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We report an experimental demonstration of anti-parity-time symmetric optical four-wave mixing in thermal rubidium vapor, where the propagation of probe and stokes fields in a double-Λ scheme is governed by a non-Hermitian Hamiltonian. We are particularly interested in studying quantum intensity correlations between the two fields near the exceptional point, taking into account loss and accompanied Langevin noise. Our experimental measurements of classical four-wave mixing gain and the associated two-mode relative-intensity squeezing are in reasonable agreement with the theoretical predictions. 

Recent studies of disorder or non-Hermiticity induced topological insulators inject new ingredients for engineering topological matter. Here, we consider the effect of purely non-Hermitian disorders, a combination of these two ingredients, in a 1D coupled-cavity array with disordered gain and loss. Topological photonic states can be induced by increasing gain-loss disorder strength with topological invariants carried by localized states in the complex bulk spectra. The system showcases rich phase diagrams and distinct topological states from Hermitian disorders. The non-Hermitian critical behavior is characterized by the biorthogonal localization length of zero-energy edge modes, which diverges at the critical transition point and establishes the bulk-edge correspondence. Furthermore, we show that the bulk topology may be experimentally accessed by measuring the biorthogonal chiral displacement, which can be extracted from a proper Ramsey interferometer that works in both clean and disordered regions. The proposed coupled-cavity photonic setup relies on techniques that have been experimentally demonstrated and, thus, provides a feasible route toward exploring such non-Hermitian disorder driven topological insulators.