After two decades of development, cavity quantum electrodynamics with superconducting circuits has emerged as a rich platform for quantum computation and simulation. Lattices of coplanar waveguide resonators constitute artificial materials for microwave photons, in which interactions between photons can be incorporateded either through the use of nonlinear resonator materials or through coupling between qubits and resonators. Here we make use of the previously overlooked property that these lattice sites are deformable and permit tight-binding lattices that are unattainable even in solid-state systems. We show that networks of coplanar waveguide resonators can create a class of materials that constitute lattices in an effective hyperbolic space with constant negative curvature. We present numerical simulations of hyperbolic analogues of the kagome lattice that show unusual densities of states in which a macroscopic number of degenerate eigenstates comprise a spectrally isolated flat band. We present a proof-of-principle experimental realization of one such lattice. This paper represents a step towards on-chip quantum simulation of materials science and interacting particles in curved space. An interconnected network made of superconducting microwave resonators is created as a step towards quantum simulations of interacting particles in hyperbolic space.

中文翻译：

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电路量子电动力学中的双曲晶格

经过二十年的发展，具有超导电路的腔量子电动力学已经成为量子计算和模拟的丰富平台。共面波导谐振器的晶格构成了微波光子的人造材料，其中光子之间的相互作用可以通过使用非线性谐振器材料或通过量子位和谐振器之间的耦合来结合。在这里，我们利用了先前被忽视的特性，即这些晶格位点是可变形的，并且允许即使在固态系统中也无法实现的紧束缚晶格。我们展示了共面波导谐振器网络可以创建一类材料，这些材料在具有恒定负曲率的有效双曲空间中构成晶格。我们提出了 Kagome 晶格的双曲类似物的数值模拟，这些模拟显示了不寻常的状态密度，其中宏观数量的简并本征态包含一个光谱隔离的平坦带。我们提出了一个这样的晶格的原理验证实验实现。这篇论文代表了材料科学和弯曲空间中相互作用粒子的片上量子模拟迈出的一步。创建由超导微波谐振器组成的互连网络，作为迈向双曲空间中相互作用粒子的量子模拟的一步。这篇论文代表了材料科学和弯曲空间中相互作用粒子的片上量子模拟迈出的一步。创建了由超导微波谐振器组成的互连网络，作为迈向双曲空间中相互作用粒子的量子模拟的一步。这篇论文代表了材料科学和弯曲空间中相互作用粒子的片上量子模拟迈出的一步。创建了由超导微波谐振器组成的互连网络，作为迈向双曲空间中相互作用粒子的量子模拟的一步。