Topological dynamics of an adiabatically varying Hamiltonian around third order exceptional points

We report an open three-state perturbed system that depends on the topological parameters, where the underlying Hamiltonian is varying quasi-statically. The effective system hosts two second order exceptional points (EP2s). Here a third order exceptional point (EP3) is encountered with simultaneous encirclement of two EP2s by adiabatic variation of topological parameters. We study the robust successive state-exchange around the EP3. Maintaining adiabaticity, we estimate the evolution of total phase accumulated by each of the interacting states during encirclement; where interestingly, the state common to the pairs of coupled state picks up three times phase shift of 2π as a signature of EP3. Such an exclusively reported scheme once implemented in an anisotropic optical waveguide can be exploited in potential applications of mode conversion, switching and lasing by manipulating topological parameters.