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 422 415 (2003) Poster P. Roulleau, CEA Saclay

3. Single electron sources 1,0 1 .8 .6 .4 .2 0 ( ) - 1 T 0,8 D 1 Objective :realisationof a single electron source similar to single photon sources 0,6 ( ) Kumar et al. PRL (1996) - Fano reduction factor T 1 T 2 2 Time controlled injection of a single electron in a quantum conductor 0,4 + 1 T 2 0,2 Electron optics with one or two electrons (entanglement…) 0,0 0. 0.5 1. 1.5 2. 2.5 Conductance 2e² / h DC biased Fermi sea is a noiseless electron source: No temporal control A. Kumar et al. Phys. Rev. Lett. 76 (1996) 2778..

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

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

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

7. The quantum RC circuit l < mm

8. The quantum RC circuit 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 70 4114, PLA180,364-369 (1993)

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

12. Complex conductance Fit by D

13. Conclusion on linear dynamics linear regime: • dot spectroscopy • charge dynamics • complete determination of experimental parameters J.Gabelli, G.Fève et al Science 313 499 (2006)

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

15. Current detection • In time domain : 16 odd harmonics of the current courant in a 1 GHz bandwidth • Measurement of the first harmonic : Fast averaging acquisition card Acquiris, Temporal resolution 500 ps. Developed by Adrien Mahé Slow excitation f=31.25 MHz « slow » dynamics 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 excitation N(e) D D<<1 , D»1 1/D << e

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

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 2 3 4 0 D 0.02 0.15 0.4 0.8 0.9 Modelling : 2eVexc -912 -907 -902 -897 -892 -887 VG (mV) Im (Iw) (ef) 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 G=X+iY local 3 cm 3 mm dc rf