  Non-Hermitian systems exhibit phenomena that are qualitatively different from
those of Hermitian systems and have been exploited to achieve a number of ends,
including the generation of exceptional points, nonreciprocal dynamics,
non-orthogonal normal modes, and topological operations. However to date these
effects have only been accessible with nearly-degenerate modes (i.e., modes
with frequency difference comparable to their linewidth and coupling rate).
Here we demonstrate an optomechanical scheme that extends topological control
to highly non-degenerate modes of a non-Hermitian system. Specifically, we
induce a "virtual exceptional point" between two mechanical modes whose
frequencies differ by >10^3 times their linewidth and coupling rate, and use
adiabatic topological operations to transfer energy between these modes. This
scheme can be readily implemented in many physical systems, potentially
extending the utility of non-Hermitian dynamics to a much wider range of
settings.
