1. A coherent subnanosecond single electron source
Gwendal Fève
Groupe de Physique Mésoscopique
Laboratoire Pierre Aigrain
ENS
Jean-Marc Berroir
Bernard Plaçais
Christian Glattli
Takis Kontos
Julien Gabelli
Adrien Mahé
Samples made at : Laboratoire de Photonique et Nanostructures (LPN)
Yong Jin
Bernard Etienne
Antonella Cavana

2. Motivation
Gaz 2D I VG
Weizmann Institute, Israel Y. Ji et al Nature (2003)
Poster P. Roulleau, CEA Saclay

3. Single electron sources
DC biased Fermi sea is a noiseless electron source: D
Kumar et al. PRL (1996)
0,0
0,2
0,4
0,6
0,8
1,0 ( ) 1 - T 2 +
Fano reduction factor
Conductance 2e² / h .8 .6 .4 .2
No temporal control
A. Kumar et al. Phys. Rev. Lett. 76 (1996)
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…)

4. Principle of single charge injection
V(t)
QPC
Gaz 2D
Boîte e D
V(t)

5. Principle of single charge injection
V(t)
QPC
Gaz 2D
Boîte e
V(t)

6. Principle of single charge injection
V(t)
QPC
Gaz 2D
Boîte e I
V(t)
100 ps for D=2.5°K and D =0.2

7. The quantum RC circuit
l < mm

8. The quantum RC circuit D=t2 No spin degeneracy
Quantum dot
D=t2
No spin degeneracy
One dimensional conductor

9. Linear dynamics of the quantum RC circuit
Linear regime,

10. The quantum RC circuit, T=0K
CPQ
, dot density of states
The resistance is constant, independent of transmission,
and equals half the resistance quantum for a single mode conductor !
M. Büttiker et al PRL , PLA180, (1993)

11. The quantum RC circuit , T=0K
Quantum dot
D=t2
kBT << DD
Coherent regime
kBT >> DD
Sequential regime

12. Complex conductance D
Fit by

13. Conclusion on linear dynamics
linear regime:
dot spectroscopy
complete determination of experimental parameters
charge dynamics
J.Gabelli, G.Fève et al Science (2006)

14. Towards single charge injection
Injection regime :
Régime linéaire :
Charge moyenne transférée
par alternance :
Mean transferred charge
by alternance :
The transferred charge is quantized

15. Current detection In time domain : Measurement of the first harmonic :
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 charge
And of the escape time in the subnanoseond domain :

16. Time domain evolution of the current
Average on 108 electrons

17. Response to a non-linear square excitation
Simplification :
non-linear :
First harmonic :

18. Response to a non-linear square excitationD
D<<1 ,
D»1
1/D
<< e

19. First harmonic measurement
2eVexc=3/2 D
2eVexc=5/4 D
2eVexc= D
2eVexc=3/4 D
2eVexc=1/2 D
2eVexc=1/4 D
(linear regime)

20. Quantization of the AC current
N(e)

21. Quantization of the AC current
N(e)

22. Quantization of the AC current
N(e)

23. Transmission dependence

24. Dot potential dependence
f = 182 MHz
N(e)

25. Escape time

26. Comparison with modelling

27. AC current diamonds 2eVexc VG (mV) Im (Iw) (ef) 2 3 4 1 Modelling : D
0.02
0.15
0.4
0.8
0.9
Modelling :
2eVexc
-912
-907
-902
-897
-892
-887
VG (mV)
Im (Iw) (ef) 2 3 4 1

28. Conclusion 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

29. Prospect Electron-electron collision : Indistinguishibility of
two independent sources

31. Experimental setup dc rf
local
G=X+iY
3 cm
3 mm