi gases have served as model systems for exploring the physics of strongly interacting fermions, including most notably magnetic ordering¹, pairing and superfluidity², and the crossover from a Bardeen–Cooper–Schrieffer superfluid to a Bose–Einstein condensate³. Here, we realize a Fermi gas featuring both strong, tunable contact interactions and photon-mediated, spatially structured long-range interactions in a transversely driven high-finesse optical cavity. Above a critical long-range interaction strength, DW order is stabilized in the system, which we identify via its superradiant light-scattering properties. We quantitatively measure the variation of the onset of DW order as the contact interaction is varied across the Bardeen–Cooper–Schrieffer superfluid and Bose–Einstein condensate crossover, in qualitative agreement with a mean-field theory. The atomic DW susceptibility varies over an order of magnitude upon tuning the strength and the sign of the long-range interactions below the self-ordering threshold, demonstrating independent and simultaneous control over the contact and long-range interactions. Therefore, our experimental setup provides a fully tunable and microscopically controllable platform for the experimental study of the interplay of superfluidity and DW order.

密度波（DW）是量子物质中长程有序的基本类型，与自组织成晶体结构有关。DW 阶数与超流性的相互作用可能会导致复杂的场景，对理论分析提出巨大的挑战。在过去的几十年中，可调谐量子费米气体已成为探索强相互作用费米子物理的模型系统，包括最著名的磁有序¹、配对和超流性²，以及从 Bardeen-Cooper-Schrieffer 超流体到 Bose- 的交叉。爱因斯坦凝聚³。在这里，我们实现了一种费米气体，它在横向驱动的高精细光学腔中具有强的、可调谐的接触相互作用和光子介导的、空间结构的长程相互作用。在超过临界长程相互作用强度时，DW 有序在系统中稳定，我们通过其超辐射光散射特性来识别这一点。我们定量测量了随着 Bardeen-Cooper-Schrieffer 超流体和 Bose-Einstein 凝聚态交叉的接触相互作用的变化，DW 阶开始的变化，这与平均场理论在定性上一致。当将长程相互作用的强度和符号调整到自排序阈值以下时，原子 DW 敏感性会发生一个数量级的变化，展示对接触和远程交互的独立和同时控制。因此，我们的实验装置为超流性和 DW 阶次相互作用的实验研究提供了一个完全可调和微观可控的平台。