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Measuring current fluctuations with a Josephson junction

Learn about Pt(n) statistics of tunnel junctions, detecting non-Gaussian noise, and using Josephson junctions as threshold detectors for current. Explore properties of It(t) and Pt(n) distributions, experimental setups, measurement procedures, and resulting switching rates. Analyze how current thresholds reveal non-Gaussian distributions and study Poisson statistics in the context of counting time and probabilities. Discover implications on supercurrent branches, hysteresis behavior, and response times in Josephson junction systems.

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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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