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. Büttiker1 1 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-223 62 Lund, Sweden Ref.: P.R.B 72, 125320 (2005) My supervisors: C.S. Chu(EP,NCTU) and C.Y. Chang(EE,NCTU)

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

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.

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

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

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

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.

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

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.

Model and Theory: current and noise

Model and Theory: Scattering approach to current and shot noise

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

Model and Theory: Scattering approach to current and shot noise

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.

Model and Theory: Dephasing probe model

Model and Theory: Dephasing probe model

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

Mach-Zenhder interferometers: A fully coherent condition

Mach-Zenhder interferometers: A fully coherent condition

Mach-Zenhder interferometers: A fully coherent condition

Mach-Zenhder interferometers: A fully coherent condition Ref. :Y. Ji et al., Nature 422, 415 (2003) I. Neder et al., P.R.L. 96, 16804 (2006)

Mach-Zenhder interferometers: A fully coherent condition

Mach-Zenhder interferometers: A fully coherent condition

Mach-Zenhder interferometers: A fully coherent condition

Mach-Zenhder interferometers: Effect of dephasing

Mach-Zenhder interferometers: Effect of dephasing

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, 245303(2004)

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/0512276

Mach-Zenhder interferometers: Effect of dephasing 1 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).

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

Hanbury Brown Twiss interferometers: A fully coherent condition 5

Hanbury Brown Twiss interferometers: A fully coherent condition 5

Hanbury Brown Twiss interferometers: A fully coherent condition

Hanbury Brown Twiss interferometers: A fully coherent condition

Hanbury Brown Twiss interferometers: Effect of dephasing

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.