Exact analytic characterization of the Autler-Townes doublet via the extended semiclassical Rabi model

We study the resonance-enhanced multiphoton ionization (REMPI) of atoms by intense, short, XUV radiation fields. To characterize Rabi oscillations and the resulting Autler-Townes doublet in the photoelectron spectrum, a minimal-state effective description is utilized, incorporating energy-level shifts, multiphoton couplings, and irreversible losses. Extending the semiclassical Rabi model with such higher-order terms, the complex population amplitudes of the Rabi cycling atom are found in simple analytic forms. This allows for the exact analytic evaluation of the photoelectron spectrum under various simultaneous physical effects. The origins of the spectral characteristics, such as the splitting, shifting, asymmetry, and multipeak pattern, are identified through the found spectrum formula. Furthermore, the dependence of these features on the field intensity, frequency detuning, and interaction time are analyzed in detail. Finally, as the simplicity of the spectrum formula is preserved when further higher-order light-matter interaction terms are added, the presented general framework is suitable for studying arbitrary ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>n</a:mi> <a:mrow> <a:mo>+</a:mo> <a:mspace width="0.16em"/> <a:mi>m</a:mi> </a:mrow> </a:math> ) photon REMPI phenomena.