A forthcoming challenge in ultracold lattice gases is the simulation of quantum magnetism. That involves both the preparation of the lattice atomic gas in the desired spin state and the probing of the state. Here we demonstrate how a probing scheme based on atom-light interfaces gives access to the order parameters of nontrivial quantum magnetic phases, allowing us to characterize univocally strongly correlated magnetic systems produced in ultracold gases. This method, which is also nondemolishing, yields spatially resolved spin correlations and can be applied to bosons or fermions. As a proof of principle, we apply this method to detect the complete phase diagram displayed by a chain of (rotationally invariant) spin-1 bosons.
Effective range is a quantity to characterize the energy dependence in two-body scattering strength and is widely used in cold atomic systems, especially across narrow resonances. Here we show that the effective range can significantly modify the magnetic property of one-dimensional (1D) spin-
1/2 fermions in the strongly repulsive regime. In particular, the effective range breaks the large spin degeneracy in the hard-core limit and induces a Heisenberg exchange term in the spin chain that is much more sensitive to the local density than that induced by the bare coupling. With an external harmonic trap, this leads to a very rich magnetic pattern where the antiferromagnetic and ferromagnetic correlations can coexist and distribute in highly tunable regions across the trap. Finally, we propose to detect the range-induced magnetic order in the tunneling experiment. Our results can be directly tested in 1D Fermi gases across narrow resonance and suggest a convenient route toward the local manipulation of quantum magnetism in cold atoms.