  We propose a new method of calculating nonlinear optical responses of
interacting electronic systems. In this method, the total Hamiltonian (system +
system-pump interaction) is transformed into a different form that (apparently)
does not have a system-pump interaction. The transformed Hamiltonian, which we
call the pump built-in Hamiltonian, has parameters that depend on the strength
of the pump beam. Using the pump built-in Hamiltonian, we can calculate
nonlinear responses (responses to probe beams as a function of the pump beam)
by applying the {\em linear} response theory. We demonstrate the basic idea of
this new method by applying it to a one-dimensional, two-band model, in the
case the pump excitation is virtual (coherent excitation). We find that the
exponent of the Fermi edge singularity varies with the pump intensity.
