6 0 V(t) I B (t) FIG. 2: Quantum point contact A. Model for quasiparticle backscattering We use the Tomonaga-Luttinger formalism to describe the right and left moving chiral excitations. In the absence of tunneling between the two edges, the Hamiltonian reads: with r = + , − for right and left movers. Here, we focus solely on the weak backscattering regime because it is already known that the PA shot noise exhibits some strong singularities. The backscattering of quasiparticles is described by the Hamiltonian: where A ( ε $^{)}$( t ) is a tunneling amplitude which depends on the applied voltage via the Peierls substitution. Here the notation ϵ = ± leaves an operator unchanged for ( ϵ = + ) or specifies its Hermitian conjugate ( ϵ = − ). Ψ$_{r}$ is the quasiparticle operator which is expressed in terms of the bosonic chiral field φ$_{r}$ : where a is a short distance cutoff and ν is the filling factor ( ν − 1 is an odd integer to describe Laughlin fractions). Choosing a time dependent voltage in the form V ( t ) = V$_{0}$ + V$_{1}$ cos( ω$_{AC}$t ) results in a tunneling amplitude: where e ∗ = νe and Γ$_{0}$ is the bare tunneling amplitude. The backscattering current is deduced from the backscattering Hamilto- nian: H$_{0}$ = ( ν$_{F}$ ℏ 4 π ) ∑ r ∫ ds ( ∂$_{s}$φ$_{r}$ ) 2 , (28) H$_{B}$ ( t ) = ∑ ε A ( ε $^{)}$( t $_{)[Ψ}$† $_{+}$( t $^{)Ψ}$−( t )] ( ε ) , (29) Ψ$_{r}$( t ) = 1 √$_{2}$$_{πa}$ e $_{i}$√$_{νφ}$$_{r}$$_{(}$$_{t}$$_{)}$ , (30) A ( ε $^{)}$( t ) = Γ$_{0}$ e iεω$_{0}$$^{t}$exp( iε e ∗ V$_{1}$ ℏ ω$_{AC}$ sin( ω$_{AC}$t )) , (31) I$_{B}$ ( t ) = ie ∗ ℏ ∑ ε εA ( ε $^{)}$( t $_{)[Ψ}$† $_{+}$( t $^{)Ψ}$−( t )] ( ε ) . (32) S ββ $^{′}$( t, t ′ ) = 〈 I β $_{B}$( t ) I β ′ B ( t ′ ) 〉 − 〈 I$_{B}$ ( t $^{β}$) 〉〈 I$_{B}$ ( t ′ β $^{′}$) 〉 . (33) S ββ $^{′}$( t, t ′ ) = − ( e ∗ ) 2 ∑ εε ′ εε ′ A ( ε $^{)}$( t ) A ( ε $^{$^{′}$)}$( t ′ ) 〈 T$_{K}$ { $_{[Ψ}$† $_{+}$( t $^{$^{β}$)Ψ}$− ( t $^{β}$)] ( ε ) $_{[Ψ}$† $_{+}$( t ′ β $^{$^{′}$)Ψ}$− ( t ′ β $^{′}$)] ( ε $^{$^{′}$)}$}〉 . (34) The general expression for the Keldysh components of the noise correlator in the Heisenberg representation is: Since we are interested in Poissonian regime only, the product of current averages can be dropped out because it contributes to higher order in the backscattering Hamiltonian. 1 Moreover, in this second order calculation in the tunneling amplitude Γ$_{0}$ , there is no difference between the Heisenberg and interaction picture. The noise then reads: This correlator is different from zero only when ε ′ = − ε because of quasiparticle conservation. Replacing the quasiparticle correlators by their bosonized expression, the noise is then written in terms of a product over averages of bosonic fields : B. Non-symmetrized noise S ββ $^{′}$( t, t ′ ) = ( e ∗ ) 2 4 π $^{2}$a2 ∑ ε εA ( ε $^{)}$( t ) A $^{(}$− ε $^{)}$( t ′ ) 〈 T$_{K}$e − $_{iε}$√$_{νφ}$$_{+}$$_{(}$$_{t}$ $^{$^{β}$)}$e $_{iε}$√$_{νφ}$$_{+}$$_{(}$$_{t}$ $_{′}$β $^{$^{′}$)}$〉〈 T$_{K}$e $_{iε}$√$_{νφ}$$_{−}$$_{(}$$_{t}$ $^{$^{β}$)}$e − $_{iε}$√$_{νφ}$$_{−}$$_{(}$$_{t}$ $_{′}$β $^{$^{′}$)}$〉 . (35)