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Center for Quantum Information ROCHESTER HARVARD CORNELL STANFORD RUTGERS LUCENT TECHNOLOGIES. Quantum Electron Optics and Electron Entanglement. Na Young Kim (Stanford, AP) Manuel Aranzana (ENS) William D. Oliver (Stanford, EE) Leo Di Carlo (Harvard)

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Center for Quantum Information

ROCHESTER HARVARD CORNELL STANFORD RUTGERS

LUCENT TECHNOLOGIES

Quantum Electron Optics

and

Electron Entanglement

Na Young Kim (Stanford, AP) Manuel Aranzana (ENS)

William D. Oliver (Stanford, EE) Leo Di Carlo (Harvard)

Fumiko Yamaguchi (Stanford, AP/EE) Gwendal Feve (ENS)

Yoshihisa Yamamoto (Stanford, AP/EE) Jungsang Kim (Lucent)

Robert Liu (UCSF)

Jing Kong (Stanford, Chem) Xavier Maitre (CNRS)

Hongjie Dai (Stanford, Chem)


R2

VR2

VL

VR1

L

R1

U

Ed

ER2

EL1

X

EL2

ER1

Electron Entanglement

via a Quantum Dot

Single electron tunneling suppressed

by energy conservation

EL =ER1 = ER2

Two-electron virtual tunneling is allowed

EL1 + EL2 = ER1 + ER2

Only singlet-state remains at output:

indistinguishability and Fermi statistics

including Pauli Exclusion Principle

Non-linearity:

Coulomb charging energy U

Optical analogy:

Chi-(3) four-wave mixing process

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


250

200 nm SWCNT

200

LED/PD

R = 17.4 kW

CNT

150

S (arb. units)

50

0

400

800

1600

0

1200

(nA)

,

I

I

CNT

PD

Noise Suppression in

Carbon Nanotubes

Experimental Fano factor (noise suppresion)

SCNT = 0.17 (2eI)

Elastic scattering: 1-T (transparent contacts)

ST = 2eI(1-T) = 0.63 (2eI)

Remainder of suppression: LL parameter g

  • S = 2e*IB= 2 (ge) I(1-T) = g (1-T) 2eI

g, elastic scattering yield noise suppression

CNT: g = 0.2 ~ 0.3 theory, g = 0.28 expt

SCNT = g(1-T) 2eI= 0.17 (2eI)


~20 nm

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)

collective excitation (CDW, SDW)

TBD: how does this effect entanglement ??

CNT as 0D and 1D structure

“Kinks”, CNT overlap, AFM tip, etc. create tunnel barrier


1

2

4

3

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

-0.1

0.8

-0.2

0.6

-0.3

Conductance (G/GQ)

Normalized xcov

-0.4

0.4

-0.5

0.2

-0.6

-0.7

-2.9

-2.8

-2.7

-2.6

-2.5

Gate Voltage (V)


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