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

Question : what is P  (n) ? VbVb Atomic contact Tunnel junction Diffusive wire   0 n t >>  I  = n e/  average current on time  Counting statistics II  I(t) 

independent tunnel events Poisson distribution P  (n) asymmetric Noise is more than  n²(  )  ! P  (n) n nn Statistics of the charge passed through a tunnel junction Gaussian with same  n²(t)  Exact (Poisson) log scale n nn

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

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

Experimental implementation of ? Measure n(t)Measure properties of I  (t) ( I  = n(  ) e/  directly measure I  (t) Bomze et al. (2005) Sample impedance »  1 M 

Experimental implementation of ? Measure properties of I  (t) ( I  = n(  ) e/  measure probability that I  (t) > I th + or that I  (t) < I th - Current threshold detector

Measurement of current statistics with a threshold detector P  (n) n I  = n(  ) e/  distribution of I  distribution of n(  )

Measurement of current statistics with a threshold detector P(I  ) I  = n(  ) e/  distribution of I  distribution of n(  ) I   /e Differences mainly in the tails  focus on large fluctuations

Measurement of current statistics with a threshold detector P(I  ) I   /e t >>  II I th + clic ! p + 0 = =

Measurement of current statistics with a threshold detector P(I  ) I   /e t >>  II I th - clic ! p - 0 = =

Detecting non-gaussian noise with a current threshold detector P(I  ) I   /e gaussian p + 0, p - 0 gaussian poisson p + 0 / p - 0 P(I  ) I   /e

Effect of the average current on p + 0 / p - 0 p + 0 / p Increase  I  Current threshold detector reveals non-gaussian distribution

The Josephson junction I V I V 2  /e I0I0 - I 0 supercurrent branch

Biasing a Josephson junction V I V I0I0 - I 0 - remains on supercurrent branch as long as |I|<I 0 - hysteretic behavior  natural threshold detector RI v b = R I + V 2  /e [Proposed by Tobiska & Nazarov Phys. Rev. Lett. 93, (2004)] vbvb

isis Using the JJ as a threshold detector Is+IIs+I I V I+ib*I+ib* ibib I0I0 Switching if  I+i b > I 0 clic !  I =I 0 -i b RbRb ibib vbvb Josephson junction VsVs * assuming I s =i s

Using the JJ as a threshold detector I V - I 0 ibib clic ! Switching if … or if  I+i b > I 0  I+i b < -I 0 isis Is+IIs+I I+ibI+ib RbRb ibib vbvb VsVs

Using the JJ as a threshold detector I V clic ! isis Is+IIs+I I+ibI+ib RbRb ibib vbvb VsVs I0I0 response time = inverse plasma freq.

Experimental setup Al Cu NS junction V isis Is+IIs+I I+ibI+ib RbRb ibib vbvb VsVs JJ (SQUID) i b -i s Is+IIs+I C C use at I s >0.2µA R t =1.16 k 

Measurement procedure C=27 pF  =180 µeV I 0 =0.84 µA t - s I 0 s I 0 tptp count # pulses on V for N pulses on i b and deduce switching rates  + and  - … V isis Is+IIs+I I+ibI+ib RbRb ibib vbvb VsVs ibib C  I =I 0 -i b =I 0 (1-s) I0I0 -I 0

Measurement procedure t - s I 0 s I 0 tptp … I+ibI+ib ibib V isis Is+IIs+I RbRb ibib vbvb VsVs C  I =I 0 -i b =I 0 (1-s) I0I0 -I 0 ibib V t

Resulting switching probabilities after a pulse lasting t p  : Switching rates Probability to exceed threshold during "counting time"   I =I 0 (1-s) p + 0, p - 0 poisson

Resulting switching probabilities after a pulse lasting t p  : Switching rates Probability to exceed threshold during "counting time"   I =I 0 (1-s) 1-s 0.23 µA 1.96 µA p + 0, p - 0 I 0 =0.83 µA  =0.65 ns

Resulting switching probabilities after a pulse lasting t p  : Switching rates Probability to exceed threshold during "counting time"   I =I 0 (1-s) 1-s p + 0, p - 0 (log scale) p+0p+0 p-0p-0 I 0 =0.83 µA  =0.65 ns 0.23 µA 1.96 µA µA 1.47 µA µA

Resulting switching probabilities after a pulse lasting t p  : Switching rates Probability to exceed threshold during "counting time"   I =I 0 (1-s) Increase  I  1-s 0.23 µA µA µA 1.47 µA 1.96 µA 1-s 1.96 µA p + 0, p µA 1.96 µA µA µA 1.47 µA p + 0 / p - 0 p+0p+0 p-0p-0 I 0 =0.83 µA  =0.65 ns

s 1mHz 1Hz 1kHz 1MHz G ± e v i a n l e d o m ++ -- Rates  ± 0.23 µA µA µA 1.47 µA  I s  = 1.96 µA s R G e v i a n l e d o m Ratio of rates 0.23 µA µA µA 1.47 µA 1.96 µA I 0 =0.83 µA  =0.65 ns Switching rates R      Resulting switching probabilities after a pulse lasting t p  : Switching rates Probability to exceed threshold during "counting time"   I =I 0 (1-s) I 0 =0.83 µA  =0.65 ns s

Characterisation at equilibrium t - s I 0 s I 0 … ibib V ibib RbRb ibib vbvb (no current) C

Characterisation at equilibrium 0 1 s 01 ideal threshold detector V ibib RbRb ibib vbvb (no current) C  NOT an ideal threshold detector

JJ dynamics I V ibib C  i rC q Josephson relations : friction U UU  supercurrent branch : r

JJ dynamics I V ibib C r  Josephson relations : friction U  inin UU Escape rate (thermal) : (Quantum tunneling disregarded)

Fit I 0 and T with theory of thermal activation : I 0 = 0.83 µA T= 115 mK Characterisation at equilibrium s s

Applying a current in the NS junction s V isis Is+IIs+I RbRb ibib vbvb VsVs R t =1.16 k  C I s =0.98 µA i s tuned arbitrarily ! ( i s  I s )  shift on s between the 2 curves

Applying a current in the NS junction s V isis Is+IIs+I RbRb ibib vbvb VsVs R t =1.16 k  C I s =0.98 µA count on N pulses =10 5 pulses (binomial distribution)  significant difference

- Qualitative agreement with naive model - Small asymetry visible : 0.23 µA µA µA 1.47 µA  I m  = 1.96 µA  +   - with a current in the NS junction s I 0 (µA) Hz 1 kHz 10 kHz 100 kHz Is=Is= s

with a current in the NS junction 0.23 µA µA µA 1.47 µA  I m  = 1.96 µA Hz 1 kHz 10 kHz 100 kHz Is=Is= s I 0 (µA) s search at larger deviations ? + artifacts

with Q(s)=(r C  p (s)) -1 1) Modification of T by  I 2  (shot noise) Beyond the ideal detector assumption (theory: J. Ankerhold) I ibib C r  inin isis Is+IIs+I VsVs i noise

s r = 1.6  Best fit of   using with Q(s)=(r C  p (s)) -1 1) Modification of T by  I 2  (shot noise) theory experiment 0.23 µA µA µA 1.47 µA I s = 1.96 µA Qualitative agreement Beyond the ideal detector assumption (theory: J. Ankerhold) s I 0 (µA) T f f e (K)

2) Rates asymmetry caused by  I 3  Beyond the ideal detector assumption Hz 1 kHz 10 kHz 100 kHz s I 0 (µA) 0.23 µA µA µA 1.47 µA I s = 1.96 µA isis Is+IIs+I RbRb ibib vbvb VsVs R t =1.16 k  C i s tuned arbitrarily ! ( i s  I s )  shift on s between the 2 curves

2) Rates asymmetry caused by  I 3  Step 1: shift curves according to theory Beyond the ideal detector assumption isis Is+IIs+I RbRb ibib vbvb VsVs R t =1.16 k  C i s tuned arbitrarily ! ( i s  I s )  shift on s between the 2 curves

2) Rates asymmetry caused by  I 3  Step 1: shift curves according to theory 0.23 µA µA µA 1.47 µA I s = 1.96 µA Quantitative agreement Beyond the ideal detector assumption s theory experiment Step 2: compare s-dependence of     with theory (using experimental T eff )

Conclusions JJ = on-chip, fast current threshold detector… … with imperfections 0.23 µA µA µA 1.47 µA I s = 1.96 µA s … able to detect 3d moment in current fluctuations

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