A coherent subnanosecond single A coherent subnanosecond single electron sourceelectron source

Jean-Marc Berroir

Bernard Plaçais

Christian Glattli

Takis Kontos

Julien Gabelli

Adrien Mahé

Groupe de Physique Mésoscopique Laboratoire Pierre Aigrain

ENS

Gwendal Fève

Samples made at : Laboratoire de Photonique et Nanostructures (LPN)

Yong Jin

Bernard Etienne

Antonella Cavana

MotivationMotivation

Weizmann Institute, Israel Y. Ji et al Nature 422 415 (2003)

I

VG

Gaz 2D

B

Poster P. Roulleau, CEA Saclay

Single Single electronelectron sources sources

DC biased Fermi sea is a noiseless electron source:

eV D

eV

h

fDeII )1(22

No temporal control

Objective : realisation of a single electron source similar to single photon sources

Time controlled injection of a single electron in a quantum conductor

Electron optics with one or two electrons (entanglement…)

103 D

Kumar et al. PRL (1996)

0,0

0,2

0,4

0,6

0,8

1,0

1 1 T

T T

T2 2

2

1

1

Fa

no

re

du

ctio

n f

act

or

Conductance 2e² / h

0. 0.5 1. 1.5 2. 2.5

1

.8

.6

.4

.2

0

A. Kumar et al. Phys. Rev. Lett. 76 (1996) 2778..

Principle of single charge injectionPrinciple of single charge injection

2eCC

V(t)

QPC Gaz 2D

Boîte

edt)t(I

e

V(t)

C

2eCC

C/e2

t

2e

C

2 exceV

B

Principle of single charge injectionPrinciple of single charge injection

2eCC

V(t)

QPC Gaz 2D

Boîte

edt)t(I

e

V(t)

C

2eCC

C/e2

t

2e

C

2 exceV

B

Principle of single charge injectionPrinciple of single charge injection

D/h

2eCC

V(t)

C

2eCC

injection

V(t)

QPC Gaz 2D

Boîte

edt)t(I

e

I

100 ps for 2.5°K and D =0.2

C/e2

t

2e

C

2 exceV

B

The quantum RC circuitThe quantum RC circuit

GV

GV

l < m exceV ( t )

I( t )

B

The quantum RC circuitThe quantum RC circuit

D=t2

Quantum dot

GVGV

B

2

4 3.1 TBNo spin degeneracy

One dimensional conductor

Linear dynamics of the quantum RC circuitLinear dynamics of the quantum RC circuit

Linear regime, exceV qR , qC

GV

GV

exceV ( t )

I( t )

B

The quantum RC circuit, T=0KThe quantum RC circuit, T=0K

2 ( )q FC e N

The resistance is constant, independent of transmission,and equals half the resistance quantum for a single mode conductor !

)( FN , dot density of states

CPQ

M. Büttiker et al PRL 70 4114, PLA180,364-369 (1993)

B

The quantum RC circuit , T=0KThe quantum RC circuit , T=0K

Quantum dot

D=t2

• kBT >> D Sequential regime

• kBT << D Coherent regime 22ehRQ

1QR / D

GVGV

B

2

Complex conductanceComplex conductance

KC

e5.0

2

KC

e5.2

2

K2

mKT 150

Fit by )( GVD

DB

-0.05

0.00

0.05

0.10

-0.91 -0.90 -0.89

-0.02

0.00

0.02

0.04

-0.2

-0.1

0.0

0.1

0.2

0.3

f = 515 MHz

Co

nd

uct

ance

G (

e2 /h

)

VG(V)

f = 180 MHz

f = 1.5 GHz

D

Conclusion on linear dynamicsConclusion on linear dynamics

0

1

2

3

4

-0,74 -0,72-0,85 -0,84 -0,83

2

4

6

8

CSample E1/2 = 1.085 GHz

Rq= h / 2e2

A

Im(Z

) (h

/e2 )

Re(

Z)

(h/e

2 ) Sample E3/2 = 1.2 GHz

Rq= h / 2e2

D

C = 2.4 fF

VG (V)

B

C = 1 fF

J.Gabelli, G.Fève et al Science 313 499 (2006)

• dot spectroscopy

• complete determination of experimental parameters

• charge dynamics

linear regime:

2 /exceV e C

( )excV t

Régime linéaire :

Towards single charge injectionTowards single charge injection

GV

GV

q e

2 exceV

t

The transferred charge is quantized

Charge moyenne transférée par alternance :

Injection regime :

22 / exceV e C

2 exceV

t

( )excV t

Mean transferred charge by alternance :

q e

B

Current detectionCurrent detection

• In time domain :

Fast averaging acquisition card Acquiris,Temporal resolution 500 ps. Developed by Adrien Mahé

Slow excitation f=31.25 MHz

16 odd harmonics of the current courant in a 1 GHz bandwidth

« slow » dynamics

• Measurement of the first harmonic :

Faster excitation f=180 MHz and f=515 MHz

More accurate determination of the transferred chargeAnd of the escape time in the subnanoseond domain :

q

Re( I ),

tan

I

Im( I )

0 5 10 15 20 25 30

Time (ns)

e

e

0 9 . ns

0 02D .31 25 f . MHz32 ns

0 5 10 15 20 25 30

Time (ns)

2 exceV2e

C

t /qI ( t ) e

0 5 10 15 20 25 30

Time (ns)

3 6 . ns

0 005D .

Average on 108 electrons

10 ns

0 002D .

0 5 10 15 20 25 30

Time (ns)

Time domain evolution of the currentTime domain evolution of the current

• non-linear : exceV

nlqR nl

qC

Response to a non-linear square excitationResponse to a non-linear square excitation

2 nlexc qq V C

nl nlq qR C

First harmonic :

Simplification : C 2e

C

] )()2( [ )( feVfNdeq exc

)]()2( [ )(

] )()2( [ )(

2

2

feVfNd

feVfNdhexc

exc

iqfI

12

t /qI( t ) e

Response to a non-linear square excitationResponse to a non-linear square excitation

2nlq

eC

q e

21 nl

q

hD , R

De

2 exceV •

,

h

D

N()

<<

D<<1

D11/

] )()2( [ )( feVfNdeq exc

(linear regime)

First harmonic measurementFirst harmonic measurement

-0.91 -0.90 -0.890

1

2

3

B=1.28T

f = 180MHz

Im(I

) (

ef )

VG (V)

2eVexc=5/4 2eVexc=

2eVexc=1/2 2eVexc=/4

2eVexc=3/2

2eVexc=3/4

D

0

1

2

3

4

2eVexc

=

f=180 MHz

VG=-901 mV

Im (I) (ef

)

2eVexc

/ 0 0.5 1 1.5

Quantization of the AC currentQuantization of the AC current

-0.91 -0.90 -0.890

1

2

3

B=1.28T

f = 180MHz

Im(I

) (

ef )

VG (V)

2 2 excIm( I ) ef f ( eV ) f ( ) N( ) d

1CR nlq

nlq

N()C

e 2 excf ( eV ) f ( )

2.0D

0

1

2

3

4

2eVexc

/

2eVexc

=

f=180 MHz

VG=-901 mV

Im (I) (ef

)

1.510.50

Quantization of the AC currentQuantization of the AC current

-0.91 -0.90 -0.890

1

2

3

B=1.28T

f = 180MHz

Im(I

) (

ef )

VG (V)

2 2 excIm( I ) ef f ( eV ) f ( ) N( ) d

1CR nlq

nlq

N()C

e 2 excf ( eV ) f ( )

0

1

2

3

4

2eVexc

/

2eVexc

=

f=180 MHz

VG=-901 mV

Im (I) (ef

)

1.510.50

Quantization of the AC currentQuantization of the AC current

-0.91 -0.90 -0.890

1

2

3

B=1.28T

f = 180MHz

Im(I

) (

ef )

VG (V)

2 2 excIm( I ) ef f ( eV ) f ( ) N( ) d

1CR nlq

nlq

N()C

e 2 excf ( eV ) f ( )

Transmission dependenceTransmission dependence

-0,91 -0,90 -0,890

1

2

3

B=1.28T

f = 180MHz

Im(I) ( ef )

VG (V)

0

1

2

3

4

2eVexc

=

2eV

exc /

VG=-901mV

VG=-893mV

VG=-880mV

Im (I) (ef)

0 0.5 1 1.5

Dot potential dependenceDot potential dependence

0

1

2

3

4

2eVexc

/

Im (I) (ef

)

VG= -902.2 mV

VG=-901.2 mV

VG=-900.8 mV

VG=-901.6 mV

VG=-880 mV

0 0.5 1 1.5

f = 182 MHz

-0.905 -0.900 -0.8950

1

2

3

B=1.28T

f = 180MHz

Im(I

) (

ef )

VG (V)

N()C

e

Escape timeEscape time

-0,910 -0,905 -0,900

0,1

1

10

Time domain = h / D

f = 515 MHz f = 180 MHz

(n

s)

VG ( V )

Comparison with modellingComparison with modelling

0

1

2

3

2eVexc

/

Im(I

) (e

f)

0 12eV

exc /

0 1

2.0D 9.0D

K5.2

mK200T

AC current diamondsAC current diamonds

-912 -907 -902 -897 -892 -887

5/

5/3

5/7

5/

5/3

5/7

2eV

exc

VG (mV)

1

D0.90.80.40.150.02

Modelling :

0 2 3 4Im (I) (ef)

ConclusionConclusion

• Quantization of the injected charge

1st stage towards the realisation of a single electron source

• Injection dyanmics measured in a large temporal range from 0.1 to 10 ns

• Excellent agreement with a simple modeling

ProspectProspect

• Electron-electron collision :

1 2 0 ?,N N ? Indistinguishibility of two independent sources

e

e

D

D

e

eR R

1N

2N

Experimental setupExperimental setup

3 cm3 mm

dc rf

local

G=X+iY