Exploring laser-driven quantum phenomena from a time-frequency analysis perspective: a comprehensive study

Abstract

Time-frequency (TF) analysis is a powerful tool for exploring ultrafast dynamics in atoms and molecules. While some TF methods have demonstrated their usefulness and potential in several quantum systems, a systematic comparison among them is still lacking. To this end, we compare a series of classical and contemporary TF methods by taking hydrogen atom in a strong laser field as a benchmark. In addition, several TF methods such as Cohen class distribution other than the Wigner-Ville distribution, reassignment methods, and the empirical mode decomposition method are first introduced to exploration of ultrafast dynamics. Among these TF methods, the synchrosqueezing transform successfully illustrates the physical mechanisms in the multiphoton ionization regime and in the tunneling ionization regime. Furthermore, an empirical procedure to analyze an unknown complicated quantum system is provided, suggesting the versatility of TF analysis as a new viable venue for exploring quantum dynamics.

Exploration of laser-driven electron-multirescattering dynamics in high-order harmonic generation

“…For the dipole moment of the laser-driven atom consists of multiple rescattering events, and that each event has its own frequency characteristics, we can extend the empirical mode decomposition (EMD) technique 21 to separate these components. The EMD technique renders a series of functions called the intrinsic mode function (IMF), on which the synchrosqueezing transform (SST) 21 22 can be applied subsequently to illustrate the instantaneous frequency, via an algorithm called the sifting process 33 34 as shown in the parts of method. According to the analysis in Ref.…”

Convex Optimization approach to signals with fast varying instantaneous frequency

“…Since it is not the focus of the current paper, we just indicate the possibility of achieving a better time-frequency representation by choosing a suitable window in SST, but not make effort to determine the optimal window. This kind of approach has been applied to the strong field atomic physics [35,45], where the window is manually but carefully chosen to extract the physically meaningful dynamics. A theoretical study regarding this topic will be reported in the near future.…”

Effect of multiple rescatterings on continuum harmonics from asymmetric molecules in multicycle lasers

“…To study the spectral and temporal structures of HHG, we perform a synchrosqueezed transform (SST) based on the Gabor transform of the acceleration dipole. 21,47,48 We note that there are other time-frequency analyses such as the Morlet wavelet transform 49 and the Hilbert transform 50 but SST is the most suitable for resolving the multiple rescatterings. 48 The SST provides the information on the emission time and intensity of the harmonics, and is defined as…”