  Propagating modes of light with negative-valued Wigner distributions are of
fundamental interest in quantum optics and represent a key resource in the
pursuit of optics-based quantum information technologies. Most schemes proposed
or implemented for the generation of such modes are probabilistic in nature and
rely on heralding by detection of a photon or on conditional methods where
photons are separated from the original field mode by a beam splitter. In this
Letter we demonstrate theoretically, using a cascaded-quantum-systems model,
the possibility of deterministic generation of Wigner-negativity in temporal
modes of the steady-state emission of a two-level system driven by
finite-bandwidth quadrature-squeezed light. Optimal negativity is obtained for
a squeezing bandwidth similar to the linewidth of the transition of the
two-level system. While the Wigner distribution associated with the incident
squeezed light is Gaussian and everywhere positive, the Wigner functions of the
outgoing temporal modes show distinct similarities and overlap with a
superposition of displaced squeezed states.
