  Following the recent success of realizing exciton-polariton condensates in
cavities, we examine the hybridization of cavity photons with the closest
analog of excitons within a superconductor, states called Bardasis-Schrieffer
(BS) modes. Though BS modes do not typically couple directly to light, one can
engineer a coupling with an externally imposed supercurrent, leading to the
formation of hybridized Bardasis-Schrieffer-polariton states, which we obtain
both via direct solution and through the derivation of an effective Hamiltonian
picture for the model. These new excitations have nontrivial overlap with both
the original photon states and $d$-wave superconducting fluctuations, implying
that their condensation could produce a finite $d$-wave component of the
superconducting order parameter--an $s\pm id$ superconducting state.
