1. Visibility of current and shot noise in electrical Mach-Zehnder and Hanbury Brown Twiss interferometers V. S.-W. Chung(鐘淑維)1,2, P. Samuelsson3 ,and M. Büttiker Départment de Physique Théorique, Université de Genève, Genève 4, CH-1211 Swizterland 2 Department of Electonics and Engineering, Chiao Tung University, HsinChu 30010, Taiwan 3 Division of Solid State Theory, Lund University, Sölvegatan 14 A, S Lund, Sweden Ref.: P.R.B 72, (2005) My supervisors: C.S. Chu(EP,NCTU) and C.Y. Chang(EE,NCTU)

2. Mach-Zehnder(MZ) interferometers
Introduction
Model and theory
Optical analogs in quantum Hall regime
current and noise
Scattering approach to current and shot noise
Dephasing probe model
Mach-Zehnder(MZ) interferometers
A fully coherent condition
Effect of dephasing
Hanbury Brown Twiss(HBT) interferometers
Conclusion

3. Introduction
With the advent of mesoscopic physics, it has become possible to experimentally investigate quantum phase coherent properties of electrons in solid state conductors in a controllable way and opens up the possibility of investigating electrical analogs of various optical phenomena.
For photons and conduction electrons, both the wave-nature of the particles as well as their quantum statistics are displayed in a clearcut fashion in interferometer structures.

4. Various with electronic interferometers ballistic transport of the electrons have been investigated experimentally last decades, as e.g.

7. Two-particle Optical HBT interferometers
Ref.: H. Brown et al., Nature 177, 27(1956)
http: //mpej.unige.ch/~buttiker/

8. One-particle electronic HBT interferometers
One-particle Optical HBT interferometers
W.D. Oliver et al.,
Science 284, 299(1999)

9. Only very recently two of the authours and Sukhorukov proposed a direct electronic analog of the optical HBT interferometer, which permits demonstrate two-particle interference in an unambiguous way.
In this work, we investigate and compare in detail the current and zero frequency noise in single particle MZ and two-particle HBT interferometers. Dephasing is studied with the help of the dephasing probe model.

10. Mach-Zehnder interferometers
Introduction
Model and theory
Optical analogs in quantum Hall regime
current and noise
Scattering approach to current and shot noise
Dephasing probe model
Mach-Zehnder interferometers
A fully coherent condition
Effect of dephasing
Hanbury Brown Twiss interferometers
Conclusion

11. Model and Theory: Optical analogs in quantum Hall regime
The transport takes place along edge states, realizing the beams of electrons.
The QPC’s work as the electronic beam splitters with controllable transparency.

12. Model and Theory: current and noise

13. Model and Theory: Scattering approach to current and shot noise

14. Model and Theory: Scattering approach to current and shot noise
Ref. : Ya. Blanter and M. Büttiker,
Phys. Rep. 336,1(2000)

15. Model and Theory: Scattering approach to current and shot noise

16. Model and Theory: Dephasing probe model
Zero currents into lead γ, achieved by the distribution fun. inside the probe, which conserves (i) total currents; (ii) currents at each energy at the probe.
Phase broken but no energy dissipated.
A phenomenological model.

17. Model and Theory: Dephasing probe model

18. Model and Theory: Dephasing probe model

19. Mach-Zehnder interferometers
Introduction
Model and theory
Optical analogs in quantum Hall regime
current and noise
Scattering approach to current and shot noise
Dephasing probe model
Mach-Zehnder interferometers
A fully coherent condition
Effect of dephasing
Hanbury Brown Twiss interferometers
Conclusion

20. Mach-Zenhder interferometers: A fully coherent condition

21. Mach-Zenhder interferometers: A fully coherent condition

22. Mach-Zenhder interferometers: A fully coherent condition

23. Mach-Zenhder interferometers: A fully coherent condition
Ref. :Y. Ji et al., Nature 422, 415 (2003)
I. Neder et al., P.R.L. 96, (2006)

24. Mach-Zenhder interferometers: A fully coherent condition

25. Mach-Zenhder interferometers: A fully coherent condition

26. Mach-Zenhder interferometers: A fully coherent condition

27. Mach-Zenhder interferometers: Effect of dephasing

28. Mach-Zenhder interferometers: Effect of dephasing

29. Mach-Zenhder interferometers: Effect of dephasing
Ref.: F. Marquardt et al., P.R.L. 92, 56805(2004)
A. A. Clerk et al., P.R.B 69, (2004)

30. Mach-Zenhder interferometers: Effect of dephasing
The effect of dephasing, introduced with the voltage probe, both for the current and noise, is for arbitrary dephasing strengnth identical to a phase average.
Ref.: S. Pilgram et al., cond-mat/

31. Mach-Zenhder interferometers: Effect of dephasing1 2 n 3 4 A B
dephasing terminals
reserviors d
Multiplicative: (1-ε)→ (1-ε)n.
(1-ε)n =exp(-L/Lφ) with Lφ =-d/ln(1- ε) and L=nd.
(1-ε)1/2→ exp(-L/2Lφ); (1-ε) → exp(-L/Lφ).

32. Mach-Zehnder interferometers
Introduction
Model and theory
Optical analogs in quantum Hall regime
current and noise
Scattering approach to current and shot noise
Dephasing probe model
Mach-Zehnder interferometers
A fully coherent condition
Effect of dephasing
Hanbury Brown Twiss interferometers
Conclusion

33. Hanbury Brown Twiss interferometers: A fully coherent condition5

34. Hanbury Brown Twiss interferometers: A fully coherent condition5

35. Hanbury Brown Twiss interferometers: A fully coherent condition

36. Hanbury Brown Twiss interferometers: A fully coherent condition

37. Hanbury Brown Twiss interferometers: Effect of dephasing

38. Thank you for your attention
Conclusion
Thank you for your attention
MZ interferometers (amplitude interferometers) exhibit the current visibility with period h/e and the shot noise visibilities with periods of both h/e and h/2e. In contrast, HBT interferometers (intensity interferometers) exhibit no AB-effect in the current and only exhibit h/e-effect in the shot noise.
Our investigation shows the shot noise visibility of HBT interferometers as a function of temperature, voltage, dephasing rate is qualitatively similar to the h/e component of MZ interferometers. It is contrary to the naive expectation that the visibility of two particle processes of HBT interferometers should be related to the two particle processes, i.e. the h/2e component of MZ interferometers. Instead it is the number of times AB flux enclosed which decides the behavior of the visibility.