  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.
