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Measuring current fluctuations with a Josephson junction

B. Huard. N. O. Birge. D. Esteve. Measuring current fluctuations with a Josephson junction. H. Pothier. Quantronics Group CEA Saclay, France. n. 0. t. 0. Counting statistics. V b. Question : what is P t (n) ?. I t = n e/ t. Tunnel junction. average current on time t. I t.

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Measuring current fluctuations with a Josephson junction

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  1. B. Huard N. O. Birge D. Esteve Measuring current fluctuations with a Josephson junction H. Pothier Quantronics Group CEA Saclay, France

  2. n 0 t 0 Counting statistics Vb Question : what is Pt(n) ? It = n e/t Tunnel junction average current on time t It  I(t)  Diffusive wire Atomic contact t >>t

  3. Exact (Poisson) Pt(n) asymmetric Gaussian with same dn²(t) Statistics of the charge passed through a tunnel junction independent tunnel events Poisson distribution n n Pt(n) log scale n n Noise is more than dn²(t) !

  4. Gustavsson et al. (2005) Sample = Quantum Dot Experimental implementation of ? Measure n(t) See next talk !

  5. Reulet et al. (2003) Sample impedance  50 W Experimental implementation of ? Measure n(t) Measure properties of It(t) ( It = n(t) e/t ) • ( It(t) - I )3  " squewness " (0 for Gaussian noise)

  6. Bomze et al. (2005) Sample impedance »1 MW Experimental implementation of ? Measure n(t) Measure properties of It(t) ( It = n(t) e/t ) directly measure It(t)

  7. Experimental implementation of ? Measure properties of It(t) ( It = n(t) e/t ) measure probability that It(t) > Ith+ or that It(t) < Ith- Current threshold detector

  8. Measurement of current statistics with a threshold detector It = n(t) e/t Pt(n) distribution of It distribution ofn(t) n

  9. Measurement of current statistics with a threshold detector It = n(t) e/t P(It) distribution of It distribution ofn(t) Itt/e Differences mainly in the tails  focus on large fluctuations

  10. - 2 10 - 4 10 - 6 10 - 8 10 5 10 15 20 25 30 35 40 45 Measurement of current statistics with a threshold detector It clic ! P(It) Ith+ t >>t Itt/e p+0= =

  11. Measurement of current statistics with a threshold detector It - 2 10 P(It) - 4 10 - 6 10 - 8 Ith- 10 t >>t 5 10 15 20 25 30 35 40 45 clic ! Itt/e p-0= =

  12. Detecting non-gaussian noise with a current threshold detector gaussian - 2 10 P(It) - 4 10 P(It) - 6 10 - 8 10 5 10 15 20 25 30 35 40 45 Itt/e Itt/e p+0, p-0 p+0 / p-0 gaussian poisson

  13. 3.5 3 2.5 2 1.5 Effect of the average current on p+0 / p-0 2000 Increase  I  p+0 / p-0 20 000 200 400 600 800 1000 Current threshold detector reveals non-gaussian distribution

  14. The Josephson junction V I I I0 supercurrent branch 2D/e V - I0

  15. vb Biasing a Josephson junction V R I vb= R I + V • remains on supercurrent branch as long as |I|<I0 • hysteretic behavior •  natural threshold detector I I0 2D/e V - I0 [Proposed by Tobiska & Nazarov Phys. Rev. Lett. 93, 106801(2004)]

  16. Vs vb Using the JJ as a threshold detector Is+dI Rb ib *assuming Is=is dI+ib* is Switching if I Josephson junction dI+ib> I0 I0 clic ! DI =I0-ib ib V

  17. Vs vb Using the JJ as a threshold detector Is+dI Rb ib dI+ib is Switching if dI+ib> I0 I clic ! ib V … or if dI+ib< -I0 - I0

  18. Vs vb Using the JJ as a threshold detector Is+dI Rb ib dI+ib is response time = inverse plasma freq. I I0 clic ! V

  19. V Is+dI Rb ib is Vs vb C dI+ib Experimental setup JJ (SQUID) Al NS junction Rt=1.16 kW ib-is Cu Is+dI C use at Is>0.2µA

  20. V Is+dI Rb ib is Vs vb C dI+ib Measurement procedure ib DI =I0-ib=I0(1-s) I0 s I0 tp … t - s I0 C=27 pF D=180 µeV I0=0.84 µA -I0 count # pulses on V for N pulses on ib and deduce switching rates G+ and G-

  21. V Is+dI Rb ib is Vs vb C Measurement procedure ib DI =I0-ib=I0(1-s) I0 s I0 tp … dI+ib t - s I0 -I0 ib t V

  22. 3.5 3 2.5 2 1.5 2000 Increase  I  p+0 / p-0 20 000 200 400 600 800 1000 Switching rates Probability to exceed threshold during "counting time" t : p+0, p-0 poisson Resulting switching probabilities after a pulse lasting tp: Switching rates DI =I0(1-s)

  23. 3.5 3 2.5 2 1.5 2000 Increase  I  p+0 / p-0 20 000 200 400 600 800 1000 Switching rates Probability to exceed threshold during "counting time" t : p+0, p-0 Resulting switching probabilities after a pulse lasting tp: 1.96 µA 0.23 µA 1-s Switching rates I0=0.83 µA t=0.65 ns DI =I0(1-s)

  24. 3.5 3 2.5 2 1.5 2000 Increase  I  p+0 / p-0 20 000 200 400 600 800 1000 Switching rates Probability to exceed threshold during "counting time" t : p+0, p-0 (log scale) p+0 p-0 Resulting switching probabilities after a pulse lasting tp: 1.47 µA 1.96 µA 0. 98 µA 0. 49 µA 0.23 µA 1-s Switching rates I0=0.83 µA t=0.65 ns DI =I0(1-s)

  25. Switching rates Probability to exceed threshold during "counting time" t : p+0, p-0 p+0 p-0 Resulting switching probabilities after a pulse lasting tp: 1.96 µA 1.47 µA 1.96 µA 0. 98 µA 0. 49 µA 0.23 µA 1-s Increase  I  0.23 µA p+0 / p-0 Switching rates 0. 49 µA 0. 98 µA 1.47 µA 1.96 µA I0=0.83 µA t=0.65 ns DI =I0(1-s) 1-s

  26. Rates G± G+ 5 l l G- e 1 MHz e d 4 d o o Is = 1.96 µA m m 1.47 µA 0. 98 µA 0. 49 µA 0.23 µA 1 kHz 3 e e v v i i a a 2 n n 1 Hz 1 ± G G R 0.85 0.9 0.95 1 1 mHz s 0.85 0.9 0.95 1 s Switching rates I0=0.83 µA t=0.65 ns Probability to exceed threshold during "counting time" t : Resulting switching probabilities after a pulse lasting tp: RG =G+/G- Ratio of rates Switching rates 1.96 µA 1.47 µA 0. 98 µA 0. 49 µA 0.23 µA I0=0.83 µA t=0.65 ns DI =I0(1-s) s

  27. 1 ib 0.8 0.6 s I0 0.4 … 0.2 vb C t 0.87 0.88 0.89 0.9 - s I0 s V Rb (no current) ib ib Characterisation at equilibrium

  28. 1 1 0.8 0.6 0.4 0.2 vb C 0 0 1 0.87 0.88 0.89 0.9 s s V Rb (no current) ib ib Characterisation at equilibrium ideal threshold detector  NOT an ideal threshold detector

  29. Josephson relations : JJ dynamics I irC r ib V d q C friction supercurrent branch : U DU d

  30. Josephson relations : JJ dynamics I r in ib V d C friction Escape rate (thermal) : U DU d (Quantum tunneling disregarded)

  31. 0.87 0.88 0.89 0.9 Characterisation at equilibrium 1 0.8 0.6 0.4 0.2 s s I0= 0.83 µA T= 115 mK Fit I0 and T with theory of thermal activation :

  32. V Is+dI 1 Rb ib 0.8 0.6 is Vs vb C Rt=1.16 kW 0.4 0.2 0 Applying a current in the NS junction Is=0.98 µA istuned arbitrarily ! (isIs)  shift on s between the 2 curves 0.76 0.78 0.8 0.82 s

  33. V Is+dI 1 Rb ib 0.8 0.6 is Vs vb C Rt=1.16 kW 0.4 0.2 0 0.76 0.78 0.8 0.82 Applying a current in the NS junction Is=0.98 µA count on Npulses=105 pulses (binomial distribution) s  significant difference

  34. 100 kHz 10 kHz 1 kHz 100 Hz 0.62 0.66 0.7 0.74 with a current in the NS junction 0. 98 µA 1.47 µA Im = 1.96 µA 0.23 µA 0. 49 µA Is= s I0 (µA) s - Qualitative agreement with naive model - Small asymetry visible : G+G-

  35. 100 kHz 10 kHz 1 kHz 100 Hz 0.62 0.66 0.7 0.74 12 10 8 6 4 2 0 0.2 0.4 0.6 0.8 1 with a current in the NS junction 0. 98 µA 1.47 µA Im = 1.96 µA 0.23 µA 0. 49 µA Is= s I0 (µA) s search at larger deviations ? + artifacts

  36. Vs Beyond the ideal detector assumption(theory: J. Ankerhold) 1) Modification of T by dI2 (shot noise) with Q(s)=(r C wp(s))-1 Is+dI I r in ib d is inoise C

  37. (K) f f e T theory experiment Beyond the ideal detector assumption(theory: J. Ankerhold) 1) Modification of T by dI2 (shot noise) with Q(s)=(r C wp(s))-1 Best fit of G+using r = 1.6 W 0.4 0. 98 µA Is = 1.96 µA 1.47 µA 0. 49 µA 0.3 0.23 µA 0.2 0.75 0.8 0.85 s I0 (µA) s Qualitative agreement

  38. 100 kHz Vs vb C 10 kHz 1 kHz 100 Hz 0.62 0.66 0.7 0.74 Beyond the ideal detector assumption 2) Rates asymmetry caused by dI3 0.23 µA 1.47 µA 0. 49 µA 0. 98 µA Is = 1.96 µA s I0 (µA) Is+dI Rb ib istuned arbitrarily ! (isIs)  shift on s between the 2 curves is Rt=1.16 kW

  39. shift from theory 100 kHz 0.23 µA 1.47 µA 0. 49 µA 0. 98 µA Is = 1.96 µA 10 kHz Vs vb C 1 kHz 100 Hz 0.62 0.66 0.7 0.74 I0s (µA) Beyond the ideal detector assumption 2) Rates asymmetry caused by dI3 Step 1: shift curves according to theory Is+dI Rb ib istuned arbitrarily ! (isIs)  shift on s between the 2 curves is Rt=1.16 kW

  40. shift from theory 100 kHz 0.23 µA 1.47 µA 0. 49 µA 0. 98 µA Is = 1.96 µA 10 kHz 1 kHz 100 Hz 0.62 0.66 0.7 0.74 I0s (µA) theory experiment Beyond the ideal detector assumption 2) Rates asymmetry caused by dI3 Step 1: shift curves according to theory Step 2: compare s-dependence of G+/G- with theory (using experimental Teff) 1.4 1.47 µA 0. 98 µA Is = 1.96 µA 1.3 0. 49 µA 1.2 0.23 µA 0.75 0.8 0.85 Quantitative agreement s

  41. 1.4 1.47 µA 0. 98 µA Is = 1.96 µA 1.3 0. 49 µA 1.2 0.23 µA 0.75 0.8 0.85 s Conclusions JJ = on-chip, fast current threshold detector… … with imperfections … able to detect 3d moment in current fluctuations

  42. to be continued …  optimized experiment on tunnel junction  experiments on other mesoscopic conductors (mesoscopic wires)

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