Shock-induced $\mathcal{P}\mathcal{T}$-symmetric potentials in gas-filled photonic crystal fibers

We have investigated the interaction between a strong soliton and a weak probe with certain configurations that allow optical trapping in gas-filled hollow-core photonic crystal fibers in the presence of the shock effect. We have shown theoretically and numerically that the shock term can lead to an unbroken parity-time $\left(\mathcal{P}\mathcal{T}\right)$ symmetry potential in these kinds of fibers. Reciprocity breaking, a remarkable feature of the $\mathcal{P}\mathcal{T}$ symmetry, is also demonstrated numerically. Our results will open different configurations and avenues for observing $\mathcal{P}\mathcal{T}$-symmetry breaking in optical fibers, without the need to resort to cumbersome dissipative structures.