Analytically controlling the laser-induced electron phase in sub-cycle motion

We develop an approach to directly control the phase of an electron's sub-cycle motion in an intense laser field. The method is established by tuning a low-frequency electric field applied on a centrosymmetric gaseous target during its interaction with a few-cycle infrared laser pulse. We find a universal analytical relation between the low-frequency electric field and its induced harmonic frequency shift, derived by the strong-field approximation. This simple relation and its universality are confirmed numerically by directly solving the time-dependent Schrödinger equation. Moreover, we demonstrate the benefits of the discovered relation in applications, including continuously and precisely tuning XUV waves and developing a method of comprehensively sampling the THz pulse. Published by the American Physical Society 2024