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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.