  We propose an experimental setup of ultracold fermions in an optical lattice
to determine the pairing gap in a superfluid state and the spin ordering in a
Mott-insulating state. The idea is to apply a periodic modulation of the
lattice potential and to use the thereby induced double occupancy to probe the
system.
  We show by full time-dependent calculation using the adaptive time dependent
density-matrix renormalization group method that the position of the peak in
the spectrum of the induced double occupancy gives the pairing energy in a
superfluid and the interaction energy in a Mott-insulator, respectively. In the
Mott-insulator we relate the spectral weight of the peak to the spin ordering
at finite temperature using perturbative calculations.
