טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentGershon Gal
SubjectAn Experimental Study of the High Order Cumulants
of Shot Noise in Mesoscopic Systems
DepartmentDepartment of Physics
Supervisor Professor Michael Reznikov
Full Thesis textFull thesis text - English Version


Abstract

We present an experimental study of the statistics of current fluctuations in nanoscaled systems beyond the second cumulant. Of particular interest are measurements of the third moment of the current fluctuations and the validation of the general expression for the statistics of the charge transmitted through a barrier, known as Levitov's formula. We measured the probability distribution function of the transmitted charge, from which we were able to extract the first three cumulants. To obtain the intrinsic quantities, corresponding to voltage-biased barrier, we employ a procedure that accounts for the characteristics of the external circuit and the amplifier. The third cumulant, obtained with a high precision, is found to agree with the prediction for the charge transfer statistics in the non-Poissonian regime.


For several decades photon counting statistics has been one of the main well-established methods of quantum optics. It is routinely used to obtain detailed information about temporal and spectral distribution of electromagnetic field, and to characterize the complexity of optical states. Experimental investigation of electron counting proves to be far more challenging than that of photons primarily because of the extremely high frequency of electron passage events at typical currents, it is especially rich and intriguing because, unlike photons, the current fluctuations are measured without extracting electrons out of the system. The electrons remain part of the many-body system while being detected, allowing quantum phenomena to fully manifest themselves. The remarkable examples are observation of the fractional charges under the Fractional Quantum Hall effect conditions, and of the charge doubling in Andreev reflection regime. The challenge in counting electrons stems from the simple fact that, while photons do not interact, the electrons, being charged, does. The electric field fluctuations produced by the electrons which are being measured can propagate out to other parts of the circuit ('environment') and perturb it. In turn, the noise due to the environment, modulated by the signal, can couple back into the region of interest, strongly affecting the measured signal.

In this work we report on the first measurement of the third moment that fully take these effects into account. The environmental effects are treated in an innovative way both experimentally and analytically allowing for the first clean extraction of the intrinsic third moment generated by a system with controllable transmission, which is a validation of Levitov's formula.