where Z$_{0}$ = 50 Ω is the input impedance of the acquis i- tion card, Δ ν is the bandpass of the two filters, centere d around the same frequency ν , and G$_{1}$$_{,}$$_{2}$ stands for t he gain of chain 1,2. The benefit of this method is that it also gives access to the cross-correlation term: where τ is the difference of propagation time of electro - magnetic waves between the sample and detectors 1 and 2. One easily gets: Equation 4 expresses the anticorrelation of current fluc- tuations δI$_{1}$ and δI$_{2}$ , modified by the phase difference of the microwave signals induced by τ . This is illustrated in Figure 2 for ν = 6 GHz with Δ ν =100 MHz. Here, τ is varied using two calibrated phase shifters inserted in both detection lines, around a value τ$_{0}$ which is a priori not known. As photons emitted at times differing by more than ∼ 1 / Δ ν do not show correlations, one needs to minimize τ before measuring the cross-correlated power fluctua- tions. As Δ ν ≪ ν , the most sensitive way to do so is to ensure that Δ δV$_{1}$δV$_{2}$$_{norm}$ is constant for various values of ν . The result of such an adjustment is shown in the inset of figure 2. Although small parasitic microwaves reflec- tions introduce extra modulations, Δ δV$_{1}$δV$_{2}$$_{norm}$ doesn’t change sign for 4GHz ≤ ν ≤ 8GHz. This implies that τ ≤ 125ps, so that Δ ντ ≪ 1 and the delay between the two lines doesn’t affect the power correlations. Third experiment: auto and cross-correlated photon noise. We now adopt the original HBT set-up [8], us- ing quadratic detectors connected to the digitizer. This gives access to S$_{P}$ out 1 P out 1 and S$_{P}$ out 2 P out 2 , and to the cross- correlation spectrum S$_{P}$ out 1 P out 2 . In the case of a tun- nel junction consisting of many weakly transmitted elec- tronic modes, one would expect [9] the emitted photons to follow a negative binomial distribution, as the emitted power results from the incoherent superposition of a large number of sources (the electronic modes of the tunnel junction). This is confirmed by the rigorous treatment of ref. [2], with corrections corresponding to emission of two photons at the same energy by the same electron. In the case of a low impedance (compared to the resis- tance quantum h/e $^{2}$), these corrections are small and one expects the photons emitted by the shot noise power of a tunnel junction to have the same counting statistics as thermal photons, although their origin is quite dif- ferent and the frequency dependence of photon occupa- tion number N ( ν ) doesn’t correspond to a Bose-Einstein which agrees with the experimental observations within 0.5%. Measurements over the entire 4-8 GHz frequency Equation 5 shows the benefit of HBT cross-correlation to study photon statistics, as it suppresses the term due to the mixing of the input power with the input noise of the amplifier. In order to get rid of imperfectly known gains and attenuation we normalize the excess autocorrelated power fluctuations by their zero voltage bias values and the cross-correlated power fluctuations by their geometric mean. Figure 3 represents the excess power fluctuations spectrum Δ S$_{P}$ out 1 P out 1 , normalized by the zero bias value S$_{P}$ out 1 P out 1 ( V$_{ds}$ = 0) as a function of Δ T$_{n}$$_{1}$/T$_{n}$$_{1}$ , measured at ν = 6 . 6 GHz ± 115 MHZ. The solid line represents the theoretical prediction: thermal distribution. The cross-correlated power fluc- tuations are then expected to be positive, reflecting the bosonic nature of the emitted photons, and proportional to the products of the power emitted in both detection branches. The autocorrelated power fluctuations are ex- pected to be enhanced by the contribution of the noise of the amplifiers [10]. Let’s note Δ ν$_{min}$ (Δ ν$_{max}$ ) the smaller (the bigger) of the bandpasses, both centered around the same frequency ν . One thus expects: FIG. 2: Normalized cross-correlation spectrum Δ δV 1 δV 2norm measured at ν =6 GHz ± 50MHz as a function of ν Δ τ . The solid line represents the sinusoidal prediction of eq. 4. Inset: Δ δV 1 δV 2norm averaged over 200 MHz, as a function of ν for two values of τ . The solid lines correspond to equation 4 for τ =83 ps (upper line) and τ =12 ps (lower line). -0,5 0,0 0,5 -1,0 -0,5 0,0 0,5 1,0 ν ( τ - τ$_{0}$ )/2 π 5 6 7 -1 0 1 ν  (GHz) τ$_{1}$ τ$_{2}$ ( ) 1/2 2 2 1 2 1 2 / V V V V δ δ δ δ Δ Δ Δ 3 Δ δV$_{1}$δV$_{2}$ = √ G$_{1}$G$_{2}$Z$_{0}$Z$_{eff}$ ∫$_{Δ}$$_{ν}$ cos(2 πντ )Δ S$_{I}$ 1 I 2 dν ( 3) Δ δV$_{1}$δV$_{2norm}$ = Δ δV 1 δV 2 √ Δ δV 2 1 Δ δV 2 2 = − sinc( π Δ ντ ) cos(2 π ν τ ) ≃ − cos(2 πντ ) for Δ ντ ≪ 1 . (4) S$_{P}$ out 1 P out 1 = 2Δ ν$_{1}$ [ G 2 $_{1}$k 2 $_{B}$( T$_{n}$$_{1}$ + Δ T$_{n}$$_{1}$ ) $^{2}$+ G$_{1}$hνk$_{B}$ ( T$_{n}$$_{1}$ + Δ T$_{n}$$_{1}$ )] ≃ 2Δ ν$_{1}$G 2 $_{1}$k 2 $_{B}$( T$_{n}$$_{1}$ + Δ T$_{n}$$_{1}$ ) 2 S$_{P}$ out 1 P out 2 = 2 G$_{1}$G$_{2}$ Δ ν$_{min}$k 2 $_{B}$Δ T$_{n}$$_{1}$ Δ T$_{n}$$_{2}$, (5) Δ S$_{P}$ out 1 P out 1 [ S$_{P}$ out 1 P out 1 ] V$_{ds}$ =0 = ( Δ T$_{n}$$_{1}$ T$_{n}$$_{1}$ ) 2 + 2 Δ T$_{n}$$_{1}$ T$_{n}$$_{1}$ ,