5 B. AC drive and temporal invariance We now turn to the main point of this section, which is to address how to deal with the presence of an AC voltage superposed to the DC one. The total bias potential V ( t ) which is applied to the mesoscopic device is thus a periodic function of time with period τ = 2 π/ω$_{AC}$ . We start by defining a correlator k ( T, t ′′ ) from the current derivative correlator of Eq. (12): Defining T = ( t + t ′ ) / 2 , t ′′ = t − t ′ , the charge correlator of Eq. (13) is rewritten as: where t$_{0}$ = ( t$_{2}$ + t$_{1}$ ) / 2 − t ′′ / 2 . Next, we define the average of the charge correlator over theperiod of the AC drive 11 as follows: Note that the last integral over the variable T is essentially a period average of the correlator k ( T, t ′′ ) with the variable T shifted by t$_{0}$ . In the presence of an AC drive, this period average does not depend on the shift t$_{0}$ , because as a function of the variable T , k ( T, t ′′ ) contains only harmonics of the drive frequency ω$_{AC}$ . This has been noticed in earlier works. 13,29,30 For our purposes, it means that we can safely replace t$_{0}$ by 0 . As a result, the period averaged charge correlator takes the form of a convolution product as was the case for the constant DC bias, and it therefore depends only on the time difference t − t ′ : K ( t, t ′ ) ≡ k ( t + t ′ 2 , t − t ′ ) . (22) 〈 T$_{K}$q $^{β}$( t ) q β $^{′}$( t ′ ) 〉 = α 2 ∫ dt$_{1}$dt$_{2}$ ∑ β$_{1}$β$_{2}$ G $^{ββ$_{2}$}$( t ′′ − t$_{2}$ ) σ β$_{2}$β$_{2}$ z k β$_{2}$$^{β$_{1}$}$( T + t$_{0}$, t$_{2}$ − t$_{1}$ ) σ β$_{1}$β$_{1}$ z G β$_{1}$β $^{′}$( t$_{1}$ ) . (23) 1 τ ∫ τ 0 dT 〈 q $^{β}$( t ) q β $^{′}$( t ′ ) 〉 = α 2 ∫ dt$_{1}$dt$_{2}$ ∑ β$_{1}$β$_{2}$ G $^{ββ$_{2}$}$( t ′′ − t$_{2}$ ) σ β$_{2}$β$_{2}$ z ∫ τ 0 dT τ k β$_{2}$$^{β$_{1}$}$( T + t$_{0}$, t$_{2}$ − t$_{1}$ ) σ β$_{1}$β$_{1}$ z G β$_{1}$β $^{′}$( t$_{1}$ ) . (24) ˆ Q ββ $^{′}$( t − t ′ ) ≡ 1 τ ∫ τ 0 dT 〈 q $^{β}$( t ) q β $^{′}$( t ′ ) 〉 = α 2 dt$_{1}$dt$_{2}$ ∑ β$_{1}$β$_{2}$ G $^{ββ$_{2}$}$( t ′′ − t$_{2}$ ) σ β$_{2}$β$_{2}$ z K β$_{2}$$^{β$_{1}$}$( t$_{2}$ − t$_{1}$ ) σ β$_{1}$β$_{1}$ z G β$_{1}$β $^{′}$( t$_{1}$ ) , (25) K β$_{2}$$^{β$_{1}$}$( t ) ≡ 1 τ ∫ τ 0 dT k β$_{2}$$^{β$_{1}$}$( T, t ) . (26) where we defined the period averaged correlator: Finally, the averaged charge correlator can be expressed in terms of the Fourier transfrom of both the LC circuit Green’s function and the period averaged current correlator: This result is the exact analog of the DC formula Eq. 21, extended to and AC drive. In addition, at t ′′ = 0 , this expression has the same form as the result of Ref. 17. We have therefore identified which quantity ( K ) characterizes the influence of the mesoscopic circuit on the response of the LC circuit. Therefore, the protocol for measuring photoassisted shot noise is the same as in the DC case provided one averages the response over the frequency of the drive. This averaging procedure restores the temporal invariance of the charge correlator. In the following sections, we will compute the current derivative correlators and their period average for a specific system: a QPC placed in theconditions of the FQHE where the elementary transport process is the Poissonian transfer of Laughlin quasiparticles. The calculation of the symmetrized photoassisted noise has been carried out in Ref. 30. Here we use the same basic model and generalize the calculations of the noise correlator to the full Keldysh matrix elements of this correlator. Next, we extract from these the noise derivative correlators which are relevant for the measurement process. ˆ Q ββ $^{′}$( t ′′ ) = α 2 ∑ β$_{1}$β$_{2}$ ∫ dω 2 π e − iωt $^{′′}$G $^{ββ$_{2}$}$( ω ) σ β$_{2}$β$_{2}$ z K β$_{2}$$^{β$_{1}$}$( ω ) σ β$_{1}$β$_{1}$ z G β$_{1}$β $^{′}$( ω ) . (27) IV. NON SYMMETRIZED PHOTO-ASSISTED NOISE IN THE FQHE