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

Motivation Gaz 2D I VG Weizmann Institute, Israel Y. Ji et al Nature 422 415 (2003) Poster P. Roulleau, CEA Saclay

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 0. 0.5 1. 1.5 2. 2.5 .8 .6 .4 .2 No temporal control A. Kumar et al. Phys. Rev. Lett. 76 (1996) 2778.. 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…)

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

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

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

The quantum RC circuit l < mm

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

Linear dynamics of the quantum RC circuit Linear regime,

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)

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

Complex conductance D Fit by

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

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

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 :

Time domain evolution of the current Average on 108 electrons

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

Response to a non-linear square excitation D D<<1 , D»1 1/D << e

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)

Quantization of the AC current N(e)

Quantization of the AC current N(e)

Quantization of the AC current N(e)

Transmission dependence

Dot potential dependence f = 182 MHz N(e)

Escape time

Comparison with modelling

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

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

Prospect Electron-electron collision : Indistinguishibility of two independent sources

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