Reverse PT phase transition across exceptional points of any order

We have recently demonstrated that higher-order exceptional points can be engineered in PT symmetric networks by means of recursive bosonic algebra. In these systems, as well as in simple PT dimers with second-order exceptional points, transitions between the broken and unbroken phases take place along specific trajectories in the parameter space. Here we show that the behaviour along some of these trajectories can be reversed through the inclusion of strongly coupled passive dimers that act as two-mode adiabatic bridges connecting different parts of the network. We illustrate our results by first discussing the case of a simple PT dimer before we demonstrate how the same technique can be employed in configurations that exhibit third- and fourth-order exceptional points.