Engineering entanglement Hamiltonians with strongly interacting cold atoms in optical traps

We present a proposal for the realization of entanglement Hamiltonians in one-dimensional critical spin systems with strongly interacting cold atoms. Our approach is based on the notion that the entanglement spectrum of such systems can be realized with a physical Hamiltonian containing a set of position-dependent couplings. We focus on reproducing the universal ratios of the entanglement spectrum for systems in two different geometries: a harmonic trap, which corresponds to a partition embedded in an infinite system, and a linear potential, which reproduces the properties of a half partition with open boundary conditions. Our results demonstrate the possibility of measuring the entanglement spectra of the Heisenberg and XX models in a realistic cold-atom experimental setting by simply using gravity and standard trapping techniques.

Automated summary

This research proposes a method to realize entanglement Hamiltonians in one-dimensional critical spin systems with strongly interacting cold atoms. By using a physical Hamiltonian containing position-dependent couplings, the study focuses on reproducing the universal ratios of the entanglement spectrum for systems in two different geometries. The results demonstrate the feasibility of measuring the entanglement spectra of the Heisenberg and XX models in a realistic cold-atom experimental setting using gravity and standard trapping techniques.