  We show that low-lying excitations of a 2D BCS superconductor are
significantly altered when coupled to an externally driven cavity, which
induces controllable long-range attractive interactions between the electrons.
We find that they combine non-linearly with intrinsic local interactions to
increase the Bogoliubov quasiparticle excitation energies, thus enlarging the
superconducting gap. The long-range nature of the driven-cavity-induced
attraction qualitatively changes the collective excitations of the
superconductor. Specifically, they lead to the appearance of additional
collective excitations of the excitonic modes. Furthermore, the Higgs mode is
pushed into the gap and now lies below the Bogoliubov quasiparticle continuum
such that it cannot decay into quasiparticles. This way, the Higgs mode's
lifetime is greatly enhanced.
