Modern experimental platforms such as superconducting circuit arrays call for the exploration of bosonic tight-binding models in unconventional situations with no counterpart in real materials. Here we investigate one such situation in which excitations are driven and damped by pairs, leading to pattern formation and exotic bosonic states emerging from a nonequilibrium quantum many-body system. Focusing on a two-dimensional driven-dissipative Bose-Hubbard model, we find that its steady states are characterized by the condensation of bosons around momenta lying on a “Bose surface,” a bosonic analog of the Fermi surface in solid-state systems. The interplay between instabilities generated by the driving, the nonlinear dissipative mode coupling, and the underlying lattice effect allows the system to equilibrate into an exotic superfluid state of bosons condensed on a closed ring in momentum space instead of discrete points. Such an unconventional state with a spatially uniform density distribution goes beyond the traditional scope of pattern formation and thus has no counterpart in the classical literature. In addition, it is a state connected to several open problems in modern condensed-matter physics. Here we provide the means to stabilize it, opening the way to its experimental study. Moreover, we also provide a concrete experimental implementation of our model in currently available superconducting circuit arrays. We also investigate the relaxation spectrum around the condensate, which shows a characteristic purely diffusive behavior.

中文翻译：

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驱动耗散的Bose-Hubbard系统中的模式形成和奇异顺序。

诸如超导电路阵列之类的现代实验平台要求在非常规情况下探索玻色紧密结合模型，而在实际材料中却没有相应的模型。在这里，我们研究了一种这样的情况，其中激发是由成对驱动和衰减的，从而导致从非平衡量子多体系统中出现图案形成和外来的玻色子状态。着眼于二维驱动耗散的Bose-Hubbard模型，我们发现其稳态的特征在于位于“ Bose表面”上的矩周围的玻色子凝结，Bose表面是固态系统中费米表面的玻色类似物。由驱动产生的不稳定性，非线性耗散模式耦合之间的相互作用，潜在的晶格效应使系统能够平衡到玻色子的奇特超流体状态，该玻色子凝聚在动量空间的封闭环中，而不是离散点。这种具有空间上均匀的密度分布的非常规状态超出了传统的图案形成范围，因此在古典文献中没有对应的状态。另外，它是与现代凝聚态物理中的几个开放问题相关的状态。在这里，我们提供了稳定它的方法，为它的实验研究开辟了道路。此外，我们还在当前可用的超导电路阵列中提供了模型的具体实验实现。我们还研究了凝结水周围的弛豫谱，它显示出特征性的纯扩散行为。