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We have performed macroscopic calculations for the thin medium or low gas density regime and a central gas jet using microscopic numerical solutions of the time-dependent Schrödinger equation. In the case of a spatial phase distribution for broadband Gaussian pulses with a negative Porras factor, our theoretical results show an interference pattern in the angular distribution of below- and near-threshold harmonics, which is not present for the monochromatic Gouy phase distribution. The interference pattern is due to off-center contributions that are in-phase with those at the central points in the focus. The location of the maxima in the interference pattern can be estimated using the well-known double-slit formula with an effective slit separation. 

Abstract Progress in ultrafast science allows for probing quantum superposition states with ultrashort laser pulses in the new regime where several linear and nonlinear ionization pathways compete. Interferences of pathways can be observed in the photoelectron angular distribution and in the past they have been analyzed for atoms and molecules in a single quantum state via anisotropy and asymmetry parameters. Those conventional parameters, however, do not provide comprehensive tools for probing superposition states in the emerging research area of bright and ultrashort light sources, such as free-electron lasers and high-order harmonic generation. We propose a new set of generalized asymmetry parameters which are sensitive to interference effects in the photoionization and the interplay of competing pathways as the laser pulse duration is shortened and the laser intensity is increased. The relevance of the parameters is demonstrated using results of state-of-the-art numerical solutions of the time-dependent Schrödinger equation for ionization of helium atom and neon atom.