How does entanglement grow between two quantum fields?

What happens when we take two initially independent one-dimensional quantum fluids and allow particles to tunnel between them? In our recent preprint, Field-Space Entanglement Dynamics Between Tunnel-Coupled Luttinger Liquids, we study how entanglement develops between two identical Luttinger liquids coupled uniformly along their length.

Working within a Gaussian approximation, we derive analytical expressions that track entanglement and correlations for time-dependent tunnelling protocols, starting from zero or finite temperature. At zero temperature, the way we switch on the coupling controls the early growth of entanglement. How we bring the two systems together shapes the quantum correlations they develop.