Photon Supression of the shot noise in a quantum point contact Eva Zakka Bajjani Julien Ségala...
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Transcript of Photon Supression of the shot noise in a quantum point contact Eva Zakka Bajjani Julien Ségala...
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
Introduction
t
(Bandwidth
QuantumConductor
2 ?I 1.
2. Frequency dependence?
3. Interplay with quantification of electromagnetic energy?
2I
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
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
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
Central limit
obey Gaussian statistic
New physic for ...
Probing shorter time scales
Finite frequency spectrum
( )IS
(0)IS
/eV h
( ) (0)I I
eV hS S
eV
Gate
Gate
Emission of a ‘photon’
eV
V
Finite frequency spectrum
( ) (0)I I
eV hS S
eV
( )IS V
V/h e
Gate
Gate
Emission of a ‘photon’
eV
V
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
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
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)
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
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
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
Experimental Set-up
V
60 mK
800 mK 4 K
300 K
Accordable
Filters 4-8 GHz
Vg
Shot
Noise
Shot
Noise
DC Bias
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
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
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
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
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
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)
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.
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)
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)
Room temperature Part
Chaîne de détection
Generateur
de creneaux
60 mK
800 mK 4 K
300 K
Lock-in
Lock-in
Filtres
Accordables 4-8 GHz
Vg
0Z
transmisP
Plasmons bidimensionnels
Plus concrètement
22
4 (1 )I
eS D D eV
h
sZ
0ZModèle
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
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
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
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
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
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
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
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