  The fermionic Kitaev chain is a canonical model featuring topological
Majorana zero modes. We report the experimental realization of its bosonic
analogue in a nano-optomechanical network where parametric interactions induce
two-mode squeezing and beamsplitter coupling among the nanomechanical modes,
equivalent to hopping and superconductor pairing in the fermionic case,
respectively. We observe several extraordinary phenomena in the bosonic
dynamics and transport, including quadrature-dependent chiral amplification,
exponential scaling of the gain with system size, and strong sensitivity to
boundary conditions. Controlling the interaction phases and amplitudes uncovers
a rich dynamical phase diagram that links the observed phenomena to
non-Hermitian topological phase transitions. Finally, we present an
experimental demonstration of an exponentially enhanced response to a small
perturbation as a consequence of non-Hermitian topology. These results
represent the demonstration of a novel synthetic phase of matter whose bosonic
dynamics do not have fermionic parallels, and establish a powerful system to
study non-Hermitian topology and its applications in signal manipulation and
sensing.
