  The response of cold atom gases to small periodic phase modulation of an
optical lattice is discussed. For bosonic gases, the energy absorption rate is
given, within linear response theory, by imaginary part of the current
correlation function. For fermionic gases in a strong lattice potential, the
same correlation function can be probed via the production rate double
occupancy. The phase modulation gives thus direct access to the conductivity of
the system, as function of the modulation frequency. We give an example of
application in the case of one dimensional bosons at zero temperature and
discuss the link between the phase- and amplitude-modulation.
