Abstract
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 \(2\pi /\omega \). 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, \(\omega \) and strength \(\alpha \) of the oscillation of the potential. These show peaks in the energy distribution, separated by \(\hbar \omega \), 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 \(\alpha \) 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 \((\alpha ,\omega )\). 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.
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Acknowledgements
We are grateful to the reviewers for bringing to our attention interesting references.
OC was partially supported by the NSF-DMS Grant 1515755 and JLL by the AFOSR Grant FA9550-16-1-0037. We thank H. Jauslin, H. Spohn and particularly L. DiMauro, C. Blaga and David Huse for very useful discussions. JLL thanks the Systems Biology division of the Institute for Advanced Study for hospitality during part of this work.
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Costin, O., Costin, R.D. & Lebowitz, J.L. Ionization by an Oscillating Field: Resonances and Photons. J Stat Phys 175, 681–689 (2019). https://doi.org/10.1007/s10955-018-2141-7
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DOI: https://doi.org/10.1007/s10955-018-2141-7