2 where signatures of photoassisted transport are most dramatic. For devices composed of normal metal junctions as well as superconducting/normal metal junctions, PA noise exhibits singularities at integer ratios of the DC voltage with respect to the AC frequency: the derivative of this noise exibits jumps at such locations. On the other hand, for a weakly pinched quantum point contact placed in the fractional quantum Hall effect regime (FQHE),$^{19–23}$the PA noise diverges when the DC voltage – multiplied by the filling factor – is a multiple of the AC frequ ency. This much stronger singularity is a motivation for us to apply our measurement scheme to the FQHE situation. We will show that as in the DC case, the measured noise captures the response of the mesoscopic circuit at the resonant frequency of the LC circuit. It exhibits a central peak at the DC voltage, which is surrounded by satellite peaks shifted by the AC frequency. These predictions have the potential to be tested in experiments. The paper is organized as follows. In Sec. II we present the model for the LC detector. We review the results for the charge correlator of the DC cirsuit in Sec. III and extend this discussion to the PA situation. Sec. IV is devoted to the presentation of the QPC in the FQHE regime and its calculation of PA noise. Plots of these quantities and of the measured noise are discussed in Sec. V. We conclude in Sec. VI. The proposed setup is the same as that presented in Ref. 17, except for the fact that the voltage source on the mesoscopic device is time dependent. A lead from such device is inductively coupled to a resonant circuit (capacitance C , inductance L , and dissipative component R ). The signal which contains information about the noise of the mesoscopic circuit is encoded in the time correlation function of the charge on the capacitor. II. MODEL FIG. 1: Mesoscopic circuit is coupled to a resonant dissipative circuit We start with the description of the detector. The basic Hamiltonian which describes the dissipative oscillator circuit reads: where is the Hamiltonian of the uncoupled system “ LC oscillator plus environment”, and $^{H$_{LC}$}$− env describes the coupling between the two. For dissipative quantum systems, it is convenient to use a path integral formalism. In the absence of dissipation and coupling to the mesoscopic device, the Keldysh action describing the charge of the LC circuit reads: where is the (inverse) Green function of an harmonic oscillator ( L is its “mass”), Ω = ( L C ) − 1 / 2 is the resonant frequency of the circuit, q T = ( q $^{+}$, q − ) is a two component vector which contains the oscillator coordinate on the forward/backward contour, and σ$_{z}$ H$_{osc}$ = H$_{0}$ + $^{H$_{LC}$}$− env , (1) H$_{0}$ = H$_{LC}$ + H$_{env}$ (2) S$_{LC}$ [ q ] = 1 2 ∫ dtdt ′ q $^{T}$( t ) $_{G}$− 1 0 ( t − t ′ ) σ$_{z}$ q ( t ′ ) , (3) $_{G}$− 1 0 ( t − t ′ ) = L [( i∂$_{t}$ ) 2 − Ω $^{2}$] δ ( t − t ′ ) , (4)