用于含时双模玻色子哈密顿量量子信息诊断的玻戈留波夫比率框架
A Bogoliubov-ratio framework for quantum-information diagnostics of time-dependent two-mode Boson System
- Jishou University（吉首大学）
- Huaihua University（怀化学院）
- Beihang University（北京航空航天大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究基于玻戈留波夫比率，为含时双模玻色子系统提出量子信息诊断框架。通过复里卡蒂方程和约化密度矩阵谱确定相关熵公式，无需逐个模型重构对角化。在宇宙学和光学领域展示效用，提供高效标准化诊断工具。
AI中文摘要：
我们基于玻戈留波夫比率$\lambda_k(\eta) \equiv \beta_k(\eta)/\alpha_k(\eta)$，提出了一个用于含时双模玻色子系统量子信息诊断的紧凑统一框架。对于一般含时二次双模哈密顿量，态动力学精确简化为关于$\lambda_k$的单个复里卡蒂方程。通过追踪一个伙伴模式，单模约化密度矩阵的谱完全由$q_k(\eta) = \vert{}\lambda_k(\eta)\vert{}^2$确定。我们能构建与模型无关的约化态纯度、线性熵、雷尼 - 2熵和冯·诺依曼熵的显式公式。我们在原初宇宙学微扰和啁啾脉冲非简并光学参量放大器这两个不同的非平稳设置中展示了该框架的效用。在宇宙学背景下，阐明了背景诱导的相位旋转和频率软化如何调节压缩增长和态混合性；在光学领域，捕捉到了由有限泵浦持续时间和频率啁啾引起的延迟起始、压缩积累抑制和后期熵饱和。该框架通过将与模型相关的驱动协议与通用信息理论度量清晰分解，为一类参数驱动的二次玻色子系统提供了高效、标准化的诊断工具。
英文摘要：
We formulate a compact dynamical representation of quantum-information diagnostics for time-dependent two-mode bosonic systems in terms of the Bogoliubov ratio $λ_k(η)=β_k(η)/α_k(η)$. For vacuum-evolved pure Gaussian pair states generated by a Hermitian quadratic Hamiltonian, $λ_k$ obeys a closed complex Riccati equation. After one partner mode is traced out, the reduced-state spectrum is determined by $q_k=|λ_k|^2$, from which the purity, linear entropy, Rényi-2 entropy, and von Neumann entropy follow directly. These Gaussian results are mathematically equivalent to those obtained from the standard density-matrix or covariance-matrix formalism; the advantage of the ratio representation is a compact separation between model-dependent dynamics and universal state diagnostics. Writing $λ_k=\sqrt{q_k}e^{iθ_k}$ further exposes how pair production drives radial growth, whereas frequency rotation and detuning act through the phase and can suppress coherent squeezing accumulation. We also establish an exact extension to non-Gaussian $SU(1,1)$ sectors. For a lowest-weight Fock seed with conserved number difference $d$, the same ratio equation governs the evolution, while the reduced spectrum becomes a negative-binomial distribution determined by $(q_k,d)$. The Gaussian formulas are recovered at $d=0$. Cosmological perturbations and a chirped-pulse optical parametric amplifier illustrate the common dynamical mechanism and its information-theoretic consequences.
