„To bunch

or not to bunch”

Tóvári EndreJournal Club2013. márc. 8.

Coherence and Indistinguishabilityof Single Electrons Emitted byIndependent Sources

Science 339, 1054 (2013)Science 339, 1041 (2013)

Two Indistinguishable ElectronsInterfere in an Electronic Device

Coherence and Indistinguishabilityof Single Electrons Emitted byIndependent SourcesE. Bocquillon,1 V. Freulon,1 J.-M Berroir,1 P. Degiovanni,2 B. Plaçais,1 A. Cavanna,3Y. Jin,3 G. Fève1*

1 Laboratoire Pierre Aigrain, Ecole Normale Supérieure, CNRS(UMR8551), Université Pierre et Marie Curie, Université ParisDiderot, 24 rue Lhomond, 75231 Paris Cedex 05, France. 2 Université de Lyon, Fédération de Physique AndréMarie Ampère, CNRS–Laboratoire de Physique de l’Ecole Normale Supérieure de Lyon 46 Allée d’Italie, 69364 Lyon Cedex 07, France. 3 CNRS–Laboratoire de Photonique et de Nanostructures Route de Nozay, 91460 Marcoussis, France.

Two Indistinguishable ElectronsInterfere in an Electronic DeviceChristian SchönenbergerDepartment of Physics, University of Basel

Új kísérletek a nanofizikában - előadásjegyzet

bunching

antibunching

coincidence Noise vs delay time

Hong-Ou-Mandel (HOM) dip

Dip size and shape depends on wave packet overlap and width τe

Indistinguishable electrons neededDC voltage: •continuous stream of electrons•but 2-e- interference cannot be interpreted as overlap between 2 single-particle wave packetsTriggered AC emitter: generating 1-e- wave packets at well-defined times

Realization:•Quantum dots: charge quantization•Quantum Hall regime: ballistic, 1D, chiral edge channels

•AlGaAs/GaAs 2DEG •n=1,9x10-11 cm-2

•µ=2,4x106 cm2/Vs•B=2,68T, ν=3 filling factor•QD addition energy Δ=1,4K•electron temperature 100 mK

QDot: •2,1 GHz square wave on top gate: p2p amplitude is the addition energy Δ e- followed by h+

•τe=58±7 ps average emission time•Tunnel coupling (with D=0,45±0,05 transmission) to an edge channel

• Tunnel emission of single particles form a discrete dot level: exponential decay confirmed

emission trigger

τe: average emission time

T=1/2

2DEG

Probability of different outputs:

2

1 2

11,1 1

2P

2

1 2

10,2 2,0 1

2P P

Probability of exiting at the same output:

(fermions)

τ>> τe: classical case

Perfectly indistinguishable states:

Normalized by the classical value e2f:2

44 / 1 eq S e f e Antibunching with the thermal excitations: if ,we must subtract the noise when both sources are switched off

0i Bk T

(one source off)

antibunching of single indistinguishable fermions

( )

Blue line:

τe=62±10 psγ=0,45±0,05 non-unit overlapτ0=13±6 ps

QDot: •τe=58±7 psa verage emission time•Tunnel coupling (with D=0,45±0,05 transmission) to an edge channel•10 ps synchronization

Red line: Floquet scattering γ = 0.5, D1 = D2 = 0.4, Δ1 = Δ2 = 1.4K, and T = 100 mK.

Non-unit overlap γ:•possibly Δ/10 difference in QD levels•maybe τc≈100 ps coherence time: