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
R2
Single electron tunneling suppressed
by energy conservation
VR2
VL
EL = ER1 = ER2
Two-electron virtual tunneling is allowed
VR1
L
R1
Only singlet-state remains at output:
indistinguishability and Fermi statistics
including Pauli Exclusion Principle
U
Ed
EL1
EL2
X
EL1 + EL2 = ER1 + ER2
ER2
ER1
W. D. Oliver et al., PRL 88, 037901 (2002)
Non-linearity:
Coulomb charging energy U
 L2
R2
Optical analogy:
 L1
Chi-(3) four-wave mixing process
 R1
Noise Suppression in
Carbon Nanotubes
LED/PD
CNT
LED/PD
200
250
Experimental Fano factor (noise suppresion)
200 nm SWCNT
V =0V
R = 17.4 kW
200
S (arb. unit)
S (arb. units)
CNT
150
F 
SlopeCNT
 0.17
Slope PD
G
100
150
Elastic scattering: 1-T (transparent contacts)
5050
1 T  1
00
-200
SCNT = 0.17 (2eI)
0
0
200
400
400
I
600
6.45kW
 0.63
17.4kW
800 1000 1200 1400 1600 1800 2000
800
1200
I CNT, IPD (nA)
CNT
1600
, I PD (nA)
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
ST = 2eI(1-T) = 0.63 (2eI)
Remainder of suppression: LL parameter g
g 
0.17
 0.27
0.63
SCNT = 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)
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
~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
-0.1
0.8
Normalized Conductance (G/GQ)
-0.2
1
0.6
0.6
2
99.08.20_A (-14dB)
plateau at p=0.8
0.7 structure at 0.7p = 0.56
0.4
0.4
-0.2
-0.3
-0.3
-0.4
-0.4
4
3
Cross Covariance
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
-0.5
-0.5
0.2
0.2
-0.6
-0.6
-2.9
-2.8
-2.7
-2.6
Input QOC Gate Voltage
-2.5
-2.9 -2.8 -2.7 -2.6 -2.5
Gate Voltage (V)
-0.7
Normalized xcov
Noise Properties of the 0.7 Structure
Conductance (G/GQ)
Integrated semiconductor / CNT structure
Bunching / Anti-bunching experiment