Over the past decade, parity-time (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 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 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 PT transitions and quantum effects in dissipative photonic configurations.

The exceptional point (EP) is one of the typical properties of parity–time-symmetric systems, arising from modes coupling with identical resonant frequencies or propagation constants in optics. Here we show that in addition to two different modes coupling, a nonuniform distribution of gain and loss leads to an offset from the original propagation constants, including both real and imaginary parts, resulting in the absence of EP. These behaviors are examined by the general coupled-mode theory from the first principle of the Maxwell equations, which yields results that are more accurate than those from the classical coupled-mode theory. Numerical verification via the finite element method is provided. In the end, we present an approach to achieve lossless propagation in a geometrically symmetric waveguide array.