Non-Hermitian systems exhibit rich physical phenomena that o
pen the door to qualitatively new forms of control. In this talk\, I will
introduce our recent work on topological and nonreciprocal dynamics in a n
on-Hermitian optomechanical system. Specifically\, we realized topological
energy transfer between nearly degenerate modes by adiabatically encircli
ng an exceptional point (a singularity of the complex spectrum). We also d
emonstrated that this energy transfer is non-reciprocal: a given topologic
al operation can only transfer energy in one direction. We have extended t
he topological and nonreciprocal dynamics to highly non-degenerate modes b
y exploiting a generic form of nonlinearity\, which should allow these eff
ects to be exploited in a very wide range of physical systems. In addition
\, we realized nonreciprocal dynamics by optomechanical interference.

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