13.30 o2 v bubanja

735 views

Published on

Research 2: V Bubanja

Published in: Technology, Spiritual
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
735
On SlideShare
0
From Embeds
0
Number of Embeds
3
Actions
Shares
0
Downloads
2
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

13.30 o2 v bubanja

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

×