玻色系统中动力学不稳定性的量子几何边界
Quantum-Geometric Bound on Dynamical Instability in Bosonic Systems
AI总结：
本文针对多模二次玻色系统，推导得到动力学不稳定性最大本征值与Fubini-Study速度的严格量子几何边界，通过共振纯squeezer实现边界饱和，并在失谐参量放大器中验证了边界的不可逆性。
AI中文摘要：
量子几何速度与动力学不稳定性是受驱量子系统的两个自然速率，即便对于可精确求解的动力学，二者的关系仍未明确。本文针对以裸模真空为参考的任意多模二次玻色系统，证明Fubini-Study速度v_FS是流的对称拉伸部分的Frobenius范数，由此得到严格边界λ_max ≤ √2 v_FS，该边界可被共振纯 squeezer 饱和。此边界不可逆：在失谐参量放大器中，固定其中一个速率，改变另一个速率即可实现相关调控。
英文摘要：
Quantum-geometric speed and dynamical instability are two natural rates for a driven quantum system, and their relation is unsettled even for exactly solvable dynamics. Here we show that for any multimode quadratic bosonic system referred to the bare-mode vacuum the Fubini-Study speed v_FS is the Frobenius norm of the symmetric, stretching part of the flow: the rate at which the vacuum becomes distinguishable from itself measures instantaneous symplectic stretching. That identity turns a classical stability estimate into a quantum-geometric bound, lambda_max <= sqrt(2) v_FS, sharp at every mode number and saturated by a resonant pure squeezer. The bound is not invertible: in a detuned parametric amplifier we hold either rate fixed while varying the other.
