Engineering entanglement Hamiltonians with strongly interacting cold atoms in optical traps

TL;DR

This paper proposes a method to realize entanglement Hamiltonians in one-dimensional critical spin systems using strongly interacting cold atoms, enabling experimental measurement of entanglement spectra.

Contribution

It introduces a physical Hamiltonian with position-dependent couplings to reproduce entanglement spectra in cold atom systems, bridging theory and experimental realization.

Findings

Demonstrates the feasibility of measuring entanglement spectra in cold-atom setups.

Shows that universal ratios of the entanglement spectrum can be reproduced in experiments.

Proposes practical trapping techniques to realize entanglement Hamiltonians.

Abstract

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.