Measuring post-quench entanglement entropy through density correlations

Following an interaction quench in an integrable system of one-dimensional fermions, we analyze the dependence of the density-density correlation function on the observation time. Using the fact that for small waiting times every one-dimensional system can be bosonized in the high-energy sector, we extract bosonic occupation numbers from the density-density correlation function, and use them to compute the bosonic entropy from an effective diagonal ensemble. Inspired by the connection between the Yang-Yang and entanglement entropy in quenched integrable quantum systems, we compare the bosonic entropy with the steady state spatial entanglement entropy per particle computed via exact diagonalization and find excellent agreement. This result provides a route to the experimental measurement of entanglement in closed quantum systems without the use of a replicated Hilbert space, and could be confirmed via Bragg spectroscopy of integrable (or nearly integrable) ultracold atom systems.