Minimum Energy and Photon Content in PT-Symmetric Metamaterials

In the context of waves in space-time modulated materials, we ask two questions: (1) how much energy does it cost to break time reversal symmetry (T-symmetry) and transition to a PT-symmetric state? and (2) 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 c_{g} 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 that 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.