Static field limit of excitation probabilities in laser-atom interactions

TL;DR

This paper derives an analytical formula for atomic excitation probabilities in laser-atom interactions at low frequencies, extending the Born-Fock adiabatic theorem's application to continuous spectra and validating it against numerical solutions.

Contribution

It introduces a novel analytical approach to estimate excitation probabilities in the static field limit, even with a continuous energy spectrum, using an adapted adiabatic theorem.

Findings

Analytical formula matches numerical solutions for low-lying excited states.

The approach extends the applicability of the adiabatic theorem to continuous spectra.

The validity domain of the formula is thoroughly discussed.

Abstract

We consider the interaction of atomic hydrogen, in its ground state, with an electromagnetic pulse whose duration is fixed in terms of the number of optical cycles. We study the probability of excitation of the atom in the static field limit i.e. for field frequencies going to zero. Despite the fact that the well known Born-Fock adiabatic theorem is valid only for a system whose energy spectrum is discrete, we show that it is still possible to use this theorem to derive, in the low frequency limit, an analytical formula which gives the probability of transition to any excited state of the atom as a function of the field intensity, the carrier envelope phase and the number of optical cycles within the pulse. The results for the probability of excitation to low-lying excited states, obtained with this formula, agree with those we get by solving the time-dependent Schroedinger equation. The domain of validity is discussed in detail.