1 High order moments of shot noise in mesoscopic systems Michael Reznikov, Technion Experiment: G. Gershon, Y. Bomze, D. Shovkun Theory: E. Sukhorukov Whether noise is noisence or signal may depend on whom you ask

2 Classical Shot Noise  f t ffff I S(  )

3 Noise in mesoscopic systems scattering approach Khlus (1987), Lesovik (1989), Yurke and Kochansky (1989) 

Magnetic Field (T) J. Smet, V. Umansky R xy (h/e 2 ) R xx (k  ) Fractional Quantum Hall Effect - Experimental Results

5 The QPC

Expected Noise….. (intuitively) = 1/3 e/3 q = e ; whole electrons q = e/3 ; quasi particles quasi particles partition whole electrons partition e partitioning barrier Both, e or e /3 lead to the same conductance ! t t

Quantum Shot Noise in QPC - Experimental Results Current Noise, S i ( A 2 /Hz) T=57 mK  =0.37 I Total Current (nA)

n s =1.1x10 11 cm -2 ; B=13 T Current Noise Measurements at bulk  preamp noise subtracted calibration at each point averaging time 4 s Lesovik’s formula, q=e/3 I=tVg 0 /3 See also : Saminadayar et. al Current Noise, S [ A 2 /Hz] Back-scattered Current, I r [pA] I r =V(g 0 /3-g)

Quantum Shot Noise at =2/5 - Weak Back Scattering - Current Noise, S [ A 2 /Hz] Conductance, g/g 0 Back-Scattered Current, I r [pA] B =2/5 t=0.86 T=85 mK e/3 e/5 =2/5 q=e/5 ! I r =V(2g 0 /5-g)

10 High-order cumulants - motivation

11 Photon counting statistics Glauber, 1963

12 Is this what is really measured? At least not always S(ω)! Lesovik, Loosen (1997)

13 Naïve calculations a b 1

14 Naïve calculations For  ~0 does not reproduce Poisson result  q 3 =g 0 V  =eI ! 1

15 “Gentle” electron counting Spin 1/2 as a galvanometer Spin 1/2 as a galvanometer L.S. Levitov and G.B. Lesovik (1993) L.S. Levitov and H. Lee (1996)

16 “Gentle” electron counting Spin 1/2 as a galvanometer Spin 1/2 as a galvanometer L.S. Levitov and G.B. Lesovik (1993) L.S. Levitov, H. Lee, G. Lesovik (1996) U=eV/T

17 Gaussian vs. Poisson distributions n=20 In our measurements n~1000

18 The PDF output voltage counts Typically 1000 electrons during 30 ns

19 Intrinsic cumulants for a single channel conductor  0.5) Khlus (1987), Lesovik (1989), Yurke and Kochansky (1989) L.S. Levitov and G.B. Lesovik (1993) L.S. Levitov and H. Lee (1996)

20 Experimental results from Yale B. Reulet, J. Senzier and D. E. Prober, 2002

21 and in QPC Filling factor =4 T=4.2 K  0.3

22 How to measure? Opening and closing of the barrier I. Klich, 2001 V0V0V0V0 Z sample V Rl Rl Rl Rl CV CV CV CV C st C st What is actually measured? 1

23 Z s >>Z l – voltage bias V0V0V0V0 Z sample V Rl Rl Rl Rl CV CV CV CV C st C st K. Nagaev – cascade corrections Kindermann, Nazarov, Beenakker (2002)

24 Z s <<Z l – current bias V0V0V0V0 Z sample V Rl Rl Rl Rl CV CV CV CV C st C st

25 General case for a tunneling junction  <<1, T<<eV In general: Kindermann, Nazarov, Beenakker (2002)

26 and in QPC Filling factor =4 T=4.2 K  0.3

27 Experimental Setup I VgVg QPC N RlRl CvCv Low temperature C st CcCc Network analyzer A/D

28 In the Tunneling Junction

29 “Intrinsic” contribution tt3t3 t2t2 t1t1 J(t) A(t) “Intrinsic” (constant voltage) contribution

30 Corrections, “environmental” and nonlinear t2t2 t1t1 t J(t) A(t)Z(t)

31 Environmental correction is not small! If we ignore peculiarities of the circuit -mostly determined by the load thermal noise Not small even when R ! 0

32 QPC characterization T=1.5K

33 QPC  ~0.3

34 Two different amplifiers

35

36 Calculation of the statistics T-ordering is to put q(0) to the right of q(t) Using e.g. wave packet approach one can get the statistics (Levitov, Lesovik, 1993)

37 How to express it through the integral of the currents (Bachman, Graf, Lesovik, 2009) Consider a slightly different object Properties: Q 3 =0 if one of t i =0. Therefore it can be expressed as: Time ordering is crucial to ensure Q3=0 for t i =0 !!!

38 “Contact” terms Differentiation ovet t 1 would generate 2 more  -functions, provided [q,j]  0. So, there are additions to the term accounted for in naïve calculations: h j(t 1 ) j(t 2 ) j(t 3 ) i

39 My favorable choice of j a 1 b L Compare with:

40 Conclusions and questions Prediction for > in QPC is verified Effect of interactions on >. Charge statistics under FQHE? Charge statistics in HT C superconductors > in diffusive systems with interactions Frequency dependence of >.

41 Setup in dilution fridge