Ultrafast laser-stimulated field emission from a metal: a non-equilibrium Green's functions approach

Ultrafast laser-assisted field emission from metallic nanotips is a promising route for generating coherent electron pulses. However, existing theoretical models often neglect many-body strong correlation effects in the emitter's electronic structure and its response to the optical field. In this work, we propose a theoretical framework based on the non-equilibrium Green's function formalism to simulate the out-of-equilibrium electron dynamics across a strongly driven matter-vacuum interface, in a one-dimensional model. Treating the tip-vacuum coupling perturbatively, we find that the interplay between strong-field emission and multi-photon emission regimes can be described in terms of a filtering of the emitter's local density of occupied states through field-dressed vacuum propagators. By including electron-electron interactions via the second-Born approximation, we show that correlation-induced modifications in the electronic structure are directly transferred to the far-field spectrum. Finally, by self-consistently solving the Dyson equation at the interface, we uncover a dynamic back-action regime driven by the optical field, characterized by a periodic polarization of the emitter, which reshapes the far-field spectrum. This shows that the non-equilibrium Green's functions approach provides a versatile framework for exploring and analyzing field emission of correlated electrons.