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