Experimental simulation of anti-parity-time symmetric Lorentz dynamics

Abstract

The recent experimental progress in parity-time (PT) symmetry has attracted great interest. However, compared with PT symmetry, there are only a few reported results on its counterpart, anti-PT symmetry, which would lead to new insights and applications. Experimentally simulating and demonstrating the properties of anti-PT symmetry is of particular interest. Here, we present experimental research for simulating the dynamics of bosonic Bogoliubov quasi-particles with anti-PT symmetry based on single photons generated from a point defect in a gallium nitride film. The dynamical evolution under a non-unitary operator is a continuous complex Lorentz transformation in a complex Minkowski space. The evolved states are located on hyperbolic curves, depending on the values of the new defined inner product, which remain invariant during the evolution. Three types of state, space-like, light-like, and time-like, which are analogous to those predicted by the special relativity, are demonstrated. The results of our work could be helpful to investigate the dynamics of quasi-particles in diverse systems and promote deep understanding of non-Hermitian quantum mechanics in open systems.