1. Quantum Electron Optics Electron Entanglement
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)

2. 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 L R2 R1 VL
VR1
VR2
ER1 Ed U
ER2 X
EL1
EL2
W. D. Oliver et al., PRL 88, (2002)

3. Noise Suppression in Carbon Nanotubes
Experimental Fano factor (noise suppresion)
LED/PD
CNT
200 nm SWCNT
R = 17.4 kW
400
800
1200
1600 I PD
(nA) , 50
150
200
250
S (arb. units)
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)

4. Integrated CNT / SC Structures for Electron Entanglement
CNT as a quantum dot (0D) structure
~20 nm
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

5. 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
-0.1
-0.2
0.6 3 1 2 4
-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)