Julien Gabelli Bertrand Reulet Non-Gaussian Shot Noise in a Tunnel Junction in the Quantum Regime Laboratoire de Physique des Solides Bât. 510, Université Paris-Sud, Orsay, France Aussois 22/03/07

Current fluctuations in conductors Characterized by the Noise spectral density S 2 in A 2 /Hz: But it is not sufficient

Gaussian vs. Non-Gaussian Noise Current fluctuations in a tunnel junction at zero frequency (h  f<<eV) Shot Noise (eV>>k B T) Discreteness of charge Equilibrium Noise (eV<<k B T) Fluctuation - dissipation theorem informations on the current probability distribution P(i) are required higher order moments – information on e-e interaction … symmetric Non- symmetric

Current statistics: frequency? Full counting statistics : measurement of P T (i) by digitalizing the current i(t) Difficulty: central limit theorem P(i) almost gaussian average during T  (band width  f  BUT well defined only at zero frequency, charge counting Yu. Bomze, G. Gershon, D. Shovkun, L. S. Levitov, and M. Reznikov Phys. Rev. Lett. 95, (2005) what happens below the characteristic time  =h/eV, Quantum regime ?

Frequency dependence: S 2  Noise spectral density S 2 (  ) at finite frequency (ћω>>k B T) beating between spectral components  and -  i()i()   … in a tunnel junction … cross-over at equilibrium noise shot noise No photon emitted at frequency ω for eV< ћω Experimental Data² T=35 mK f=6 GHz

Higher order moments at finite frequency Frequency dependent higher order moments, S 3 B. Reulet, J. Senzier, and D. E. Prober Phys. Rev. Lett. 91, (2003) “classical regime” ћω<eV,k B T

Higher order moments at finite frequency Frequency dependent higher order moments, S 3 Quantum regime S 3 (ω, ω’) no photon emitted by zero point fluctuations at T=0 ? no time irreversibility at equilibrium theory J. Salo, F. W. J. Hekking, J. P. Pekola Phys. Rev. B 74, (2006) independent of ω 1, ω 2 A. V. Galaktionov, D. S. Golubev, A. D. Zaikin Phys. Rev. B 68, (2003)

Measurement of S 3 (ω, 0) Δf (HF) Δf (LF) with Experimental setup: S 3 (ω,0) 50  Al/Al 2 O 3 /Al, 1*5 µm² Lafe Spietz, Yale imperfect voltage bias → voltage fluctuations → feedback and noise of the environment S 3 (ω,0) Δf (HF) Δf (LF) Δω~200 MHz ω~6 GHz S v 2 (ω) Δf (HF) voltage biased sample (V 0 ) current measurement (δi) BUT current biased sample (I 0 ) voltage measurement (δV) Theoretically: Experimentally:

Feedback and noise of the environment measured voltage shot noise: V dependent Independent of V 3 rd moment: expand 2 nd moment: we are looking for part of

Feedback and noise susceptibility Kindermann,Nazarov, Beenakker PRL 90, (2003) Example of fluctuations (at  1 ) due to environment but if  1 ~  2 noise cannot follow excitation B. Reulet, J. Senzier, D. E. Prober PRL 91, (2003) if  1 ~  slow noise modulation δi env δiδi Χ δi env

Noise susceptibility Noise dynamics measured at ω 2 when excited at ω 1 J. Gabelli and B. Reulet, unpublished Calculated and measured for a tunnel junction in the quantum limit ћω>>eV,k B T New correlation function The noise does not follow the excitation V dc V ac

Feedback and noise susceptibility

fluctuations due to noise of sample itself fluctuations due to noise of environment what we are looking for… what we measure

Fitting parameters (S 3 temperature independent) Data at different temperatures Fit compatible measurements Fitting parameters

S 3 measurement Ћω>eV

Conclusion Very non intuitive result if we consider a photo-detection scheme Is S 3 (ћω>eV)≠0 due to zero point fluctuations detected with a linear amplifier ? We demonstrate experimentally S 3 (ω,0) = e 2 I, independent of ω even if ћω > eV J. Salo, F. W. J. Hekking, J. P. Pekola what is S 3 in the regime ћω < eV ? no photon but S 3 ≠0 ћωћω eV ћωћω ћωћω Observed in Quantum optics cf: Y. Yamamoto, P. Grangier correlation between electrons and photons what happens in the quantum regime ћω > eV ?

Thanks to NS 2 team Marco Aprili Francesca Chiodi Rossella Latempa Ivana Petkovic Edgar Patino Bertrand Reulet