Unbroken $${{{\mathscr{P}}}}{{{\mathscr{T}}}}$$-symmetry in the absence of gain or loss

Abstract

Abstract The concept of parity-time symmetry has firmly established non-Hermiticity as a versatile degree of freedom on a variety of physical platforms. In general, the non-Hermitian dynamics of open systems are perceived to be inextricably linked to complex-valued potentials facilitating the local attenuation and coherent amplification in wave mechanics. Along these lines, time reversal symmetry is associated with a complex conjugation of the potential landscape, in essence swapping gain and loss. Here we leverage nonorthogonal coupled-mode theory to synthesize genuinely non-Hermitian dynamics without either gain or loss, and experimentally demonstrate parity-time symmetry via fluorescence measurements in femtosecond-laser-written arrays. Our projective approach allows features of non-Hermiticity to be utilized in scenarios where actual amplification and/or attenuation may disrupt the desired physics, e.g. in nonlinear systems or quantum optics.