来自秩一淬火的最大秩压缩：高斯玻色系统的精确谱可达性定理
Maximal-Rank Squeezing from Rank-One Quenches: An Exact Spectral-Reachability Theorem for Gaussian Bosonic Systems
AI总结：
该研究证明高斯玻色系统有限秩二次淬火产生多模压缩的精确谱可达性定理，揭示微扰秩不限制激活压缩通道数，给出暗区等特性，为多模高斯系统提供硬件筛选原则。
AI中文摘要：
我们证明了高斯玻色系统中由有限秩二次淬火产生的多模压缩的精确谱可达性定理。对于稳定的符号确定刚度淬火$\Omega^2 \to \Omega^2+\varepsilon U U^T$，反常Bogoliubov块的核、值域和秩完全由$\Omega$和$U$生成的块Krylov子空间确定。具体而言，$\operatorname{rank}(β_\varepsilon)=\sum_a \operatorname{rank}(P_a U)$，其中$P_a$是投影到每个不同自由频率本征空间的投影算子。由此可得，微扰的微观秩并不限制其能激活的压缩通道数量：对于简单谱，一个与所有模式都有非零交叠的单秩一元在每个非零稳定耦合下都会产生满秩的反常Bogoliubov响应。带符号的Lyapunov-Gramian路径表明，谱可达方向不会通过有限耦合抵消而消失。该定理还能在无需计算完整Bogoliubov变换的情况下给出精确的暗区、简并瓶颈和致动器位置规则。这些结果为多模高斯系统提供了直接的硬件筛选原则：一个或少数物理元件可同时支持多个正则压缩通道，不过仅代数秩并不意味着强压缩或独立可调谐性。
英文摘要：
We prove an exact spectral-reachability theorem for multimode squeezing generated by finite-rank quadratic quenches in Gaussian bosonic systems. For a stable sign-definite stiffness quench $Ω^2 \to Ω^2+\varepsilon U U^T$, the kernel, range, and rank of the anomalous Bogoliubov block are determined exactly by the block-Krylov subspace generated by $Ω$ and $U$. In particular, $\operatorname{rank}(β_\varepsilon)=\sum_a \operatorname{rank}(P_a U)$, where $P_a$ projects onto each distinct free-frequency eigenspace. Consequently, the microscopic rank of a perturbation does not bound the number of squeezing channels it can activate: for a simple spectrum, a single rank-one element with nonzero overlap with every mode produces a full-rank anomalous Bogoliubov response at every nonzero stable coupling. A signed Lyapunov-Gramian path shows that spectrally reachable directions cannot disappear through finite-coupling cancellation. The theorem also gives exact dark sectors, degeneracy bottlenecks, and actuator-position rules without computing the full Bogoliubov transformation. These results provide a direct hardware-screening principle for multimode Gaussian systems: one or a few physical elements can provide simultaneous support across many canonical squeezing channels, although algebraic rank alone does not imply strong squeezing or independent tunability.
