Two-mode squeezing in Floquet engineered power-law interacting spin models

We study the non-equilibrium dynamics of a quantum spin 1/2 XXZ model realized in a two-dimensional bi-layer system, with couplings mediated by inverse power-law interactions, falling off with distance r as 1/r^α. Starting from an initial state of spins with opposite magnetization in the two layers we find exponential growth of correlated pairs of excitations. We demonstrate that for a broad range of parameters, the system shows collective behavior resulting in exponential generation of entanglement. Specifically, we study the effects of the range of the interactions via the inverse power, α, and the interlayer spacing, a_Z, on the entanglement dynamics. This work demonstrates that metrologically useful entanglement in the form of two-mode squeezed states separated in bilayers can be generated via power-law interactions, making it accessible in a wide variety of experimental atomic, molecular, and optical platforms, with potential applications in quantum-enhanced sensing.