State Orthogonality, Boson Bunching Parameter and Bosonic Enhancement Factor

TL;DR

This paper derives a simple formula relating the bosonic bunching ratio to the initial wavefunction overlap, showing it as a constant of motion and explaining experimental observations of bosonic enhancement and bunching behavior.

Contribution

It introduces a universal relation between the bunching parameter and wavefunction overlap, generalizes it to multiple particles, and clarifies conditions for bosonic enhancement.

Findings

Bunching ratio depends only on initial wavefunction overlap.

Orthogonal initial states yield maximum bunching ratio of 2.

Bosonic enhancement occurs only when all states are orthogonal.

Abstract

It is emphasized that the bunching parameter $\beta=P_B/P_D$ , i.e. the ratio between the probability to measure two bosons and two distinguishable particles at the same state, is a constant of motion and depends only on the overlap between the initial wavefunctions. This ratio is equal to $\beta=2/(1+I^2)$ , where $I$ is the overlap integral between the initial wavefunctions. That is, only when the initial wavefunctions are orthogonal this ratio is equal to 2, however, this bunching ratio can be reduced to 1, when the two wavefunctions are identical. This simple equation explains the experimental evidences of a beam splitter. A straightforward conclusion is that by measuring the local bunching parameter $\beta$ (at any point in space and time) it is possible to evaluate a global parameter$ I$ (the overlap between the initial wavefunctions). The bunching parameter is then generalized to arbitrary number of particles, and in an analogy to the two-particles scenario, the well-known bosonic enhancement appears only when all states are orthogonal.