Many-body correlations in a one-dimensional spin chain with simplified dipole-dipole interactions

We address the possibility of generating many-body quantum correlations in cold atomic ensembles scattering light. In particular, we consider an ordered 1D chain of two-level spins under the influence of a magnetic field that orients their dipole moments along the magic angle, thus simplifying the dipolar interactions solely to terms $\propto 1/r$. For the subwavelength limit where the lattice spacing $a < \lambda$, implying that dipole-dipole interactions are dominant and can induce stronger correlations, we observe an anti-ferromagnetic steady-state solution of the coherent dipole master equation. We thus analyze this state's tomography, measuring the pair-wise spin concurrence and other quantum-correlation quantifiers. We extend our analysis to a more complex system of multi-level atoms. Current experiments with atoms trapped by optical tweezers are particularly interesting platforms to implement this limit, due to the high degree of control they offer.