  The non-trivial topological features in the energy band of non-Hermitian
systems provide promising pathways to achieve robust physical behaviors in
classical or quantum open systems. A key topological feature, unique to
non-Hermitian systems, is the non-trivial winding of the energy band in the
complex energy plane. Here we provide direct experimental demonstrations of
such non-trivial winding, by implementing non-Hermitian lattice Hamiltonians
along a frequency synthetic dimension formed in a ring resonator undergoing
simultaneous phase and amplitude modulations, and by directly characterizing
the complex band structures. Moreover, we show that the topological winding can
be straightforwardly controlled by changing the modulation waveform. Our
results open a pathway for the experimental synthesis and characterization of
topologically non-trivial phases in non-conservative systems.
