Dynamical phase transition in a strongly hybridized phonon-triplon chain

We study a dimerized spin-1/2 chain, such as ${\mathrm{CuGeO}}_{3}$, hosting triplon excitations coupled to optical phonons under weak terahertz laser driving. Both phonons and triplons weakly lose energy into the surrounding baths, forming a nonequilibrium steady state. In the strong phonon-triplon coupling regime, phonons near the two-triplon continuum hybridize strongly with triplons. Using mean-field Lindblad dynamics, we show that strong hybridization induces sharp first-order phase transitions---either single or simultaneous double---in the emission spectrum, mainly due to nonlinearities in the chain and the instantaneous breaking of spatial inversion symmetry, as captured by the phonon displacement. Using mean-field Floquet analysis of harmonic modes in both sectors, we analytically confirm the existence of these phase transitions. Furthermore, we map the complete steady-state phase diagram by varying key control parameters and provide experimentally relevant parameters for observing these transitions in laser-driven ${\mathrm{CuGeO}}_{3}$.