Minimum energy and photon content in PT symmetric metamaterials

Abstract

In the context of waves in space time modulated materials, we ask two questions how much energy does it cost to break time reversal symmetry and transition to a PT symmetric state. and can a PT symmetric system have a ground state in the sense that no photons are present. Our model system is a periodic metamaterial set in virtual motion with velocity cg to become a space-time crystal. We find that the expectation of energy content is always increased on breaking symmetry. At the same time breaking T symmetry introduces photon-pairs even when we start from a T symmetric ground state empty of photons, except in certain pathological examples which we describe. For a range of velocities, PT symmetry is broken so that energy must be continuously invested to preserve motion, creating a trail of photon pairs. Here energy must be continuously invested to preserve motion. We make an analogy with acoustic radiation generated from breaking the sound barrier.