Quantum-Geometric Length Scale for Long-distance Squeezing in Bosonic Bogoliubov Systems

How can continuous-variable quantum systems achieve long-distance phase-sensitive correlations and sub-vacuum collective-mode squeezing across bosonic lattices without relying on dispersive propagation?

The authors investigate a one-dimensional bosonic lattice with two modes per unit cell, incorporating parametric pairing alongside standard number-conserving hopping terms. By tuning these parameters, they engineer an isolated, exactly flat Bogoliubov band. Although the localized compact generators span only neighboring cells, enforcing canonical bosonic commutation relations forces the true Bogoliubov modes to become spatially extended superpositions. The spatial decay of these modes and the momentum-space concentration of the resulting squeezing-sector symplectic quantum metric are both governed by a complex-momentum singularity in the analytically continued canonical modes.

The quantum-geometric length scale—determined by the zeros of the denominator in the Bogoliubov spectrum—directly dictates the exponential decay length of anomalous correlations. Because these correlations extend far beyond the compact generator support, sub-vacuum squeezing of spatially separated collective modes can be achieved over long distances. The squeezing range scales linearly with this intrinsic quantum-geometric length. Furthermore, even when exact flatness is weakly broken by dispersion, the long-distance correlations persist via multiple decay channels, and localized defects or boundaries provide complementary probes of the underlying quantum geometry.

This work bridges quantum geometry and continuous-variable quantum information by establishing that pairing-induced quantum geometry in flat-band bosonic systems can act as a robust mechanism for distributing nonclassical quantum resources over extended spatial ranges.