  This study introduces a new adaptive time-frequency (TF) analysis technique,
synchrosqueezing transform (SST), to explore the dynamics of a laser-driven
hydrogen atom at an {\it ab initio} level, upon which we have demonstrated its
versatility as a new viable venue for further exploring quantum dynamics. For a
signal composed of oscillatory components which can be characterized by
instantaneous frequency, the SST enables rendering the decomposed signal based
on the phase information inherited in the linear TF representation with
mathematical support. Compared with the classical type TF methods, the SST
clearly depicts several intrinsic quantum dynamical processes such as selection
rules, AC Stark effects, and high harmonic generation.

Data Analysis, Statistics and Probability;Numerical Analysis