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Abstract
This dissertation examines the effect of Coulomb interactions in Hanbury Brown–Twiss (HBT) type experiments with electrons. HBT experiments deal with intensity interference, which is related to the second-order correlation function of the particle field. This is an extension of the usual amplitude interference experiment, such as Young's double-slit experiment and the Michelson interferometry, which are related to the first-order correlation function of the particle field. Depending on the exchange symmetry (or anti-symmetry) of the wave function for identical bosons (or fermions) at the detectors, the second-order correlation function shows an enhancement (or a reduction) at small separation with respect to the statistical independent value, i.e., a correlation of the intensities at small separation, either in real or momentum space.
Following this idea, several experiments have been done with electrons under various experimental conditions for the purpose of demonstrating the HBT effect with fermions, the effect due to the exchange anti-symmetry of the wave function for fermions, i.e., Fermi-Dirac statistics. The experiments, however, have been previously analyzed in the formalism of non-interacting fermions, neglecting the effect of Coulomb interactions between electrons. The experimental data need to be more carefully analyzed and the experiments better understood. We examine the experimental setup in detail and construct a classical model to show that Coulomb interaction is in fact dominant over quantum statistics under certain experimental conditions, and calculate the corrections due to Coulomb interactions in these cases.
The second-order correlation function, i.e., the intensity correlation function, is not the only characterization of the two-particle interference. There are other different yet equivalent characterizations, which we examine in this thesis. We investigate the relationship between different characterizations and illustrate the connections between them.
