Optical PT-symmetry in the absence of gain or loss

Our conventional understanding of physics is based on the fundamental concept of energy conservation that manifests itself in the real-valued energy spectra of Hermitian Hamiltonians. However, so-called open systems can exchange energy with their environment, and, as subsystems of a larger whole, may exhibit non-Hermitian dynamics. Along these lines, non-Hermiticity established by local attenuation and coherent amplification has been firmly established on a variety of platforms. More recently, the concept of parity-time symmetry has been associated with the wave-mechanical interplay of gain and loss in complex-valued potentials. Here, by contrast, we present a projective approach to synthesize genuinely non-Hermitian dynamics without any injection or removal of intensity from the system. To demonstrate the capabilities of our technique, we observe nonorthogonal modes in femtosecond laser-written waveguide arrays and leverage the fluorescent properties of the waveguide cores to selectively probe the on-site intensities. Projective parity-time symmetry makes features of non-Hermiticity accessible in scenarios where actual amplification and/or attenuation may be unavailable or would disrupt the desired physics, e.g. in quantum optics or nonlinear systems.