Floquet Topological Frequency-Converting Amplifier

We introduce a driven-dissipative Floquet model in which a single harmonic oscillator with modulated frequency and decay realizes a non-Hermitian synthetic lattice with an effective electric field gradient in frequency space. Using the Floquet-Green's function and its doubled-space representation, we identify a topological regime that supports directional amplification and frequency conversion, accurately captured by a local winding number. The underlying mode structure is well described by a Jackiw-Rebbi-like continuum theory with Dirac cones and solitonic zero modes in synthetic frequency. Our results establish a simple and experimentally feasible route to non-Hermitian topological amplification, naturally implementable in current quantum technologies such as superconducting circuits.