发表机构
Universidad Autonoma de Chihuahua; Universidad Autonoma Metropolitana-Cuajimalpa（奇瓦瓦自治大学; 墨西哥自治大学-夸希马尔帕分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种非微扰高斯闭合方法，有效研究transmon超导电路，推导闭式哈密顿量并验证其优于Kerr近似，且Bateman动力学在弱阻尼下保持海森堡界限并匹配Lindblad基准。
AI 中文摘要
我们将重要的量子力学形式应用于transmon区域中超导电路的非微扰研究，推导出裸约瑟夫森结（JJ）、腔-JJ系统以及耗散谐振器的有效运动方程。对量子矩层级的高斯闭合将完整的余弦非线性重求和为闭式有效哈密顿量 $\tfrac{1}{2}[V(\phi+\phi_s)+V(\phi-\phi_s)]$，该哈密顿量是非微扰的，并在所有相位幅度下保持约瑟夫森势的周期性和有界性；标准Kerr（Duffing）近似作为特例被恢复。我们推导了量子修饰频率 $\omega_{\rm eff}=\Omega_p\sqrt{\cos(\phi_{\rm zpf}/\phi_0)}$，并将有效动力学与精确的Mathieu函数对角化进行基准比较，其中量子宽度 $G^{2,0}(t)$ 提供了对闭合有效性的最敏感诊断，并且比 $\langle\hat\phi\rangle(t)$ 更清晰地标记了高斯近似的边界。我们比较了Caldirola-Kanai、Bateman和Lindblad描述：Bateman动力学，通过切换辛结构量子化，保持了海森堡界限，允许精确的闭式矩解，并在弱阻尼下重现Lindblad基准，即在解析误差界 $(\lambda/\omega_1)^2\\,\phi_{\rm zpf}^2$ 内。
英文摘要
We apply the momentous quantum mechanics formalism to the non-perturbative study of superconducting circuits in the transmon regime, deriving effective equations of motion for the bare Josephson junction (JJ), the cavity--JJ system, and a dissipative resonator. A Gaussian closure on the hierarchy of quantum moments resums the full cosine nonlinearity into the closed-form effective Hamiltonian $\tfrac{1}{2}[V(ϕ+ϕ_s)+V(ϕ-ϕ_s)]$, which is non-perturbative and preserves the periodicity and boundedness of the Josephson potential at all phase amplitudes; the standard Kerr (Duffing) approximation is recovered as a special case. We derive the quantum-dressed frequency $ω_{\rm eff}=Ω_p\sqrt{\cos(ϕ_{\rm zpf}/ϕ_0)}$, and benchmark the effective dynamics against exact Mathieu-function diagonalization, with the quantum width $G^{2,0}(t)$ providing the most sensitive diagnostic of the closure's validity and marks the boundary of the Gaussian approximation more sharply than $\langle\hatϕ\rangle(t)$ does. We compare the Caldirola--Kanai, Bateman, and Lindblad descriptions: the Bateman dynamics, quantized with a switched symplectic structure, preserves the Heisenberg bound, admits exact closed-form moment solutions, and reproduces the Lindblad benchmark for weak damping, i.e., within the analytic error bound $(λ/ω_1)^2\,ϕ_{\rm zpf}^2$.
