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Julien Gabelli Bertrand Reulet

Non-Gaussian Shot Noise in a Tunnel Junction in the Quantum Regime. Julien Gabelli Bertrand Reulet. Laboratoire de Physique des Solides Bât. 510, Université Paris-Sud, 91405 Orsay, France. Aussois 22/03/07. Current fluctuations in conductors.

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Julien Gabelli Bertrand Reulet

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  1. Non-Gaussian Shot Noise in a Tunnel Junction in the Quantum Regime Julien Gabelli Bertrand Reulet Laboratoire de Physique des Solides Bât. 510, Université Paris-Sud, 91405 Orsay, France Aussois 22/03/07

  2. Current fluctuations in conductors Characterized by the Noise spectral density S2 in A2/Hz: But it is not sufficient

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

  4. BUT average during T(band width Df) Current statistics: frequency? Difficulty: central limit theorem P(i) almost gaussian Full counting statistics: measurement of PT(i) by digitalizing the current i(t) Yu. Bomze, G. Gershon, D. Shovkun, L. S. Levitov, and M. ReznikovPhys. Rev. Lett. 95, 176601 (2005) well defined only at zero frequency, charge counting what happens below the characteristic time t=h/eV , Quantum regime ?

  5. i(w) -w +w … in a tunnel junction … cross-over at equilibrium noise shot noise No photon emitted at frequency ω for eV< ћω Frequency dependence: S2(w) Noise spectral density S2(w) at finite frequency (ћω>>kBT) beating between spectral components w and -w T=35 mK f=6 GHz Experimental Data²

  6. “classical regime” ћω<eV,kBT B. Reulet, J. Senzier, and D. E. ProberPhys. Rev. Lett. 91, 196601 (2003) Higher order moments at finite frequency Frequency dependent higher order moments, S3

  7. Quantum regime S3(ω, ω’) no photon emitted by zero point fluctuations at T=0 ? no time irreversibility at equilibrium J. Salo, F. W. J. Hekking, J. P. PekolaPhys. Rev. B 74, 125427 (2006) theory independent of ω1, ω2 A. V. Galaktionov, D. S. Golubev, A. D. ZaikinPhys. Rev. B 68, 235333 (2003) Higher order moments at finite frequency Frequency dependent higher order moments, S3

  8. Sv2(ω) Δf(HF) S3(ω,0) Δf(HF)Δf(LF) ω~6 GHz Δω~200 MHz voltage biased sample (V0) current measurement (δi) Theoretically: BUT current biased sample (I0) voltage measurement (δV) Experimentally: Experimental setup: S3(ω,0) 50 W Al/Al2O3/Al, 1*5 µm² Lafe Spietz, Yale Measurement of S3(ω, 0) Δf(HF) Δf(LF) with imperfect voltage bias → voltage fluctuations → feedback and noise of the environment

  9. 2nd moment: 3rd moment: expand we are looking for part of Feedback and noise of the environment measured voltage shot noise: V dependent Independent of V

  10. B. Reulet, J. Senzier, D. E. ProberPRL 91, 196601 (2003) ifw1~ 0slow noise modulation but if w1~w2 noise cannot follow excitation δi δienv Χδienv Feedback and noise susceptibility Example of fluctuations (at w1) due to environment Kindermann,Nazarov, Beenakker PRL 90, 176802 (2003)

  11. Noise susceptibility Noise dynamics measured at ω2 when excited at ω1 New correlation function Calculated and measured for a tunnel junction in the quantum limit ћω>>eV,kBT The noise does not follow the excitation Vac Vdc J. Gabelli and B. Reulet, unpublished

  12. Feedback and noise susceptibility

  13. fluctuations due to noise of sample itself what we are looking for… what we measure fluctuations due to noise of environment Feedback and noise susceptibility

  14. Fitting parameters (S3 temperature independent) Data at different temperatures Fit Fitting parameters compatible measurements

  15. Ћω>eV S3 measurement

  16. ћω ћω eV ћω Conclusion We demonstrate experimentally S3(ω,0) = e2 I, independent of ω even if ћω > eV J. Salo, F. W. J. Hekking, J. P. Pekola Very non intuitive result if we consider a photo-detection scheme what is S3 in the regime ћω < eV? correlation between electrons and photons Observed in Quantum optics cf: Y. Yamamoto, P. Grangier what happens in the quantum regime ћω > eV? no photon but S3≠0 Is S3(ћω>eV)≠0 due to zero point fluctuations detected with a linear amplifier ?

  17. Thanks to NS2 team Marco Aprili Francesca Chiodi Rossella Latempa Ivana Petkovic Edgar Patino Bertrand Reulet

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