玻色子Bogoliubov系统中长距离压缩的量子几何长度尺度
Quantum-Geometric Length Scale for Long-distance Squeezing in Bosonic Bogoliubov Systems
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中文总结 AI 辅助
该研究提出玻色子Bogoliubov系统中，参量配对可产生长程量子关联与压缩，其空间范围由量子几何长度尺度调控，为连续变量量子技术提供了新的量子资源机制。
中文摘要 AI 辅助
多模压缩是连续变量量子技术的关键资源，但它在玻色子晶格中的空间范围通常与色散传播相关联。本文表明，参量配对可生成由紧致Bogoliubov生成元张成的完全平坦Bogoliubov带，同时产生对相位敏感的反常关联及远超出其有限支撑的亚真空集体模式压缩。每个紧致生成元混合湮灭与产生算符，从而编码Bogoliubov压缩结构，相邻平移后的生成元可具有非零对易子重叠。满足正则玻色子对易关系需要这些平移后的紧致生成元的空间扩展线性组合，其定义了正则Bogoliubov模式。这些模式的压缩变换随动量变化，由压缩区辛量子度量量化。解析延拓后的正则Bogoliubov模式的复动量奇点既决定了反常关联的衰减长度，也决定了该度量的动量空间宽度，定义了本征量子几何长度尺度。该奇点可在保持完全平坦的同时连续调谐，从而控制关联与压缩的空间范围。偏离完全平坦时，长程关联仍会通过多个衰减通道持续存在，而由缺陷和二聚化边界局域化的模式为 underlying量子几何提供互补探针。在弱阻尼极限下，可从频率滤波的双端口关联中提取相同的量子几何长度尺度。我们的结果确立了正则Bogoliubov模式的量子几何作为由紧致Bogoliubov生成元产生的空间扩展量子资源的机制。
英文摘要
Multimode squeezing is a key resource for continuous-variable quantum technologies, but its spatial range in bosonic lattices is usually tied to dispersive propagation. Here we show that parametric pairing can create an exactly flat Bogoliubov band spanned by compact Bogoliubov generators, while producing phase-sensitive anomalous correlations and sub-vacuum collective-mode squeezing that extend far beyond their finite support. Each compact generator mixes annihilation and creation operators, thereby encoding the Bogoliubov squeezing structure, and neighboring translated generators can have nonzero commutator overlap. Enforcing canonical bosonic commutation relations therefore requires spatially extended linear combinations of these translated compact generators, which define the canonical Bogoliubov modes. The squeezing transformation of these modes varies with momentum and is quantified by the squeezing-sector symplectic quantum metric. A complex-momentum singularity of the analytically continued canonical Bogoliubov modes sets both the anomalous-correlation decay length and the momentum-space width of this metric, defining an intrinsic quantum-geometric length scale. This singularity can be tuned continuously while preserving exact flatness, thereby controlling the spatial range of correlations and squeezing. Away from exact flatness, long-distance correlations persist through multiple decay channels, while modes localized by defects and dimerized boundaries provide complementary probes of the underlying quantum geometry. In the weak-damping limit, the same quantum-geometric length scale can be extracted from frequency-filtered two-port correlations. Our results establish the quantum geometry of canonical Bogoliubov modes as a mechanism for spatially extended quantum resources arising from compact Bogoliubov generators.
