Anomalous dynamical energy flows via nonlinear phononics in spin-Peierls chains
We investigate the nonequilibrium spin-phonon dynamics and energy cascades in a strongly dimerized spin-Peierls chain using a multi-tiered nonlinear phononics architecture. To bypass linear selection rules prohibiting the direct excitation of the Raman-active dimerization mode, a terahertz laser drives an infrared mode that nonlinearly couples to the Raman lattice displacement, subsequently modulating the magnetic exchange. Employing a bond-operator formalism with a second-order cumulant expansion of the Lindblad master equation, we show that maximum energy transfer into the magnetic sector is governed by a dynamical impedance-matching condition rather than the unperturbed triplon density of states. We find that the sustained energy input of continuous-wave driving builds high excitation densities that severely back-act on the lattice, overdamping the primary phonon and smearing magnetic features via power broadening. Conversely, the small time-integrated energy of a pulse keeps the response perturbative, terminating before back-action accumulates and preserving sharp Fano-like quantum interferences. These insights establish limits for controlling dynamic magnetic states without quenching the driving lattice modes.