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Research 2: V Bubanja
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1 1
VLADIMIR BUBANJA
METROLOGY WITH SINGLE ELECTRONS
2
Single Electronics
3
Single Electronics
M.C. Esher
4
Single Electronics
M.C. Esher
5 5
Outline
• Metallic islands • Superconducting islands • Solid state entanglers
Summary
6 6
Outline
• Metallic islands • Superconducting islands • Solid state entanglers
Summary
7 7
8 8
9 9
10 10
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
−+ − += =∑
11
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
12
Odintsov, Bubanja and Schön, Phys. Rev. B, 46, 6875
13
Odintsov, Bubanja and Schön, Phys. Rev. B, 46, 6875
Zorin et al., J. Appl. Phys. 88, 2665.
14 14
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)
15 15
-0.075 -0.05 -0.025 0.025 0.05 0.075
-0.075
-0.05
-0.025
0.025
0.05
0.075
16
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
17 17
-0.075 -0.05 -0.025 0.025 0.05 0.075
-0.075
-0.05
-0.025
0.025
0.05
0.075
18 18
Elastic cotunneling
19 19
20 20
21 21
22 22
23 23
24 24
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)
25 25
Outline
• Metallic islands • Superconducting islands • Solid state entanglers
Summary
26 26
Hybrid SET transistor
N S
A
VL VR
VG
CG
N
27 27
Pekola et al, Nature Physics 4, 120 (2008)
28 28
29 29
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:
30 30
31 31
Z(ω)
32 32
Nucleon pairing
33 33
There is a quasiparticle on the island when gate voltage is adjusted so that:
34 34
Ec
Δ
35 35
36 36
37 37
38 38
In the resolvent formalism current can be expressed as:
39 39
Conclusion: promising for metrology, 10-8 can be achieved!
Bubanja, Phys. Rev. B 83, 195312 (2011)
40 40
Outline
• Metallic islands • Superconducting islands • Solid state entanglers
Summary
41 41
• Andreev reflection • Crossed Andreev reflection
NS interface
42 42
Nonlinear optics
Regular mirror Phase conjugating mirror
43 43
44 44
J. Feinberg, Opt. Lett. 7, 486 (1982)
45 45
N I N S e
e e
h
46 46
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 = −
∑∫
∫
47 47
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 = =
48 48
Wei & Chandrasekhar, Nature Physics 6, 494 (2010)
Cross-correlations measurement
Solid-state entangler
49 49
Wei & Chandrasekhar, Nature Physics 6, 494 (2010)
Experimental and theoretical results of voltage noise power at 0.4K, 0.3K, and 0.25K
50 50
Circuit influence on entanglement current
51 51
52 52
53
Bubanja and Iwabuchi, Phys. Rev. B 84, 094501 (2011)
54 54
Outline
• Metallic islands • Superconducting islands • Solid state entanglers
Summary
55 55
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.