Passive $\mathcal{PT}$-symmetry breaking transitions without exceptional points in dissipative photonic systems

Abstract: Over the past decade, parity-time ($\mathcal{PT}$)-symmetric Hamiltonians have been experimentally realized in classical, optical settings with balanced gain and loss, or in quantum systems with localized loss. In both realizations, the $\mathcal{PT}$-symmetry breaking transition occurs at the exceptional point of the non-Hermitian Hamiltonian, where its eigenvalues and the corresponding eigenvectors both coincide. Here, we show that in lossy systems, the $\mathcal{PT}$ transition is a phenomenon that broadly occurs without an attendant exceptional point, and is driven by the potential asymmetry between the neutral and the lossy regions. With experimentally realizable quantum models in mind, we investigate dimer and trimer waveguide configurations with one lossy waveguide. We validate the tight-binding model results by using the beam propagation method analysis. Our results pave a robust way toward studying the interplay between passive $\mathcal{PT}$ transitions and quantum effects in dissipative photonic configurations.