  Driven-dissipative physics lie at the core of quantum optics. However, the
full interplay between a driven quantum many-body system and its environment
remains relatively unexplored in the solid state realm. In this work, we
inspect this interplay beyond the commonly employed stroboscopic Hamiltonian
picture based on the specific example of a driven superconductor. Using the
Shirley-Floquet and Keldysh formalisms as well as a generalization of the
notion of superconducting fitness to the driven case, we show how a drive which
anti-commutes with the superconducting gap operator generically induces an
unusual particle-hole structure in the spectral functions from the perspective
of the thermal bath. Concomitant with a driving frequency which is near
resonant with the intrinsic cutoff frequency of the underlying interaction,
this spectral structure can be harnessed to enhance the superconducting
transition temperature. Our work paves the way for further studies for
driven-dissipative engineering of exotic phases of matter in solid-state
systems.
