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. Unlike the first-order phase transition in the nonequilibrium steady state of the system without a cavity or with a high-quality cavity, we find that a realistic dissipation in a low-quality driven cavity process prevents such a transition. Without realistic photon loss from the cavity, the transition survives only for the lower phonon-polariton branch with strong drive; a weak laser field fails to induce the phase transition and renders the polaritons symmetrical. The ability to control the phase transition is crucial for realizing strongly modulated steady states; we propose experimentally feasible regimes where this occurs.

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• Dynamical phase transitions
• Electron-phonon coupling
• First order phase transitions
• Optical phonons
• Phonon polariton
• Strong interaction
• Superconductivity
• Nonequilibrium systems
• Lindblad equation
• Mean field theory
• Optical pumping
• Optical-pump terahertz-probe spectroscopy
• Tight-binding model