Dips in high-order harmonics spectra from a subcycle-driven two-level system reflected in the negativity structure of the time-frequency Wigner function

We investigate high-order harmonics spectra radiated from a two-level model system driven by strong, ultrabroadband half- and single-cycle pulses, which are shorter than the inverse of the transition frequency. In this driving regime, the plateau in frequency spectra typical for radiation from strongly driven systems, has noticeable modulation in amplitude due to interference between waves of a same frequency and emitted at different time instants. Specifically, there is a characteristic `dips' structure at a set of frequencies in the radiation spectra, where the corresponding amplitudes are suppressed by several orders of magnitude. Understanding of this structure is required for applications such as generation of attosecond pulse, where number of composing modes and their relative phases are important. Therefore, we demonstrate a systematic way to find frequencies at which the dips are formed. To further illustrate the interference mechanism, we extract the phase information with the help of time-frequency distribution functions, namely the Husimi and Wigner functions. Especially, we found that the negativity structure of the Wigner function corresponds to each dip frequency and that the information regarding the type of interference is encoded in the pattern of the negative region of the Wigner function. Since such time-frequency Wigner function can actually be measured, we envisage utilizing its negativity structure to extract the phase information between radiation components emitted at time points within a subcycle time scale. This should provide an efficient tool for understanding and designing photonic applications, including short-wavelength coherent light sources.