Reconstruction of attosecond beating by interference of two-photon transitions with higher-order processes

The reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) method is a leading technique for time-resolved investigation of photoionization processes. Interpretation of RABBITT spectra is limited to a lowest-order description, while new variants of the technique necessitate higher intensity infrared fields where this description breaks down. Here, we present an extension of RABBITT theory which can account for higher-order processes (RABBITT-HOP), and demonstrate RABBITT-HOP's ability to predict and describe higher-order processes through simulation of a RABBITT experiment targeting the high-lying <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mn>1</a:mn><a:mi>s</a:mi><a:mi>n</a:mi><a:mi>p</a:mi></a:mrow></a:math> Rydberg series of helium. We demonstrate that the signature line shape imparted by the resonances in the <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mn>2</b:mn><b:mi>ω</b:mi></b:mrow></b:math> phase of the lowest sideband can also be observed in the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mn>2</c:mn><c:mi>ω</c:mi></c:mrow></c:math> phase of the next mainband, as well as in the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mn>4</d:mn><d:mi>ω</d:mi></d:mrow></d:math> phases of the next sideband and mainband—each with additional phase shifts predicted under RABBITT-HOP. Repeating this analysis for a range of infrared intensities, we determine the lower limits of intensities required for these higher-order processes to become observable and upper limits beyond which nonperturbative effects begin to dominate. This new theoretical framework forms a much-needed basis for accurate interpretation of RABBITT spectra in experiments involving more intense fields, and paves the way for the development of new RABBITT-like techniques which take advantage of this new understanding of how atomic resonance effects may be propagated beyond their nearest sideband.