Statistical correlation for the composite Boson

TL;DR

This paper investigates the statistical correlation effects of composite Bosons formed from spin singlet entangled electron pairs, revealing Bosonic behavior at low voltages and oscillations between Fermionic and Bosonic behavior at high voltages.

Contribution

It is the first study to analyze the correlation effects of composite Bosons made from entangled electron pairs using nonequilibrium Green's functions.

Findings

Positive cross correlation at low voltages indicating Bosonic behavior.

Negative cross correlation at high voltages showing Fermionic contributions.

Oscillation between Fermionic and Bosonic behavior with changing voltage and resonant levels.

Abstract

It is well known that the particles in a beam of Boson obeying Bose-Einstein statistics tend to cluster (bunching effect), while the particles in a degenerate beam of Fermion obeying Fermi-Dirac statistics expel each other (anti-bunching effect). Here we investigate, for the first time, the statistical correlation effect for the composite Boson, which is formed from a spin singlet entangled electron pair. By using nonequilibrium Green's function technique, we obtain a positive cross correlation for this kind of the composite Boson when the external voltage is smaller than the gap energy, which demonstrates that a spin singlet entangled electron pair looks like a composite Boson. In the larger voltage limit, the cross correlation becomes negative due to the contribution of the quasiparticles. At large voltages, the oscillation between Fermionic and Bosonic behavior of cross correlation is also observed in the strong coupling regime as one changes the position of the resonant levels. Our result can be easily tested in a three-terminal normal-superconductor-superconductor (N-S-S) hybrid mesoscopic system.