Center for Quantum Information

ROCHESTER HARVARD CORNELL STANFORD RUTGERS LUCENT TECHNOLOGIES

Quantum Electron Optics and Electron Entanglement

Na Young Kim (Stanford, AP) William D. Oliver (Stanford, EE) Fumiko Yamaguchi (Stanford, AP/EE) Yoshihisa Yamamoto (Stanford, AP/EE) Jing Kong (Stanford, Chem) Hongjie Dai (Stanford, Chem) Manuel Aranzana (ENS) Leo Di Carlo (Harvard) Gwendal Feve (ENS) Jungsang Kim (Lucent) Robert Liu (UCSF) Xavier Maitre (CNRS)

Electron Entanglement via a Quantum Dot

L V L V R2 V R1 R2 R1 Single electron tunneling suppressed by energy conservation E L = E R1 = E R2 Two-electron virtual tunneling is allowed E L1 + E L2 = E R1 + E R2 E L1 E L2 X U E d E R2 E R1

W. D. Oliver et al., PRL 88, 037901 (2002)

Only singlet-state remains at output :

indistinguishability and Fermi statistics including Pauli Exclusion Principle

Non-linearity:

Coulomb charging energy U



L

2

Optical analogy:

Chi-(3) four-wave mixing process



L

1 

R

2 

R

1

Noise Suppression in Carbon Nanotubes

LED/PD CNT

V G CNT

200 nm SWCNT

=0V

R = 17.4 k

W

Experimental Fano factor (noise suppresion)

F



Slope CNT Slope PD

S CNT

 0

= 0.17 (2eI)

.

17

50

50

0

0 -200

Elastic scattering: 1-T (transparent contacts)

1 

T

 1  6 .

45

k

W 17 .

4

k

W  0 .

63 200 600

I

I CNT

CNT

, I

, I

(nA)

PD (nA) S T = 2eI(1-T) = 0.63 (2eI)

S = 2 e* I B = 2 ( ge ) I(1-T) = g (1-T) 2eI g, elastic scattering yield noise suppression

Remainder of suppression: LL parameter g

g

 0 .

17 0 .

63  0 .

27

CNT: g = 0.2 ~ 0.3 theory, g = 0.28 expt S CNT = g(1-T) 2eI= 0.17 (2eI)

Integrated CNT / SC Structures for Electron Entanglement

CNT as a quantum dot (0D) structure Easy to make strong tunnel barriers Strong confinement w/out surface depletion effect Very small CNT quantum dot entangler CNT as a quantum wire (1D) structure “Ideal” 1D channel, minimize intermode coupling Reduced scattering phase space (cf., 2D leads) “interconnect” with long mean free path (?) Caveat: LL quasi-particle not free electron (cf., Fermi Liquid) TBD: collective excitation (CDW, SDW) how does this effect entanglement ??

CNT as 0D and 1D structure “Kinks”, CNT overlap, AFM tip, etc. create tunnel barrier ~20 nm

Future Directions

Theory of regulated entangled pair generation “

unitary limit” of conductance with resonant biasing ….. “natural regulation” turnstile like operation ….. “engineered regulation” Luttinger Liquid theory

Experimental demonstration of electron entangler

Integrated semiconductor / CNT structure Bunching / Anti-bunching experiment

Noise Properties of the 0.7 Structure

HBT-type Experiment: shows noise suppression one channel in unitary limit one channel partially conducting Collision experiment: spin polarized vs. unpolarized

0.8

0.8

-0.1

-0.1

-0.2

-0.2

0.6

0.6

1 2

-0.3

-0.3

0.4

0.4

3

99.08.20_A (-14dB) plateau at p=0.8

0.7 structure at 0.7p = 0.56

4

-0.4

-0.4

-0.5

-0.5

0.2

0.2

-0.6

-0.6

-2.9

-2.8

-2.7

-2.6

-2.5

Input QOC Gate Voltage

-2.9 -2.8 -2.7 -2.6 -2.5

Gate Voltage (V) -0.7