Observing antiferromagnetic correlations in ultracold fermions on optical lattices is an important step towards quantum simulation of the repulsive Hubbard model. We show that optical lattice modulation spectroscopy can be used to detect antiferromagnetic order and probe the nature of quasiparticle excitations in a fermionic Mott insulator. At high temperatures, the rate of creation of double occupancies shows a broad peak at frequency of the on-site repulsion U, reflecting the incoherent nature of the hole excitations. At low temperatures, antiferromagnetic order leads to fine structure in the response consisting of a sharp absorption edge reflecting coherent propagation of holes and oscillations as a function of modulation frequency representing spin-wave shake-off processes.
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