Probing the conformal Calabrese-Cardy scaling with cold atoms

We demonstrate that current experiments using cold bosonic atoms trapped in one-dimensional optical lattices and designed to measure the second-order R\'enyi entanglement entropy S₂ can be used to verify detailed predictions of conformal field theory (CFT) and estimate the central charge c. We discuss the adiabatic preparation of the ground state at half filling and small hopping parameter $J/U$, where we expect a CFT with $c=1$. We provide two complementary methods to estimate and subtract the classical entropy generated by the experimental preparation and imaging processes. We compare numerical calculations for the classical O(2) model with a chemical potential on a ($1+1$)-dimensional lattice, and the quantum Bose-Hubbard Hamiltonian implemented in the experiments. S₂ is very similar for the two models and follows closely the Calabrese-Cardy scaling, (c/8)ln(Nₛ), for Nₛ sites with open boundary conditions, provided that the large subleading corrections are taken into account.