Experimental determination of the statistics of photons emitted by a tunnel junction arXiv:1001.1411v1 [cond-mat.mes-hall] 9 Jan 2010 Eva Zakka-Bajjani, J. Dufouleur, ∗ N. Coulombel, P. Roche, D.C. Glattli, † and F. Portier ‡ Service de Physique de l’Etat Condens´e/IRAMIS/DSM (CNRS URA 2464), CEA Saclay, F-91191 Gif-sur-Yvette, France (Dated: September 7, 2018) We report on a microwave Hanbury-Brown Twiss experiment probing the statistics of GHz photons emitted by a tunnel junction in the shot noise regime at low temperature. By measuring the cross- correlated fluctuations of the occupation numbers of the photon modes of both detection branches we show that, while the statistics of electrons is Poissonian, the photons obey chaotic statistics. This is observed even for low photon occupation number when the voltage across the junction is close to hν/e . PACS numbers: 73.23.-b,73.50.Td,42.50.-p,42.50.Ar What is the statistics of microwave photons radiated by the current fluctuations of a quantum conductor? When the conductor is at equilibrium at temperature T , the statistics is that of a black body radiation [1]. How- ever little is known about the statistics of the photons emitted in the non-equilibrium case where the conductor is biased by a voltage V ≫ k$_{B}$T/e and the current fluc- tuations are due to quantum shot noise. An intriguing question is the link between the statistics of electrons and that of the emitted photons. This problem has recently attracted theoretical interest and the full range of pho- ton statistics, from chaotic to non-classical, has been pre- dicted. The result depends on the competition between the fermionic and bosonic statistics of electrons and pho- tons respectively [2]. On the one hand, the Pauli principle makes electrons emitted by a contact essentially noiseless and the current noise only results from electron scatter- ing with sub-Poissonian statistics. On the other hand photons emitted by electrons may show bunching effect transforming their initial statistics from sub-Poissonian to super- Poissonian. More generally, this rich physics re- lates to the problem of the electron Full Counting Statis- tics [3], as the second moment of the photon noise di- rectly links to a fourth-moment of the current fluctua- tions [2, 4, 13]. In this work, we present the first measurements of the statistics of photons radiated by a quantum conductor in the shot noise regime. For the simplest quantum conduc- tor studied here, a tunnel junction, although the statis- tics of electrons crossing the conductor is Poissonian, the photon statistics is shown to be chaotic. This is found even in the regime of vanishing electron shot noise where the voltage is close to the photon energy ( eV ≳ hν ), so that the photon population is small, in agreement with the prediction of [2]. As a by-product, our experi- mental method based on Hanbury-Brown Twiss (HBT) microwave photon correlation is found to provide a di- rect measurement of the non symmetrized current noise power, called emission noise. Here, the experiments lin- early amplifies the field amplitude to a classical level and further detects the microwave power and its fluctuations. This contrasts with experiments measuring the average power with on-chip quantum detectors such as quantum dots or superconducting tunnel junctions [5]. The relation between current noise and photon emis- sion can be understood following Nyquist’s approach [1]. Consider a conductor of resistance R connected to a cir- cuit made of a lossless transmission line of characteristic impedance Z$_{c}$ terminated by a matched resistor. To sim- plify, let’s assume that Z$_{c}$ ≪ R . When electrons in the conductor generate a current fluctuation I ( t ), a voltage V ( t ) = Z$_{c}$I ( t ) builds up at the input of the transmis- sion line exciting an electromagnetic mode which prop- agates and is finally absorbed in the resistive load. In- troducing the spectral density of the current fluctuation S$_{I}$ ( ν ) = 2 ∫ + ∞ −∞ 〈 I (0) I ( τ ) 〉 e i 2 $^{πντ}$dτ , we can express the electromagnetic power radiated by the conductor in fre- quency range ν, ν + dν as dP = Z$_{c}$S$_{I}$ ( ν ) dν = N ( ν ) hνdν , where N ( ν ) is the mean photon population of the elec- tromagnetic mode at frequency ν . This establishes a di- rect link between S$_{I}$ ( ν ) and N ( ν ). Let us take a further step and consider the (low frequency) fluctuations δN 2 of the photon population. They originate from the in- trinsic fluctuations of the current noise in the conductor (the ’noise’ of the noise). However the problem of the connection between the statistics of the photons and the electrons is complicated by the bunching effect occurring when several photons are simultaneously emitted into the transmission line. The photon distribution emitted by a classical current was first addressed by Glauber who showed that the photon statistics is Poissonian [6]. Solv- ing the same problem in the case of quantum electronic shot noise requires a model that treats electrons and the detecting environment on the same quantum footing. Such a treatment was recently developed by Schomerus and Beenakker [2]. In particular they have shown that a tunnel junction emits photons with chaotic statistics. This occurs even in the regime of small photon number when the applied voltage on the junction is close to hν/e . This is the regime addressed by our experiments. The experimental set-up, shown in figure 1, is similar to the one described in [7]. An Al/AlO$_{x}$/Al tunnel junc- tion of resistance R$_{t}$ = 502Ω ± 1Ω was cooled to ∼ 30 MA in a dilution fridge. A 0.1 T magnetic field sup-