介观量子电路中的合成扭曲几何：几何电容与手性模式劈裂

中文摘要 AI 辅助

我们提出了一种在介观量子电路中编码螺旋状扭曲合成几何的路径。一个带有扭曲参数$\Om$的无扭转空间度量定义了一个静电电容核，其角-轴向扇区包含手性耦合$-2\Om mk$。我们证明该核可以通过一个仅由正二节点电容器构成的有限、可量子化的电路图来实现：对角桥产生交叉项，无量纲扭曲是对角电容与总角向电容之比。所得电容矩阵通过$C^{-1}(\etaT)$进入哈密顿量，并劈裂反向旋转的合成模式。精确的有限图对角化证实了解析谱，并表明需要闭合的纵向循环；对于开放边界，桥相位是可规范移除的，双重态保持简并。模拟光谱分辨出手性扇，而无序模拟表明，在校准的百分比级反应性无序下，所考虑的参数范围内确定性劈裂不会被掩盖。扭曲纹理产生界面模式，约瑟夫森非线性使Kerr扇区具有手性依赖性，同一双重态为非厄米奇异点控制提供了失谐旋钮。对于代表性的电路量子电动力学参数，劈裂在数十兆赫兹范围内，远高于典型的谐振器线宽。

英文摘要

We propose a route for encoding a helicoidally twisted synthetic geometry in mesoscopic quantum circuits. A torsionless spatial metric with twist parameter $\Om$ defines an electrostatic capacitance kernel whose angular--axial sector contains the chiral coupling $-2\Om mk$. We show that this kernel can be implemented by a finite, quantizable circuit graph built only from positive two-node capacitors: diagonal bridges generate the cross term, and the dimensionless twist is the ratio of diagonal to total angular capacitance. The resulting capacitance matrix enters the Hamiltonian through $C^{-1}(\etaT)$ and splits counter-rotating synthetic modes. Exact finite-graph diagonalization confirms the analytic spectrum and shows that closed longitudinal circulation is required; with open boundaries the bridge phase is gauge removable and the doublets remain degenerate. Simulated spectroscopy resolves the chiral fan, while disorder simulations indicate that calibrated percent-level reactive disorder does not obscure the deterministic splitting in the parameter range considered. Twist textures produce interface modes, Josephson nonlinearities make the Kerr sector chirality dependent, and the same doublet provides a detuning knob for non-Hermitian exceptional-point control. For representative circuit-QED parameters the splitting is in the tens-of-MHz range, well above typical resonator linewidths.

发表机构

• Universidade Federal do Maranhão（马拉尼昂联邦大学）

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11 figures, 1 table