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13.30 o2 v bubanja
 

13.30 o2 v bubanja

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Research 2: V Bubanja

Research 2: V Bubanja

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    13.30 o2 v bubanja 13.30 o2 v bubanja Presentation Transcript

    • METROLOGY WITH SINGLE ELECTRONS VLADIMIR BUBANJA 1
    • Single Electronics 2
    • Single Electronics M.C. Esher 3
    • Single Electronics M.C. Esher 4
    • Outline• Metallic islands• Superconducting islands• Solid state entanglers Summary 5
    • Outline• Metallic islands• Superconducting islands• Solid state entanglers Summary 6
    • 7
    • 8
    • 9
    • Hamiltonian of the system: H H 0 + HT , ==H0 ∑ i=S ,I ,D H i + H env ∑ (l  H i = + eVi )cl†,i cl ,i ,(i = l S , D)=HI ∑α α cα cα + Q 2 / 2CΣ † H env = ∑ ωα bα bα † α H T = H T 2 , H Ti = H i− , HT 1 + H i+ + =H1+ ∑ = ( H i+ )† Tα p cα (t )c p (t )e − iϕ1 ( t ) , H i− α,p † 10
    • Inelastic cotunnelingγ ∝ ∫ d ε1 ∫ d ε 2 Γ1 (ε1 + eV1 ) Re[ D(ε1 , ε 2 )] Γ 2 (ε 2 + eV2 )Γi (eV ) ∝ ∫ d ε1 ∫ d ε 2 f (ε1 )[1 − f (ε 2 )] P(ε1 − ε 2 + eV )P( E ) ∝ ∫ dt exp( J (t ) + iEt / ) d ω Re[ Z (ω )] β ωJ (t ) ∫ ω RK [coth 2 (cos(ωt ) − 1) − isin(ωt )] 11
    • Odintsov, Bubanja and Schön, Phys. Rev. B, 46, 6875 12
    • Odintsov, Bubanja and Schön, Phys. Rev. B, 46, 6875Zorin et al., J. Appl. Phys. 88, 2665. 13
    • EU Project COUNT: R-pump 4j-2pTr-3p T+ T- G2 Drain G3 G1 Sou G2 G4 T+ G T- G3 T+ G1 G3 G1 T- 5j+Tr (Pad No.1) 4j+Tr SouG G Pad No.2) G2 Source T+ 5j 4j 4jG1 3j 4j T+ SL_KPN3 T+Source G1 3j+Tr 4j+Tr G G (Pad No.4) (Pad No.3)) Sou T-G2 T- G2 T- G T+ G2 Sou G1 G33j-2p Drain G2 Source G1 G3 4j+Tr (Pad No.5) Lotkhov et al, Appl. Phys. Lett. 78, 946 (2001) 14
    • 005 .7 00 .5 005 .2-.7 -.5 -.2 005 00 005 005 .2 00 .5 005 .7 -.2 005 -.5 00 -.7 005 15
    • Quantum Metrological Triangle hV =n f f 2e I = ef R-pumpJosephson Effect SET LNE, France V Quantum Hall I Effect 1 h= = 1,2,...) V 2 I (n ne 16
    • 005 .7 00 .5 005 .2-.7 -.5 -.2 005 00 005 005 .2 00 .5 005 .7 -.2 005 -.5 00 -.7 005 17
    • Elastic cotunneling 18
    • 19
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    • 23
    • Current through the system: I = 〈 S −1 (t , −∞) I (t ) S (t , −∞)〉 ˆ 1+ 2 z 1  eV  I=   (2π ) 2 Γ(2 + 2 z )e 4ν Ω 0  Ω 0  ∫ d d  F ( ) F ( ) α β α β ×∫ d x1dx 2 g1 (x1 ) g 2 (x 2 ) ∫ dte i ( α −β ) t /  P(x1 ,0; x 2 ,| t |)  2C1C2 z E1 +   F ( ) = 1, 2 + [1 − f ( )]U ,   (C1 + C2 ) Ω 0  2  2C1C2 z E2 −   − f ( )U 1, 2 + ,   (C1 + C2 ) Ω 0  2Bubanja, Phys. Rev. B 78, 155423 (2008) 24
    • Outline• Metallic islands• Superconducting islands• Solid state entanglers Summary 25
    • Hybrid SET transistor N S N A CGVL VR VG 26
    • Pekola et al, Nature Physics 4, 120 (2008) 27
    • 28
    • Motivation:Averin and Pekola, Phys. Rev. Lett. 101, 066801 (2008).Achievable error rates: 10-6 – 10-7.Therefore NISIN transistor is not suitable for metrology. 29
    • 30
    • Z(ω) 31
    • Nucleon pairing 32
    • There is a quasiparticle on the island when gate voltage is adjusted so that: 33
    • EcΔ 34
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    • 37
    • In the resolvent formalism current can be expressed as: 38
    • Conclusion: promising for metrology, 10-8 can be achieved! Bubanja, Phys. Rev. B 83, 195312 (2011) 39
    • Outline• Metallic islands• Superconducting islands• Solid state entanglers Summary 40
    • NS interface• Andreev reflection• Crossed Andreev reflection 41
    • Nonlinear opticsRegular mirror Phase conjugating mirror 42
    • 43
    • J. Feinberg, Opt. Lett. 7, 486 (1982) 44
    • eN I N e S e h 45
    • Bogoliubov-de Gennes approach 1  e= ∑ ∫ d r Ψσ (r )[H BCS 3 ( ∇ − A(r )) 2 + U (r ) − µ ]Ψσ (r ) † σ 2m i c + ∫ d 3 r [∆(r ) Ψ † (r )Ψ † (r ) + ∆* (r )Ψ ↓ (r )Ψ ↑ (r )] ↑ ↓ ∆(r ) = (r ) Ψ ↓ (r )Ψ ↑ (r ) −g {Ψσ (r ), Ψσ (r )}+ δσ ,σ δ (r − r ) † = 46
    • ∆( x) = ∆ Θ( x); U ( x) = U 0δ ( x); Z = mU 0 /  2 k F A Z=0 A Z=1 B B E/∆ E/∆ A: Probability of Andreev reflection B: Probability of ordinary reflectionBlonder, Tinkham, and Klapwijk: Phys. Rev. B 25, 4515 (1982) 47
    • Cross-correlations measurement Solid-state entanglerWei & Chandrasekhar, Nature Physics 6, 494 (2010) 48
    • Experimental and theoretical results of voltage noise power at 0.4K, 0.3K, and 0.25K Wei & Chandrasekhar, Nature Physics 6, 494 (2010) 49
    • Circuit influence on entanglement current 50
    • 51
    • 52
    • Bubanja and Iwabuchi, Phys. Rev. B 84, 094501 (2011) 53
    • Outline• Metallic islands• Superconducting islands• Solid state entanglers Summary 54
    • 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. 55