Maximal-Rank Squeezing from Rank-One Quenches: An Exact Spectral-Reachability Theorem for Gaussian Bosonic Systems

• URL: http://arxiv.org/abs/2608.21434v1
• Date: Mon, 17 Aug 2026 17:12:19 GMT
• Title: Maximal-Rank Squeezing from Rank-One Quenches: An Exact Spectral-Reachability Theorem for Gaussian Bosonic Systems
• Abstract summary: We prove an exact spectral-reachability theorem for multimode squeezing generated by finite-rank quadratic quenches in Gaussian bosonic systems.<n>A single rank-one element with nonzero overlap with every mode produces a full-rank anomalous Bogoliubov response at every nonzero stable coupling.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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