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Modulation Spectroscopy and Dynamics of Double Occupancies in a Fermionic Mott Insulator

We calculate the rate of creation of double occupancies in a 3D Fermionic Mott insulator near half-filling by modulation of optical lattice potential. At high temperatures, incoherent holes lead to a broad response peaked at the Hubbard repulsion $U$. At low temperatures, antiferromagnetic order leads to a coherent peak for the hole along with broad features representing spin wave shake-off processes. This is manifested in the doublon creation rate as a sharp absorption edge and oscillations as a function of modulating frequency. Thus, modulation spectroscopy can be used as a probe of antiferromagnetic order and nature of quasiparticle excitations in the system.