Open quantum simulator for $\cal PT$-symmetry breaking localization transitions

Phase transitions in non-Hermitian systems are at the focus of cutting edge theoretical and experimental research. On the one hand, parity-time- ($\cal PT$-) and anti-$\cal PT$-symmetric physics have gained ever-growing interest, due to the existence of non-Hermitian spectral singularities called exceptional points (EPs). The great majority of previous studies exclusively focus on non-Hermitian Hamiltonians, whose realization requires an {\it a priori} fine-tuned $\cal PT$-symmetric extended lattices to exhibit topological and localization transition phenomena. In this work, we take an opposite approach and propose an alternative way of simulating lattice non-Hermitian spectral, topological, and localization phenomena by introducing an open quantum simulator. Namely, on the example of a zero-dimensional bosonic anti-$\cal PT$-symmetric dimer, we demonstrate the emergence of spectral, topological, and localization properties in the synthetic vector space, spanned by its field moments. Indeed, the field moment equations of motion can describe an equivalent (quasi-)particle moving in a one-dimensional (1D) synthetic lattice. This synthetic field moments space exhibits a nontrivial, even anomalous, localization transition induced by the presence of highly-degenerate EPs. The approach has a clear experimental advantage by requiring to tune only a few system parameters to observe lattice effects. Our results can thus be directly verified in state-of-the-art optical setups, such as superconducting circuits and toroidal resonators, by measuring photon correlation functions, allowing the observation of rich spectral and localization non-Hermitian phenomena.