Field-Space Entanglement Dynamics Between Tunnel-Coupled Luttinger Liquids

This study investigates how entanglement and quantum correlations emerge and evolve between two initially decoupled, one-dimensional quantum fields (Luttinger liquids) when a time-dependent tunneling interaction is applied. While spatial entanglement in quantum field theory is well-understood, the dynamics of field-space entanglement—where the partition is defined by the physical species rather than spatial regions—remains largely unexplored in non-equilibrium settings.

The authors model the two Luttinger liquids as bosonic fields coupled by a time-dependent tunneling strength. By employing a Gaussian approximation, they map the system's dynamics onto a set of mode-dependent Ermakov equations. This allows them to derive exact analytical expressions for information-theoretic measures, including logarithmic negativity, mutual information, and Rényi entropies, for arbitrary coupling protocols and initial thermal states.

The researchers demonstrate that the early-time growth of entanglement is determined by the first non-zero derivative of the tunneling protocol. They provide a unified framework where the long-time asymptotic behavior of correlations is fully characterized by the saturation value of the coupling and the Ermakov factors. The study highlights that while mutual information captures both classical and quantum correlations, the logarithmic negativity serves as a robust measure of entanglement in mixed-state (finite temperature) scenarios. The analytical solutions also allow for a clear characterization of the crossover from non-adiabatic to adiabatic dynamics.

This work bridges a gap in non-equilibrium quantum field theory by extending entanglement studies to field-space partitions. Because these dynamics are potentially observable in experiments with ultracold atoms in double-well potentials, the findings provide a theoretical foundation for interpreting future measurements of quantum correlations in synthetic quantum systems.