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 modes lifetime is greatly enhanced.
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