Measuring current fluctuations with a Josephson junction

1
Measuring current fluctuations with a Josephson
junction
H. Pothier
Quantronics Group CEA Saclay, France
2
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 gtgtt
3
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
Experimental implementation of ?
Measure n(t)
See next talk !
5
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)

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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) gt Ith or that
It(t) lt Ith-
Current threshold detector
8
Measurement of current statistics with a
threshold detector
It n(t) e/t
Pt(n)
distribution of It distribution of n(t)
n
9
Measurement of current statistics with a
threshold detector
It n(t) e/t
P(It)
distribution of It distribution of n(t)
It t/e
Differences mainly in the tails ? focus on large
fluctuations
10
Measurement of current statistics with a
threshold detector
It
clic !
P(It)
Ith
t gtgtt
It t/e
p0
11
Measurement of current statistics with a
threshold detector
It
-
2
10
P(It)
-
4
10
-
6
10
-
8
Ith-
10
t gtgtt
5
10
15
20
25
30
35
40
45
clic !
It t/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
It t/e
It t/e
p0, p-0
p0 / p-0
gaussian poisson
13
Effect of the average current on p0 / p-0
2000
Increase ? I ?
p0 / 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
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Biasing a Josephson junction
V
R
I
vb R I V

• remains on supercurrent branch as long as IltI0
• hysteretic behavior
• ? natural threshold detector

I
I0
2D/e
V
- I0
Proposed by Tobiska Nazarov Phys. Rev. Lett.
93, 106801(2004)
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Using the JJ as a threshold detector
IsdI
Rb
ib
dIib
assuming Isis
is
Switching if
I
Josephson junction
dIib gt I0
I0
clic !
DI I0-ib
ib
V
17
Using the JJ as a threshold detector
IsdI
Rb
ib
dIib
is
Switching if
dIib gt I0
I
clic !
ib
V
or if
dIib lt -I0
- I0
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Using the JJ as a threshold detector
IsdI
Rb
ib
dIib
is
response time inverse plasma freq.
I
I0
clic !
V
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Experimental setup
JJ (SQUID)
Al
NS junction
Rt1.16 kW
ib-is
Cu
IsdI
C
use at Isgt0.2µA
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Measurement procedure
ib
DI I0-ibI0(1-s)
I0
s I0
tp

t
- s I0
C27 pF D180 µeV I00.84 µA
-I0
count pulses on V for N pulses on ib and deduce
switching rates G and G-
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Measurement procedure
ib
DI I0-ibI0(1-s)
I0
s I0
tp

dIib
t
- s I0
-I0
ib
t
V
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Switching rates
Probability to exceed threshold during "counting
time" t
p0, p-0
poisson
Resulting switching probabilities after a pulse
lasting tp
Switching rates
DI I0(1-s)
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Switching rates
Probability to exceed threshold during "counting
time" t
p0, p-0
Resulting switching probabilities after a pulse
lasting tp
1.96 µA
0.23 µA
1-s
Switching rates
I00.83 µA t0.65 ns
DI I0(1-s)
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Switching rates
Probability to exceed threshold during "counting
time" t
p0, p-0 (log scale)
p0
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
I00.83 µA t0.65 ns
DI I0(1-s)
25
Switching rates
Probability to exceed threshold during "counting
time" t
p0, p-0
p0
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
p0 / p-0
Switching rates
0. 49 µA
0. 98 µA
1.47 µA
1.96 µA
I00.83 µA t0.65 ns
DI I0(1-s)
1-s
26
Switching rates
I00.83 µA t0.65 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
I00.83 µA t0.65 ns
DI I0(1-s)
s
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Characterisation at equilibrium
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Characterisation at equilibrium
ideal threshold detector
? NOT an ideal threshold detector
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JJ dynamics
I
irC
r
ib
V
d
q
C
friction
supercurrent branch
U
DU
d
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JJ dynamics
I
r
in
ib
V
d
C
friction
Escape rate (thermal)
U
DU
d
(Quantum tunneling disregarded)
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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
Applying a current in the NS junction
Is0.98 µA
is tuned arbitrarily ! (is?Is) ? shift on s
between the 2 curves
0.76
0.78
0.8
0.82
s
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Applying a current in the NS junction
Is0.98 µA
count on Npulses105 pulses
(binomial distribution)
s
? significant difference
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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-
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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
Beyond the ideal detector assumption(theory J.
Ankerhold)
1) Modification of T by ?dI2? (shot noise)
with Q(s)(r C wp(s))-1
IsdI
I
r
in
ib
d
is
inoise
C
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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
s I0 (µA)
Qualitative agreement
38
Beyond the ideal detector assumption
2) Rates asymmetry caused by ?dI3?
0.23 µA
0. 49 µA
0. 98 µA
1.47 µA
Is 1.96 µA
s I0 (µA)
IsdI
Rb
ib
is tuned arbitrarily ! (is?Is) ? shift on s
between the 2 curves
is
Rt1.16 kW
39
Beyond the ideal detector assumption
2) Rates asymmetry caused by ?dI3?
Step 1 shift curves according to theory
IsdI
Rb
ib
is tuned arbitrarily ! (is?Is) ? shift on s
between the 2 curves
is
Rt1.16 kW
40
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
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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)