Dynamical control of electron-phonon interactions with high-frequency light

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This work addresses the one-dimensional problem of Bloch electrons when they are rapidly driven by a homogeneous time-periodic light and linearly coupled to vibrational modes. Starting from a generic time-periodic electron-phonon Hamiltonian, we derive a time-independent effective Hamiltonian that describes the stroboscopic dynamics up to the third order in the high-frequency limit. This yields nonequilibrium corrections to the electron-phonon coupling that are controllable dynamically via the driving strength. This shows in particular that local Holstein interactions in equilibrium are corrected by nonlocal Peierls interactions out of equilibrium, as well as by phonon-assisted hopping processes that make the dynamical Wannier-Stark localization of Bloch electrons impossible. Subsequently, we revisit the Holstein polaron problem out of equilibrium in terms of effective Green functions, and specify explicitly how the binding energy and effective mass of the polaron can be controlled dynamically. These tunable properties are reported within the weak- and strong-coupling regimes since both can be visited within the same material when varying the driving strength. This work provides some insight into controllable microscopic mechanisms that may be involved during the multicycle laser irradiations of organic molecular crystals in ultrafast pump-probe experiments, although it should also be suitable for realizations in shaken optical lattices of ultracold atoms.