Role of the ponderomotive energy in two-color photodetachment of an ion

We study, within a time-independent framework, the photodetachment of an ion by a weak high-frequency field in the presence of a field of low frequency ${\mathrm{\omega }}_{\mathit{L}}$. We explore the role played by the ponderomotive energy ${\mathit{P}}_{\mathit{L}}$ due to the low-frequency (LF) field. If ${\mathit{P}}_{\mathit{L}}$≪ħ${\mathrm{\omega }}_{\mathit{L}}$, the threshold energy for photodetachment by the high-frequency field is increased by the amount ${\mathit{P}}_{\mathit{L}}$, while if ${\mathit{P}}_{\mathit{L}}$≳ħ${\mathrm{\omega }}_{\mathit{L}}$ the threshold energy is Idecreased,P due to tunneling through the barrier formed by the atomic potential and the LF field. If ${\mathit{P}}_{\mathit{L}}$>ħ${\mathrm{\omega }}_{\mathit{L}}$ the low-frequency field behaves like a dc field, but the strong repulsive barrier has a characteristic height of 2${\mathit{P}}_{\mathit{L}}$, in contrast to the case of a true dc field (where the height is infinite). If the kinetic energy of the outgoing photoelectron is smaller than or comparable to 2${\mathit{P}}_{\mathit{L}}$, the photodetachment probability is sensitive to the polarization of the low-frequency field, and exhibits ripples as the high frequency varies. These ripples are due to the interference of the direct photoelectron wave and the wave that reflects from the repulsive barrier. The differences between the low-frequency field and a true dc field are elucidated.