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In this paper, we revisit one of the prototypical PT-symmetric oligomers,namely the trimer. We find all the relevant branches of "regular" solutions andanalyze the bifurcations and instabilities thereof. Our work generalizes theformulation that was proposed recently in the case of dimers for the so-called"ghost states" of trimers, which we also identify and connect tosymmetry-breaking bifurcations from the regular states. We also examine thedynamics of unstable trimers, as well as those of the ghost states in theparametric regime where the latter are found to exist. Finally, we present thecurrent state of the art for optical experiments in PT-symmetric trimers, aswell as experimental results in a gain-loss-gain three channel waveguidestructure.

Revisiting the PT-symmetric Trimer: Bifurcations, Ghost States and Associated Dynamics