  Photo-assisted transport through a mesoscopic conductor occurs when an
oscillatory (AC) voltage is superposed to the constant (DC) bias which is
imposed on this conductor. Of particular interest is the photo assisted shot
noise, which has been investigated theoretically and experimentally for several
types of samples. For DC biased conductors, a detection scheme for finite
frequency noise using a dissipative resonant circuit, which is inductively
coupled to the mesoscopic device, was developped recently. We argue that the
detection of the finite frequency photo-assisted shot noise can be achieved
with the same setup, despite the fact that time translational invariance is
absent here. We show that a measure of the photo-assisted shot noise can be
obtained through the charge correlator associated with the resonant circuit,
where the latter is averaged over the AC drive frequency. We test our
predictions for a point contact placed in the fractional quantum Hall effect
regime, for the case of weak backscattering. The Keldysh elements of the
photo-assisted noise correlator are computed. For simple Laughlin fractions,
the measured photo-assisted shot noise displays peaks at the frequency
corresponding to the DC bias voltage, as well as satellite peaks separated by
the AC drive frequency.
