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

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 antisymmetric 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's 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.

Figure 1

Third-order correction ${\eta }_{k,q}$ (left) and effective electron-phonon coupling ${\gamma }_{k,q}$ in units of $g_q$ (right) for $\mathrm{\Omega }=5\nu$ and $z=1.8$.

Figure 2

Field-renormalized hopping and nonequilibrium corrections to the electron-phonon interaction as a function of the driving strength for $\mathrm{\Omega }=5\nu$ and $g_0=\nu$.

Figure 3

Diagrammatic representation of the electron-phonon interaction in a second-order perturbation theory (left) which is regarded here along Schwinger-Keldysh contour $C$ (right).

Figure 4

Real and imaginary parts of the retarded component of the effective self-energy for a single electron at room temperature. Analytics (full lines) are compared to numerics (dashed lines) for $\mathrm{\Omega }=5\nu$, ${\omega }_0=0.1\nu$, $g_0=0.2\nu$, $z=1.8$, $\delta =0.01$, and $k=0$.

Figure 5

Effective and Floquet spectral functions for $\mathrm{\Omega }=5\nu$ (left) and $\mathrm{\Omega }=\nu$ (right), respectively. Both spectral functions have been computed for zero temperature with the following parameters: ${\omega }_0=0.1\nu$, $g_0=0.2\nu$, $z=1.8$, and $\delta =0.01$.

Figure 6

Effective and Floquet local spectral functions for $\mathrm{\Omega }=5\nu$ (left) and $\mathrm{\Omega }=\nu$ (right), respectively. Both plots corresponds to the case of zero temperature with ${\omega }_0=0.1\nu$, $z=1.8$, $\delta =0.01$, and $g_0=0.0\nu$ (dashed line) or $g_0=0.2\nu$ (full line).

Figure 7

Variations of the polaron binding energy (left) and of its nearest- and next-nearest-neighbor hopping amplitudes (right) for $\mathrm{\Omega }=5\nu$, $g_0=\nu$, ${\omega }_0=0.1\nu$, and zero temperature.

Figure 8

Real and imaginary parts of the retarded component of the effective self-energy for a single electron at room temperature. Analytics (full lines) are compared to numerics (dashed lines) for $\mathrm{\Omega }=5\nu$, ${\omega }_0=0.1\nu$, $g_0=0.2\nu$, $z=1.8$, $\delta =0.01$, and $k=0$.