1. Positive HBT/noise cross-correlations in superconducting hybrids: Role of disorder
R. Melin, C. Benjamin and T. Martin,
Phys. Rev. B 77, (2008) 1

2. Noise: An Introduction Noise and entanglement: Historical perspective
Talk outline:
Noise: An Introduction
Noise and entanglement: Historical perspective
NSN junctions: CAR and EC
Positive noise correlations in spite of negative crossed conductance
Implications of disorder. 2

3. The noise is the signal (R. Landauer)

4. Johnson-Nyquist noise and Shot noise
① Johnson-Nyquist noise for equilibrium circuit
information about resistance & temperature
… just disturbance
Harry Nyquist
( : U.S.)
② Shot noise in a vacuum tube
Electrons are emitted by thermal agitation

5. classical picture of current
noise power
“simple way to measure the charge of electron”
Annals der Physik (1918)
Walter Schottky
( : Germany)
classical picture of current
Electrons are emitted
Independently from each other:
Poissonian process.

6. QUANTUM TRANSPORT: scattering approach
Reservoirs + S matrix

7. Hanbury Brown and Twiss experiment
Bunching effect: positive correlations
Fermions:
Negative correlations
(T. Martin & R. Landauer
M. Buttiker, PRB ’s 92)
Exp: Schonenberger 99, Yamamoto 99 (Science)

8. Noise in Normal metal/Superconducting junctions
Andreev reflection
Positive noise correlation in a « Andreev interferometer » M P Anantram & S. Datta, PRB (1996)
Positive noise correlation in a « NS fork »
J.Torrès, T. Martin, EPJB (99)

9. Why do positive cross-correlations imply entanglement
Motivation: To build a solid state entangler
Why do positive cross-correlations imply entanglement
+ve cross-correlations in a fermionic system
Reason for this anomaly: correlations between fermions
(a)Electron co-tunneling
-ve correlations
(b) Crossed Andreev
reflection
+ve correlations

10. Noise correlations: BTK approach

11. Noise correlations: Greens function approach

12. Noise cross-correlations: The half metallic case
Anti-parallel alignment: completely positive (crossed Andreev processes)
Parallel alignment: completely negative (elastic co-tunneling)
At Vb=+Va (P/AP) noise vanishes due to Pauli blocking
For fermions: f=f 2

13. Noise cross-correlations: NSN
Transparent interfaces: Noise cross-correlations +ve
Semi-transparent interfaces: Noise cross-correlations –ve
Tunneling limit: -ve for EC and +ve for CAR [Bignon, et. al., EPL(2004)]

14. Novelty of our work (1)
In NSN systems: Crossed conductance = CAR-EC
Negative crossed conductance does not imply negative cross-correlations!

15. Novelty of our work (2)
Interpretation:
(a) double Andreev reflection
(b) double non-local Andreev process

16. Transmission: Two barrier case

17. Weak localization: Three barriers
F. Marquardt, Lecture notes on weak localization

19. Classical result

20. V1 V2
Non local conductance is enhanced by weak localization
Noise cross correlations enhanced by weak localization

21. Perspective
Probing interesting physics in the weak localization regime
Probing entanglement in nanophysics-This study constitutes what is the next generation in the evolving project to detect the splitting of cooper pairs into different leads.