  We study the effect of a terahertz field-driven single cavity mode for
ultrafast control of a fermion chain with dissipation-induced nonlinearity and
quadratic coupling to an infrared-active phonon mode. Without photon loss from
the cavity, we uncover a first-order phase transition in the nonequilibrium
steady state only for the lower phonon-polariton, accompanied by polaritons
whose frequency response is asymmetric with respect to the photon frequency due
to the direct laser-induced dressing effect on the photon. A weak laser field
fails to induce the phase transition but renders the polaritons symmetrical.
Finally, we show that sufficiently strong photon loss from the cavity
eliminates the polaritons and the associated phase transition. The experimental
feasibility of these phenomena is also proposed.
