Ionization by an Oscillating Field: Resonances and Photons: To the memory of Pierre Hohenberg

We describe new exact results for a model of ionization of a bound state in a 1d delta function potential, induced by periodic oscillations of the potential of period 2 π/ ω. In particular we have obtained exact expressions, in the form of Borel summed transseries for the energy distribution of the emitted particle as a function of time, ω and strength α of the oscillation of the potential. These show peaks in the energy distribution, separated by ħω, which look like single or multi-photon absorption. The peaks are very sharp when the time is large and the strength of the oscillating potential is small but are still clearly visible for large fields, and even for time-periods of a few oscillations. These features are similar to those observed in laser induced electron emission from solids or atoms (Phys Rev Lett 105:257601, 2010). For large α the model exhibits peak-suppression. The ionization probability is not monotone in the strength of the oscillating potential: there are windows of much slower ionization at special pairs (α, ω). This shows that ionization processes by time-periodic fields exhibit universal features whose mathematical origin are resonances which pump energy into the system represented by singularities in the complex energy plane. All these features are proven in our simple model system without the use of any approximations.