13.30 o2 v bubanja
DESCRIPTION
Research 2: V BubanjaTRANSCRIPT
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VLADIMIR BUBANJA
METROLOGY WITH SINGLE ELECTRONS
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Single Electronics
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Single Electronics
M.C. Esher
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Single Electronics
M.C. Esher
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Outline
• Metallic islands • Superconducting islands • Solid state entanglers
Summary
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Outline
• Metallic islands • Superconducting islands • Solid state entanglers
Summary
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Hamiltonian of the system:
0 ,TH H H= +
0, ,
i envi S I D
H H H=
= +∑
, ,†( ) , ( , )i l i l i l i
l
H eV c c i S D= + =∑
† 2 / 2IH c c Q Cα α αα
Σ= +∑†
envH b bα α αα
ω=∑
1 2 , ,T T T Ti i iH H H H H H+ −= + = +
1† ( )
,
†1 ( ) ( ) , ( )i t
p p i ip
H T c t c t e H Hϕα α
α
−+ − += =∑
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1 2 1 1 1 1 2 2 2 2
1 2 1 2 1 2
( )Re[ ( , )] ( )
( ) ( )[1 ( )] ( )
( ) exp( ( ) / )
Re[ ( )]( ) [coth (cos( ) 1) sin( )]2
i
K
d d eV D eV
eV d d f f P eV
P E dt J t iEt
d ZJ t t i tR
γ ε ε ε ε ε ε
ε ε ε ε ε ε
ω ω β ω ω ωω
∝ Γ + Γ +
Γ ∝ − − +
∝ +
= − −
∫ ∫
∫ ∫
∫
∫
Inelastic cotunneling
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Odintsov, Bubanja and Schön, Phys. Rev. B, 46, 6875
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Odintsov, Bubanja and Schön, Phys. Rev. B, 46, 6875
Zorin et al., J. Appl. Phys. 88, 2665.
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5j
3j
4j
4j
4j
G3 G1 Source G2 Drain
T+ G T- G2
Sou G1
G2
Source
G1
G
T+
G
T-
G3
G1 Sou G2 G4
T-
T+
T+ G2 Drain G3
G1
Source
T+ G T- G3
G1
Sou
G2
T+
G
T-
T+
G
T-
G3 G1 Sou G2
4j+Tr
4j+Tr
4j+Tr 5j+Tr
3j+Tr
4j-2p
3j-2p
Tr-3p
Pad No.2) (Pad No.1)
(Pad No.3)) (Pad No.4)
(Pad No.5)
SL_KPN3
EU Project COUNT: R-pump
Lotkhov et al, Appl. Phys. Lett. 78, 946 (2001)
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-0.075 -0.05 -0.025 0.025 0.05 0.075
-0.075
-0.05
-0.025
0.025
0.05
0.075
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Quantum Metrological Triangle
f
V I
Josephson Effect
Quantum Hall Effect
SET
2hV n fe
= I e f=
= =21 ( 1,2,...)hV I nn e
R-pump LNE, France
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-0.075 -0.05 -0.025 0.025 0.05 0.075
-0.075
-0.05
-0.025
0.025
0.05
0.075
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Elastic cotunneling
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Current through the system:
1 2
2 40 0
1 ( ) ( )(2 ) (2 2 )
zeVI d d F F
z e α β α βπ ν
+
= Γ + Ω Ω ∫
( ) /1 2 1 1 2 2 1 2( ) ( ) e ( ,0; ,| |)i td d g g dt P tα β−×∫ ∫x x x x x x
1 2 12
1 2 0
1 2 22
1 2 0
2( ) [1 ( )] 1,2 ,( )
2( ) 1,2 ,( )
C C z EF f UC C
C C z Ef UC C
+= − + + Ω
−− + + Ω
1 ˆ( , ) ( ) ( , )I S t I t S t−= ⟨ −∞ −∞ ⟩
Bubanja, Phys. Rev. B 78, 155423 (2008)
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Outline
• Metallic islands • Superconducting islands • Solid state entanglers
Summary
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Hybrid SET transistor
N S
A
VL VR
VG
CG
N
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Pekola et al, Nature Physics 4, 120 (2008)
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Averin and Pekola, Phys. Rev. Lett. 101, 066801 (2008). Achievable error rates: 10-6 – 10-7. Therefore NISIN transistor is not suitable for metrology.
Motivation:
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Z(ω)
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Nucleon pairing
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There is a quasiparticle on the island when gate voltage is adjusted so that:
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Ec
Δ
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In the resolvent formalism current can be expressed as:
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Conclusion: promising for metrology, 10-8 can be achieved!
Bubanja, Phys. Rev. B 83, 195312 (2011)
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Outline
• Metallic islands • Superconducting islands • Solid state entanglers
Summary
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• Andreev reflection • Crossed Andreev reflection
NS interface
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Nonlinear optics
Regular mirror Phase conjugating mirror
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J. Feinberg, Opt. Lett. 7, 486 (1982)
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N I N S e
e e
h
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Bogoliubov-de Gennes approach
3 † 2BCS
3 † † *
†' , '
1H ( )[ ( ( )) ( ) ] ( )2
[ ( ) ( ) ( ) ( ) ( ) ( )]
( ) ( ) ( ) ( )
( ), ( ') ( ')
ed r r A r U r rm i c
d r r r r r r r
r g r r r
r r r r
σ σσ
σ σ σ σ
µ
δ δ
↑ ↓ ↓ ↑
↓ ↑
+
= Ψ ∇− + − Ψ
+ ∆ Ψ Ψ +∆ Ψ Ψ
∆ = − Ψ Ψ
Ψ Ψ = −
∑∫
∫
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E / ∆
A
B
E / ∆
A
B
A: Probability of Andreev reflection B: Probability of ordinary reflection
Z=0 Z=1
Blonder, Tinkham, and Klapwijk: Phys. Rev. B 25, 4515 (1982)
20 0( ) ( ); ( ) ( ); / Fx x U x U x Z mU kδ∆ = ∆Θ = =
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Wei & Chandrasekhar, Nature Physics 6, 494 (2010)
Cross-correlations measurement
Solid-state entangler
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Wei & Chandrasekhar, Nature Physics 6, 494 (2010)
Experimental and theoretical results of voltage noise power at 0.4K, 0.3K, and 0.25K
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Circuit influence on entanglement current
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Bubanja and Iwabuchi, Phys. Rev. B 84, 094501 (2011)
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Outline
• Metallic islands • Superconducting islands • Solid state entanglers
Summary
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Summary
• We have developed theories of electron transport in: semiconducting QD’s, metallic, superconducting islands, and carbon nanotubes taking into account charging as well as the effects of the electromagnetic environment.
• Applications include most accurate SET devices and their use in metrology, computing and sensing.