Area laws and thermalization from classical entropies in spin-1 Bose-Einstein condensate

by Moritz Reh (Ruprecht-Karls-Universität Heidelberg)

Thursday 30 Nov 2023, 14:15 → 15:30 Europe/Berlin

Abbeanum/Ground floor-HS 2 - Hörsaal 2 (TPI, FSU Jena)

The scaling of local quantum entropies is of utmost interest for characterizing quantum fields, many-body systems and gravity. Despite their importance, being nonlinear functionals of the underlying quantum state hinders their theoretical as well as experimental accessibility. Here, we show that suitably chosen classical entropies capture the very same features as their quantum analogs for an experimentally relevant setting. We describe the post-quench dynamics of a multi-well spin-1 Bose-Einstein condensate from an initial product state via measurement distributions of spin observables and estimate the corresponding entropies using the asymptotically unbiased $k$-nearest neighbor method. We observe the dynamical build-up of quantum correlations signaled by an area law, as well as local thermalization revealed by a transition to a volume law, both in regimes characterized by non-Gaussian quantum states. We emphasize that all relevant features can be observed at small sample numbers without assuming a specific functional form of the distributions, rendering our method directly applicable to a large variety of models and experimental platforms.