Atomic and Free Electrons in a Strong Light Field

Photoionization of hydrogen atoms by coherent intense high-frequency short laser pulses: Direct propagation of electron wave packets on large spatial grids

“…Moreover, the time evolution of the cycle-averaged total energy follows the pulse intensity envelope g 2 (t), which is also shown in the figure by a thick solid curve in red to guide the eye. Importantly, the maximal shift of the cycle-averaged total energy during the pulse is about ∼ 3.5 eV, and it coincides with the value of U p = E 2 0 /4ω 2 ≈ 3.5 eV expected in the highfrequency limit for a field with an intensity as that at the pulse maximum [42]. This fact clearly illustrates the accuracy of the present numerical calculations.…”

“…It is well known [42,43] that in strong laser fields each electronic state experiences an AC Stark shift, including the ground state, Rydberg levels, and electron continuous states. Since an electron in the continuum interacting with an oscillating field cannot have an energy smaller than the average energy of its quiver-motion (known as ponderomotive energy), one argues that a strong field shifts the ionization threshold by this ponderomotive energy.…”

“…Since an electron in the continuum interacting with an oscillating field cannot have an energy smaller than the average energy of its quiver-motion (known as ponderomotive energy), one argues that a strong field shifts the ionization threshold by this ponderomotive energy. There is a common belief [42] that in the high-frequency limit, when the carrier frequency is much larger than the field-free ionization potential of a system (ω ≫ IP ), each electronic state acquires the same AC Stark shift given by the universal formula for the ponderomotive potential U p = E 2 0 /4ω 2 (all quantities in atomic units). For this reason, at all intensities during the pulse the AC Stark shifts of the ground state and of the ionization threshold are expected to compensate each other [42].…”

“…There is a common belief [42] that in the high-frequency limit, when the carrier frequency is much larger than the field-free ionization potential of a system (ω ≫ IP ), each electronic state acquires the same AC Stark shift given by the universal formula for the ponderomotive potential U p = E 2 0 /4ω 2 (all quantities in atomic units). For this reason, at all intensities during the pulse the AC Stark shifts of the ground state and of the ionization threshold are expected to compensate each other [42]. In turn, this would of course eliminate the dynamic interference effects as these vanish if the shift in the spectrum vanishes [10].…”

“…limit [42], it is expected that a free electron gains the ponderomotive energy U p , which is an average energy of its quiver-motion induced by a strong oscillating external field. In order to check this prediction in the case of short pulses, we start with the electronic wave packet given by the 1s ground state of hydrogen, and propagate this wave packet without the attractive Coulomb potential exerted by the nucleus.…”