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

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.