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Photon Supression of the shot noise
in a quantum point contact
Eva Zakka Bajjani
Julien Ségala
Joseph Dufouleur
Fabien Portier
Patrice Roche
Christian Glattli
Yong Jin
Antonella Cavanna
Nano-electronic group
SPEC, CEA Saclay
LPN, CNRS, Marcoussis
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Introduction
t
(Bandwidth
QuantumConductor
2 ?I 1.
2. Frequency dependence?
3. Interplay with quantification of electromagnetic energy?
2I
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Outline
1. Introduction
2. Conductance and zero frequency shot noise of a single mode conductor
3. Finite frequency shot noise
4. From an experimentalist’s point of view
5. Experimental Set up
6. Results
7. Perspectives
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The wave packet approach Martin and Landauer (1992)
Observation time :
Emission time :
Number of events :
Incoming current :
1 channel conductor
DReservoir Reservoir
LL
V
I
0I
( i ) ( t )
( r )
)(tI
)(Lf
)(Rf
eV
t
eVI e D
h
D1 D
t ii
eVI e D
h
0tN DN
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The wave packet approach Martin and Landauer (1992)
Observation time :
Time scale :
Number of events :
1 channel conductor
DReservoir Reservoir
LL
V
I
0I
( i ) ( t )
( r )
)(tI
)(Lf
)(Rf
eV
Due to Fermi statistics the incoming current (I0) is noiseless
And due to transmission uncertainty :
20
2 0
(1 )
(1 )t
t
N N D D
eI D DI
t
22( 0) (1 )I i i
i
eS D D eV
D1 D
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Central limit
obey Gaussian statistic
New physic for ...
Probing shorter time scales
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Finite frequency spectrum
( )IS
(0)IS
/eV h
( ) (0)I I
eV hS S
eV
Gate
Gate
Emission of a ‘photon’
eV
V
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Finite frequency spectrum
( ) (0)I I
eV hS S
eV
( )IS V
V/h e
Gate
Gate
Emission of a ‘photon’
eV
V
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Experimental requirements
10 mK 1 GHz
10 μVeT
V
B ek T h eV Thermal population of photons negligible
0Z
Gate
Gate
Corresponding wavelength ~ 10 cm propagation effect have to be taken into account
V
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Coupling to a transmission line
20
transm 2
0
( )sI
s
Z ZP S
Z Z
Transmitted power:
Zs≈25 kΩ Zo=50Ω
Maximum for 0 sZ Z
0Z
transmPISsZ 0ZIS
sZ 0Z
max ( )4
sI
ZP S
0
transm max2
0
0max max
4
4
s
s
s
Z ZP P
Z Z
ZP P
Z
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First solution: adapt the source impedance to the detection impedance
R. J. Schoelkopf et al.
Phys. Rev. Lett. 78 , 3370 (1997).
(Diffusive Conductor R≈50Ω)
Advantage: good coupling and sensitivity Disadvantage: many modes, impossibility to tune their transmission. Feedback of amplifier?
Quantitative agreement with theoretical predictions, with Te=100 mK (Tfridge=40 mK)
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Second solution: on chip detection
E. Onac et al.
Phys. Rev. Lett. 96 , 176601 (2006).
Advantage: good coupling to a high impedance (single mode) source Disadvantage: coupling constant and bandwidth unknown
Photocurrent Q D(1-D) Onset current 4 times higher than expected
FE
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Third solution: adapt the detection impedance
0Z
ISsZ 0Z
0kZ
20k Z
/ 4
2 2
0transm 22
0
( )sI
s
k Z ZP S
Z k Z
Quarter wavelength impedance adapatation
ISsZ 2
0k Z
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Implementation
3 140Z 1 70Z 0 50Z 12906 /sZ D
Bias T
k≈1.4, Zeff≈200Ω
rayonnée eff ( )IP Z S d
DC Bias
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Experimental Set-up
V
60 mK
800 mK 4 K
300 K
Accordable
Filters 4-8 GHz
Vg
Shot
Noise
Shot
Noise
DC Bias
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Transmission of the Quantum Point Contact
D1,D2,D3 … (VG)
-0,50 -0,45 -0,40 -0,35 -0,30 -0,250,0
0,5
1,0
1,5
2,0
2,5
3,0
Conductance'Saddle Point Model' Fit
V
g(V)
G
sam
ple/
G0
-0,50 -0,45 -0,40 -0,35 -0,30 -0,250,0
0,5
1,0
1,5
2,0
2,5
3,0
Conductance'Saddle Point Model' Fit
D3
D1
D2
V
g(V)
G
sam
ple/
G0
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Excess Noise Power at D=1/2
-60 -40 -20 0 20 40 600
200
400
600
800
2V0
(2 X 4.22 GHz)
Shot noise at 4.22GHz
T
Noi
se(
K)
(on
50
)
VDrain-Source
(µV)
4.22GHz
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Excess Noise Power at D=1/2
-60 -40 -20 0 20 40 600
200
400
600
800
2V0 (2 X 7.63 GHz)
2V0
(2 X 4.22 GHz)
Shot noise at 7.63GHz and 4.22GHz
T
Noi
se(
K (
on
50
)
VDrain-Source
(µV)
7.63GHz 4.22GHz
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Threshold versus frequency
0 5 10 15 20 25 30 350
5
10
15
20
25
30
35
Intercept
Thr
esho
ld V
0 (µ
V)
h/e [µV]
0 2 4 6 8
Frequency [GHz]
B elec2k T
0 /
asymptote
V h e
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Threshold versus frequency
0 5 10 15 20 25 30 350
5
10
15
20
25
30
35
Intercept Fit to theory
yields Telec
= 72mK (fridge temp = 68 mK)
Thr
esho
ld V
0 (µ
V)
h/e [µV]
0 2 4 6 8
B elec2k T
0 /
asymptote
V h e
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Dependence with transmission
0,0 0,5 1,0 1,5 2,00,0
0,1
0,2
0,3
d S
I / d
(eV
DS)
(G0)
GQPC
/G0
-0,5 -0,4 -0,30
1
2
GS
ampl
e/G
0
Vg (V)
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CONCLUSION
• We have measured the quantum partition noise of a Quantum Point Contact at finite frequency.
•Quantitative agreement of the observed shot-noise power dependence with bias voltage and frequency.
•Our method opens the way to cross-correlation measurements probing the statistical properties of the photons emitted by a phase coherent conductor.
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Fit with no free paramater, exept coupling
-150 -100 -50 0 50 100 1500,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,40
Shot noise à 5.95GHzT
Noi
se(µ
V)
VDrain-Source
(µV)
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2
21)( I
GZ
ZdhNtP
Z C
R Load = ZC
h (detector + filter)quantumconductor
( G )
)(tI
NNNtPPtP )()(
)( tI /1
)( tP
Pf/1
t
t
fhNP 222)(tP
2
0
0
0
2242 IIN
V
Photon noise = noise of electrical noise power
MHz)( nsfluctuatiopower of
bandwidthfrequency low : f
GHz)(~ bandwidthfrequency high :
d Can the sub-Poissonian (fermionic) statistics
of electrons be imprinted on photons? Yes, provided that only one or two mode are transmitted, and excitation voltage is not too high (Beenaker Schomerus 2004)
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Room temperature Part
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Chaîne de détection
Generateur
de creneaux
60 mK
800 mK 4 K
300 K
Lock-in
Lock-in
Filtres
Accordables 4-8 GHz
Vg
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0Z
transmisP
Plasmons bidimensionnels
Plus concrètement
22
4 (1 )I
eS D D eV
h
sZ
0ZModèle
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Experimental requirements
50 mK 2 1 GHz
10 μVeT
V
B ek T eV Thermal population of photons negligible
Amplifier noise temperature / frequency as small as possible
Conductance of the sample independent of bias voltage up to /V e
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Quarter wavelength impedance adapatation
1Z
→ Reflected wave
2Z
1 1 1
2 2 2
V Z I
V Z I
1I 2I
3Z
2 / 422 1 3Z Z Z → Perfect transmission
2 2 / 4l perfect matching for given frequency
compromise between bandwidth and compensated mismatch
1Z2Z
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Effet de Chauffage?
B
B
2
2 2elec 0 2
mesa mesa B
elec 2mesa mesa B
23 32
2 2B mesa
24 21
2
24 21
2
2 2 244 (1 )
1
h
k TI
h
k T
G G eVT T
G G k
G G eVT
G G k
dS e e h e GD D D
dV h h k T Ge
Ordre de grandeur:
Pour Rmesa=200Ω//200Ω, D=1, eV=100μeV, on obtient Telec=100 mK
Le facteur thermique est alors de l’ordre de 0.5, et on obtient
3
5/ 28(1 ) 0.06IdS e
D D DdV h
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Signal attendu
•Mesa: -3 dB (estimation à partir des courbes G(vG))
•Couplage ligne 140Ω/70Ω/50Ω : -2dB (mesure sur une boîte ‘vide’)
•Attenuation dûe aux câbles: -2 dB (mesures à 4.2K)
•Circulateurs: 2 X -0.3 dB (idem)
•I inox:- 0.2 dB (idem)
2
rayonnée eff eff
2noise
eff
2( ) 4 (1 )
1 24 0.062
(1 ) ( )
I
eP Z S d Z D D eV
h
dT eZ
D D d eV h
noise 0.0024 0.0006( )
dT
d eV noise 0.0022
( )
dT
d eV
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Variation du seuil avec la frequence
0 5 10 15 20 25 30 350
10
20
30
40
D:\Julien\Projets\RF\07_01_23\analysefiltres.OPJ-[Seuil(frequence)]
Données Fit 1.18x/tanh(0.0716x) Fit 6.8+x
Seuil en fonction de la fréquence
Se
uil
en
µe
V
Fréquence en µeV
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Est ce bien du bruit de grenaille quantique?
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,00,000
0,001
0,002
0,003
0,004
D:\Julien\Projets\RF\07_01_16\T(1-T).OPJ-[T(1-T)theo/exp]
Dépendance du bruit avec la transmission du QPC à 5.95GHz
d
TN/d
VD
S
Transmission du QPC
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Effet de Chauffage?
0 1 2
0,000
0,001
0,002
0,003
0,004
0,005
0,006
D:\Julien\Projets\RF\07_01_16\T(1-T).OPJ-[T(1-T)theo/exp]
Dépendance du bruit avec la transmission du QPC à 5.95GHz
dT
N/d
VD
S
Transmission du QPC
Sans effet de chauffage : [T
1(1-T
1)+T
2(1-T
2)+T
3(1-T
3)+T
4(1-T
4)]
Avec effet de chauffage :
[T1(1-T
1)+T
2(1-T
2)+T
3(1-T
3)+T
4(1-T
4)+0.065*T5/2]
Données
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Mesure a differentes frequences
-200 -150 -100 -50 0 50 100 150 2000,0
0,2
0,4
0,6
0,8
1,0
D:\Julien\Projets\RF\07_01_23\analysefiltres.OPJ-[4.47et7.63/T(1-T)]
Shot noise rescalé par le T(1-T)T
Noi
se(µ
V)/
(T(1
-T))
VDrain-Source
(µV)
4.47GHz 7.63GHz