Laser-driven nonlinear phononics in a dissipative electronic chain

Direct excitation of phonons through laser fields at terahertz and mid-infrared frequencies leads to large phonon amplitudes. In a one-dimensional system in which interactions couple an electron and optical infrared-active phonons to a thermal bath after it was driven out of equilibrium by a laser field, one would expect mutual transient feedback effects to be reflected in the relaxation process. Here we adapt a driven-dissipative electronic chain beyond linear lattice excitation to model the reflection of this feedback in the dissipators of the Lindblad quantum master equation. We develop it in a way that the dressed electron dispersion prevents the instability of the chain in the nonlinear regime. From the set of parameters, we first create a coherent nonequilibrium steady state (NESS), tune it, and preserve it up to the infinity-time. Secondly, we show that a maximal (minimal) phonon displacement (electron density) in the NESS takes place at a critical nonlinear electron-phonon coupling with a strength that strongly depends on the driving frequency in resonance with the phonon frequency. While the off-resonant regime of driving causes a novel bistability effect for which the main requirement is a phonon of a reasonably high frequency with a frequency that depends modestly on the electron density. Nonlinear phononics is growing in various experimental platforms as an ultrafast route to lattice control and the present theoretical proposition for the relaxation process would improve our understanding of damping effects.