Quantum statistical signature of $\mathcal{PT}$ symmetry breaking

TL;DR

This paper reveals a quantum statistical signature of $ ext{PT}$ symmetry breaking in optical systems, showing how coincidence probabilities for bosons and fermions equalize at the phase transition and reverse in the broken phase.

Contribution

It demonstrates a novel quantum statistical signature of $ ext{PT}$ symmetry breaking, linking particle statistics with phase transition behavior in optical systems.

Findings

Coincidence probabilities for bosons and fermions are equal at the $ ext{PT}$ symmetry breaking point.

In the broken $ ext{PT}$ phase, the usual inequality $P^{(bos)}<P^{(ferm)}$ reverses.

The effect is exemplified using a passive $ ext{PT}$-symmetric optical directional coupler.

Abstract

In multiparticle quantum interference, bosons show rather generally the tendency to bunch together, while fermions can not. This behavior, which is rooted in the different statistics of the particles, results in a higher coincidence rate $P$ for fermions than for bosons, i.e. $P^{(bos)}<P^{(ferm)}$. However, in lossy systems such a general rule can be violated because bosons can avoid lossy regions. Here it is shown that, in a rather general optical system showing passive parity-time ($\mathcal{PT}$) symmetry, at the $\mathcal{PT}$ symmetry breaking phase transition point the coincidence probabilities for bosons and fermions are equalized, while in the broken $\mathcal{PT}$ phase the reversal $P^{(bos)}>P^{(ferm)}$ is observed. Such effect is exemplified by considering the passive $\mathcal{PT}$-symmetric optical directional coupler.